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Title: Re: assuming too much math knowledge?
Post by: ellaminnow on October 15, 2010, 12:17:05 PM
You are an evil person, benazi.  Evil.  You do not deserve the generosity of anyone's attention and I sincerely hope that you dissolve into oblivion. 

I am done reading this thread - it's a gory tragedy and here's where I reign in my morbid curiosity.  Nothing good can come from reading any more of this garbage. 

 

Chronicle of Higher Education?

 

Careers => In the Classroom => Topic started by: mccfan on April 21, 2008, 10:31:48 AM



Title: assuming too much math knowledge?
Post by: mccfan on April 21, 2008, 10:31:48 AM
I am teaching Data Analysis to jr level Sociology and Poli Sci majors again this year, but I have had a new experience.  On the last exam, the students had to solve a simple equation

(z= X - mean of X  /   standard deviation)

I gave them 3 of the 4 values in a word problem, then they had to solve for the unknown quantity.  As I was going over the answers in class the other day, I said "using simple algebra which you had in high school..." when one of my students said she had never had algebra.  I was so surprised I asked "then how did you get into college?"  I thought everyone had to have algebra 1 in order to graduate high school, much less qualify for college admission.  I guess not.  Argh! 

When I followed up to find out more, she said her high school teacher kicked her out of algebra class because he thought she was too dumb to learn it.  I told her she ought to write a letter to her school board to complain.   Wow.


Title: Re: assuming too much math knowledge?
Post by: galactic_hedgehog on April 21, 2008, 10:39:30 AM
Is there a math prereq for your class?


Title: Re: assuming too much math knowledge?
Post by: fossil on April 21, 2008, 10:42:04 AM
How in the world can students be allowed to enroll in a quantitative methods class like yours without at least some background in one-variable calculus (or, preerably, multivariable) and linear algebra?  Shouldn't there be a warning to that effect in your course catalog?


Title: Re: assuming too much math knowledge?
Post by: zharkov on April 21, 2008, 10:59:21 AM

HS math requirements vary a lot by state, and sometimes by communities within a state.

I had an advisee who told me he had not actually passed math since middle school, took the two years of HS math as required, but flunked them and went to summer school.  (In a city where re-taking the class in summer school was a defacto pass.)

A state or two over, the high stakes HS leaving exam tests students in algebra, so all HS students must take a year of algebra.

While teaching at a pretty good SLAC, in a soph/junior class, not math, I drew the cartestian plane on the board, drew a line, and asked, "Everyone know the equation of the line is y=mx + b, right?"

I got looks of horror and spent the rest of the class reviewing linear functions.





Title: Re: assuming too much math knowledge?
Post by: math_prof on April 21, 2008, 11:15:14 AM
This is exactly why, at my community college, over 60% of entering freshmen must take a remedial math course before they are able to register for a college level math course.  It's frightening because each year that percentage increases.  And I'm not talking remedial math as in one level below College Algebra.  Nope, I'm talking about Pre-Algebra for some of these students.  That's sixth-grade levelmathematics, as in adding and subtracting integers, dividing, multiplying, etc.  I've seen some students spend three-four years here at the CC just to get their math requirements out of the way so that they can move on to a university.

Of course, that doesn't explain why the OP's students couldn't solve a simple algebraic equation.  My guess is that they couldn't see that it was an equation.  In other words, the "words" threw them off.  Students freak out about word problems.  If you had given them " z = (d - m)/s ", I bet more of them could have solved it.


Title: Re: assuming too much math knowledge?
Post by: mountain_ivy on April 21, 2008, 11:17:35 AM
I took and passed two years of algebra and geometry in highschool.  Math is a definite weakness, so I figured out how to avoid it in college.  Then I got to grad school and had to take a quantitative methods course.  The prof kew that many of us were weak in the basics, so she gave us a basic math test, telling us that if we didn't do well on that test, then we probably wouldn't do well in the class.  She was absolutely right!!!  I'm not surprised that liberall arts/social science students are underprepared for OP's class.  I would definitelyrecommend a basic math test at the beginning of thesemester.


Title: Re: assuming too much math knowledge?
Post by: fishbrains on April 21, 2008, 12:09:37 PM
To paraphrase Menken: Nobody ever went broke underestimating the math knowledge of the American public.

Of course, the current mortgage crisis may soon prove this theory to be incorrect.


Title: Re: assuming too much math knowledge?
Post by: wittgenstein on April 21, 2008, 01:39:18 PM
My syllabus for Statistics now contains the following phrases:

"Will I pass this class?

That depends on your arithmetic skills. In particular, you need to know how to change 0.575 to a percent and how to change 47.2% to a decimal. You also need to be able to tell me which is larger, 0.006 or 0.052. If you cannot do these things, I am telling you on day one of the class that I do not expect you to pass the class unless you spend a  substantial amount of time in the learning center beginning today."

You would be amazed how many of my students think 0.006 is larger than 0.052. This makes p-values difficult to discuss.


Title: Re: assuming too much math knowledge?
Post by: immigrant on April 21, 2008, 02:26:03 PM
Funny timing...I was covering z-scores today, also in a non-math/non-stats class.

My 'handle' shows that I probably didn't go to high school in the U.S., and I took my last maths class half a lifetime ago. What irks me now is that I *used* to be really strong in math, but really struggle now with even basic algebraic operations; I've had to re-teach myself to do things I used to be able to do easily, but have relied on computers to do for years!

Some people choose majors they think will allow them to stay as far away as math as possible. Our majors are some of these people, and I feel their pain.

Still, I was pleasantly surprised at how many people were very comfortable with some of these admittedly quite basic operations.


Title: Re: assuming too much math knowledge?
Post by: gourmetless on April 21, 2008, 02:31:19 PM
In particular, you need to know how to change 0.575 to a percent and how to change 47.2% to a decimal. You also need to be able to tell me which is larger, 0.006 or 0.052.

I just want to check if I am right....

57.5%
.472
.052 is larger

Either I will be right, and vindicated.  Or wrong and a ridiculous figure of scorn and derision.

Signed, a performing arts humanities person


Title: Re: assuming too much math knowledge?
Post by: math_prof on April 21, 2008, 07:38:27 PM
Vindicated.  You have escaped scorn...this time.


Title: Re: assuming too much math knowledge?
Post by: geonerd on April 21, 2008, 07:48:33 PM
At my state university > 50% of all incoming students take remedial math and remedial reading. How are these people passing the high stakes tests and graduating from high school?? Part of me wants to cry, part of me sees a money making opportunity if I switch from academia to selling sub-prime mortgages.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 21, 2008, 08:06:46 PM

Clearly, some explicit math prerequisites need to be added to the description of this class.


Title: Re: assuming too much math knowledge?
Post by: zharkov on April 21, 2008, 10:07:52 PM
At my state university > 50% of all incoming students take remedial math and remedial reading. How are these people passing the high stakes tests and graduating from high school?? Part of me wants to cry, part of me sees a money making opportunity if I switch from academia to selling sub-prime mortgages.

One of the most sensible proposals I have seen is making the HS high stakes test the entrance exam for state colleges, or at least CCs.  Thus, passing the high stakes test should imply the student does not need those remedial classes.

Maine sort of does this, in that they use the SAT as their NCLB test, although the US Dept of Ed isn't too thrilled with the approach.


Title: Re: assuming too much math knowledge?
Post by: asstprofjr on April 21, 2008, 10:15:58 PM
My students cannot compute their own averages, which are....

Points obtained/ points attempted. Says so on the syllabus. With alphabetical grade correspondence.

Compare percentage to grading rubric on syllabus for A/B/C/D/F equivalence. And I'm a humanist.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 21, 2008, 10:44:01 PM
Your University's math and/or statistics department probably has some form of placement exam into their courses.  You could ask if you could make your potential students take the same exam, perhaps offer a bit of money or a TA to help pay for the grading for the extra students. - DvF


Title: Re: assuming too much math knowledge?
Post by: smart_e_pantz on April 22, 2008, 02:14:56 AM
Have you seen some of those high stakes tests?  I saw a copy of the practice questions for the LEAP test (the Louisiana exit exam).  Anyone who completed 7th grade should have been able to pass it.  This is one of the reasons I think that whole exit exam thing is a joke.  Those tests merely certify that the students aren't COMPLETE idiots!


Title: Re: assuming too much math knowledge?
Post by: smart_e_pantz on April 22, 2008, 02:17:14 AM
Oh.. OP...

I feel your pain.  I spent two years teaching statistics at a college that was ranked in the top ten in it's region by U.S. News and World Report.

I had several students come up with a sum greater than 100 when I asked them to add 10 numbers all less than 5!


Title: Re: assuming too much math knowledge?
Post by: yatchie on April 22, 2008, 09:18:35 AM
I've also had people in my statistics classes add up a list of positive numbers and get a negative answer.  Not only that, but they couldn't understand why it was wrong!


Title: Re: assuming too much math knowledge?
Post by: jackofallchem on April 22, 2008, 03:17:05 PM

Clearly, some explicit math prerequisites need to be added to the description of this class.
You wouldn't be allowed to add math requirements for poli sci and sociology.  Those majors are for people who don't want to take math classes. 


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 22, 2008, 03:49:59 PM

Clearly, some explicit math prerequisites need to be added to the description of this class.
You wouldn't be allowed to add math requirements for poli sci and sociology.  Those majors are for people who don't want to take math classes. 
Many social science courses at many schools have mathematics prerequisites.   - DvF


Title: Re: assuming too much math knowledge?
Post by: concordancia on April 22, 2008, 03:54:45 PM
At my state university > 50% of all incoming students take remedial math and remedial reading. How are these people passing the high stakes tests and graduating from high school?? Part of me wants to cry, part of me sees a money making opportunity if I switch from academia to selling sub-prime mortgages.

We say it as a joke, but I recently heard an op-ed piece where the writer was complaining about loosing their house because they hadn't realized that insurance wasn't included in the mortgage and needed to be paid again on a regular basis. They were able to get the insurance added on, but SURPRISE it changed the monthly payments.


Title: Re: assuming too much math knowledge?
Post by: conjugate on April 22, 2008, 04:00:50 PM
How in the world can students be allowed to enroll in a quantitative methods class like yours without at least some background in one-variable calculus (or, preerably, multivariable) and linear algebra?  Shouldn't there be a warning to that effect in your course catalog?

No, lots of those courses where I am require only Intro Stat, which has a pre-requisite of HS Algebra II (Intermediate Algebra, no longer satisfying the Gen Ed math requirement).  Our institution offers no fewer than two lower-level courses that are required of students to be able to take Intermediate Algebra if they can't place into it directly.  It's scary how little they know.

OP still has not answered concerning math prereqs for the course in question, I think (or if there was an answer, I missed it).  But I've seen intro-stat courses at many schools that require only Intermediate Algebra, so I suspect that lots of students all across the country are struggling over the same issues.  Also, the courses I mention above are not technically "remedial," but "developmental," which is lucky since the state will not pay for "remediation."


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 22, 2008, 04:14:16 PM
But I've seen intro-stat courses at many schools that require only Intermediate Algebra, so I suspect that lots of students all across the country are struggling over the same issues.

My University has a large number of Intro Stats courses with nearly identical syllabi (and similar texts) but housed in many different departments, and numbered from freshman-level through graduate-level.  The prerequisites differ wildly.  Interestingly, the ones with the highest prerequisites (the ones offered by the Math and Econ departments with a Calc prerequisite) apparently have the lowest average grades.  - DvF


Title: Re: assuming too much math knowledge?
Post by: math_prof on April 23, 2008, 12:56:06 AM
How in the world can students be allowed to enroll in a quantitative methods class like yours without at least some background in one-variable calculus (or, preerably, multivariable) and linear algebra?  Shouldn't there be a warning to that effect in your course catalog?

No, lots of those courses where I am require only Intro Stat, which has a pre-requisite of HS Algebra II (Intermediate Algebra, no longer satisfying the Gen Ed math requirement).  Our institution offers no fewer than two lower-level courses that are required of students to be able to take Intermediate Algebra if they can't place into it directly.  It's scary how little they know.

OP still has not answered concerning math prereqs for the course in question, I think (or if there was an answer, I missed it).  But I've seen intro-stat courses at many schools that require only Intermediate Algebra, so I suspect that lots of students all across the country are struggling over the same issues.  Also, the courses I mention above are not technically "remedial," but "developmental," which is lucky since the state will not pay for "remediation."

Even if the prereq is only Intermediate Algebra, the necessary skills are taught in that class.  I just completed a semester teaching said course and we spent 2-3 class sessions on solving "formulas" for a specified variable, even if the formula contained only variables and no "numbers".

But as I said before, I'm guessing the biggest problem is that there is a disconnect between the information given as a problem statement, and the translation of the information into the equation to be solved.  This is a skill that, in my opinion, is not developed nearly enough in any of the developmental math courses.


Title: Re: assuming too much math knowledge?
Post by: poiuy on April 23, 2008, 03:55:34 AM

But as I said before, I'm guessing the biggest problem is that there is a disconnect between the information given as a problem statement, and the translation of the information into the equation to be solved.  This is a skill that, in my opinion, is not developed nearly enough in any of the developmental math courses.

(I hope I have done the quote thing correctly).

Preach it, math prof!   I think you are very correct.  They are supposed to do this from the youngest K-12 grades, but it's either the most difficult skill to acquire and apply; or it's just not emphasized and developed enough; likely both. 

Poiuy


Title: Re: assuming too much math knowledge?
Post by: yatchie on April 23, 2008, 09:30:49 AM

But as I said before, I'm guessing the biggest problem is that there is a disconnect between the information given as a problem statement, and the translation of the information into the equation to be solved.  This is a skill that, in my opinion, is not developed nearly enough in any of the developmental math courses.

(I hope I have done the quote thing correctly).

Preach it, math prof!   I think you are very correct.  They are supposed to do this from the youngest K-12 grades, but it's either the most difficult skill to acquire and apply; or it's just not emphasized and developed enough; likely both. 

Poiuy

In response to my transfer level math students not knowing where to begin on word problems, I spend quite a bit of time in my developmental math classes on word problems, problem solving, and critical thinking.  However, I find that many of my algebra students have very little desire to do anything that is not exactly like the examples in the book or require more than two inches of space on their papers to work.  I tell them ahead of time that word problems will make up at least 30% of the exam where a lot of points are awarded just for defining variables, identifying facts, and setting up the problem.  Heck, sometimes I even do the solving and just have them define the variables and interpret the answer.  Very few do the homework that involves word problems and that gets reflected on their test scores.  So I guess my question is, how do we work to change the attitudes of students who don't see the value in problem solving?  (Yes, I've tried making the problems relevant to their every day lives.)


Title: Re: assuming too much math knowledge?
Post by: mccfan on April 23, 2008, 10:26:10 AM
There is no college level math prerequisite for my course.  We do require that they take a class in research design first, but that does not include much math (it covers issues like qualitative vs. quantitative approaches, etc). 

Here is the original problem so that you can evaluate the ease or difficulty of translating the words into numbers in the formula.

"Last year over 20,000 people participated in the Big City Marathon. Let's assume that their race completion times were normally distributed.  The average runner completed the race in 6 hours.  The standard deviation in race completion times was half an hour. 

What is the z score for a runner who took 4.5 hours to finish?  What is the z score for a runner who took 8 hours to finish?  How long did it take a runner with a z score of 1.2 to finish the race?"

The student who did not have algebra in high school did not remember the formula for z, so I can't evaluate her ease in translating from words to numbers.  There were two others problems, and she plugged the values in correctly for one and incorrectly for the other.  None of the other students had a hard time translating the word problem into the formula, so I don't think in this instance it was a "word problem" problem. 

Of course, most social science students are word people, so part of the point is to teach them how to use numbers to solve problems that they perceive in words.


Title: Re: assuming too much math knowledge?
Post by: fossil on April 23, 2008, 11:11:29 AM
There is no college level math prerequisite for my course.  We do require that they take a class in research design first, but that does not include much math (it covers issues like qualitative vs. quantitative approaches, etc). 

Here is the original problem so that you can evaluate the ease or difficulty of translating the words into numbers in the formula.

"Last year over 20,000 people participated in the Big City Marathon. Let's assume that their race completion times were normally distributed.  The average runner completed the race in 6 hours.  The standard deviation in race completion times was half an hour. 

What is the z score for a runner who took 4.5 hours to finish?  What is the z score for a runner who took 8 hours to finish?  How long did it take a runner with a z score of 1.2 to finish the race?"

The student who did not have algebra in high school did not remember the formula for z, so I can't evaluate her ease in translating from words to numbers.  There were two others problems, and she plugged the values in correctly for one and incorrectly for the other.  None of the other students had a hard time translating the word problem into the formula, so I don't think in this instance it was a "word problem" problem. 

Of course, most social science students are word people, so part of the point is to teach them how to use numbers to solve problems that they perceive in words.


As I see it, the big problem with teaching this kind of course to students who aspire to work in fields where quantitative research methods is that at best it leaves them with the capacity to make little computations like the one illustrated here, but without the intellectual tools to think conceptually about the underlying phenomena.  For instance, if you asked them why they might expect this particular parameter to be normally distributed, I doubt they'd know where to begin (indeed, why should a piece of raw data like this exhibit a normal distribution "on the nose", as opposed, say, to a unimodal distribution that has to be reparameterized to become Gaussian?)  The same problem arises in terms of curve-fitting: why should a dependence relation be strictly linear?  How should one conceive or argue these matters, which, all too often, soical scientists simply avoid?  Likewise, how do you adjudicate between Bayesian and frequentist points of view?

Cookbook courses on basic stat simply can't bring students to the point of understanding what's at issue in questions like this, even though they are often of the essence in any sophisticated analysis.  To do that analysis, one must have fairly powerful mathematical insights at one's disposal, going far beyond ability to turn the crank on some simple computational machinery.

I suppose that, in the end, what I'm saying is rather snobbish:  We give a lot of kids a mere shadow of an education because that's all they're able, or at least willing, to handle.  But real life actually does vouch for this snobbery.  We mathematicians have a real-live folk hero these days, a guy who did some crackerjack pure math, but then decided to make a pile by developing analytical tools for dealing with the "market" in its many manifestations and then turning them loose with real money at stake.  His annual personal income is now in the ten-figure range.  He's made a lot of his employees filthy rich as well--but they, of course, are all professional mathematicians by training.  To top it all, he's now gone back to doing serious work, which is to say, pure mathematics.

The moral of the story is that to build good mathematical models of how people behave, one must be, inter alia, a pretty good mathematician, not merely someone who has been trained to feed the appropriate numbers into the appropriate canned software.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 23, 2008, 11:52:19 AM

I don't know.  It depends what you mean by a "pretty good mathematicians".  I think we need to distinguish between (1) mathematics, as taught in math departments, which, at least traditionally, places most of the emphasis on proof and the process of proof of theorums, and (2) "applied" mathematics, as taught by physicists and engineers which places most of the emphasis on the usage of mathematics and the translation of physical phenomena into mathematical terms, and the visualization of problems mathematically.

Most physicists are not great mathematicians in the sense that a mathematician is.  But they often have deep insights into the math and its physical meaning.

Clearly (1) is not necessary in this case.  If we're talking about the different types of distributions, there are excellent examples which allow one to understand, say, the basis of the normal distribution, without necessarily being able to derive it de novo.


Title: Re: assuming too much math knowledge?
Post by: math_prof on April 23, 2008, 12:12:00 PM
OP...Your problem is worded exactly as it would have been in my Stats course.  And unfortunately, if my students had not previously seen an example worded the exact same way, they would not have been able to solve it. 

It seems that Statistics is being taught from two different viewpoints these days.  Either it's completely computation-based, such as "compute the standard deviation given the following data values" or "find the z-score of data value x given the following information", etc.  Or, at the other extreme, it's from a more applied point of view, with questions like "What does it mean when we say that a set of data values has a standard deviation of 0.8?"

Of course, the best method would be one that combines both of these approaches, but I fear that it's asking too much of the students to make the connection between the two, given the limited amount of experience they have had making such connections in their previous math courses. 

Don't get me wrong...I am not making excuses for the students.  But I have been working with this level of students for the past five years and each year I see a less-prepared student.  I do my best to teach them the whole picture, but I'm afraid that many of them leave with the same confused look on their face that they had on the first day of class.


Title: Re: assuming too much math knowledge?
Post by: fossil on April 23, 2008, 12:18:25 PM

I don't know.  It depends what you mean by a "pretty good mathematicians".  I think we need to distinguish between (1) mathematics, as taught in math departments, which, at least traditionally, places most of the emphasis on proof and the process of proof of theorums, and (2) "applied" mathematics, as taught by physicists and engineers which places most of the emphasis on the usage of mathematics and the translation of physical phenomena into mathematical terms, and the visualization of problems mathematically.

Most physicists are not great mathematicians in the sense that a mathematician is.  But they often have deep insights into the math and its physical meaning.

Clearly (1) is not necessary in this case.  If we're talking about the different types of distributions, there are excellent examples which allow one to understand, say, the basis of the normal distribution, without necessarily being able to derive it de novo.

I don't think the distinction between pure and applied math is very hard and fast; some of the best "pure" mathematicians I know are, officially, "applied" mathematicians.  I am officially a "pure" mathematician, but on occassion, almost by accident, I've found myself doing "applied" math.  But then, I've taken some ideas that appeared in an "applied math" context and used them to do "pure" math.

I'd also remind you that perhaps the most admired physicist in the world, Ed Witten, has won a Fields Medal for "pure" math (but not a physics Nobel--yet).  Some of my friends hop back and forth between "physics" and "math", depending on what interests them at the moment.

But all this is a digression.  My point is that most of the students subjected (that's the right word) to these intro stat courses have neither the interest nor the talent necessary to think deeply about the fit between the models they're taught to use and the reality they're trying to describe.  This, of course, is in addition to the difficulty they encounter in merely trying to grasp the mechanics.

I'm curious: how do the people who teach this stuff envision, for instance, correlation co-efficients?  Is it in terms of the standard "formula", or do you, like most mathematicians, simply think about the angle (and thus the dot product) between two vectors in some k-dimensional space?  The latter view simplifies everything enormously.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 23, 2008, 12:26:16 PM

I don't know.  It depends what you mean by a "pretty good mathematicians".  I think we need to distinguish between (1) mathematics, as taught in math departments, which, at least traditionally, places most of the emphasis on proof and the process of proof of theorums, and (2) "applied" mathematics, as taught by physicists and engineers which places most of the emphasis on the usage of mathematics and the translation of physical phenomena into mathematical terms, and the visualization of problems mathematically.

Most physicists are not great mathematicians in the sense that a mathematician is.  But they often have deep insights into the math and its physical meaning.

Clearly (1) is not necessary in this case.  If we're talking about the different types of distributions, there are excellent examples which allow one to understand, say, the basis of the normal distribution, without necessarily being able to derive it de novo.

I don't think the distinction between pure and applied math is very hard and fast; some of the best "pure" mathematicians I know are, officially, "applied" mathematicians.  I am officially a "pure" mathematician, but on occassion, almost by accident, I've found myself doing "applied" math.  But then, I've taken some ideas that appeared in an "applied math" context and used them to do "pure" math.

I'd also remind you that perhaps the most admired physicist in the world, Ed Witten, has won a Fields Medal for "pure" math (but not a physics Nobel--yet).  Some of my friends hop back and forth between "physics" and "math", depending on what interests them at the moment.

Well they are often quite distinct in the way they are taught.

Quote
But all this is a digression.  My point is that most of the students subjected (that's the right word) to these intro stat courses have neither the interest nor the talent necessary to think deeply about the fit between the models they're taught to use and the reality they're trying to describe.  This, of course, is in addition to the difficulty they encounter in merely trying to grasp the mechanics.

I'm curious: how do the people who teach this stuff envision, for instance, correlation co-efficients?  Is it in terms of the standard "formula", or do you, like most mathematicians, simply think about the angle (and thus the dot product) between two vectors in some k-dimensional space?  The latter view simplifies everything enormously.

But most statistics books (intro and otherwise) are absolutely dreadful, at many levels.  And I've recently sat in on a rather dreadful statistics course taught by a person with a PhD in statistics.  It is a particularly difficult subject to teach.  I'm not inclined to put all of the blame on the students.



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 23, 2008, 01:35:28 PM
Of course, most social science students are word people, so part of the point is to teach them how to use numbers to solve problems that they perceive in words.

I think that the first part of this is false, in the sense that social science students are no more "word people" than are math students.  In particular, both sets of students prefer problems that just consist of plugging into a formula, and both will equally despise problems that make them interpret words.  One expects that given two equally intelligent students, one who is "interested"in math and one in a social science, the former will be better at exact reasoning and the latter at interpretation and evaluation, but in reality I think this is only the case for the very best students.

If you look at textbooks for the typical "math for nonscientists" college course, they are written at the 6th-8th grade level when judged on prose. Lots of big color pictures, gee-whiz text with exclamation marks, few big words, and so on.  In fact, the presumptive reading ability is below that of a math or physics text for a course for majors. - DvF


Title: Re: assuming too much math knowledge?
Post by: mccfan on April 23, 2008, 02:27:12 PM
A combined reply.  to mathprof who says "OP...Your problem is worded exactly as it would have been in my Stats course.  And unfortunately, if my students had not previously seen an example worded the exact same way, they would not have been able to solve it.  "

I did a problem that was almost exactly like this one in class.  The only difference was that the scenario involved income instead of race times.  I agree that giving them a new situation throws them off even more than giving them the same problem with a slightly different situation as the premise.

I am trying to span the gap between "add these up and plug these in" and "here's the theory behind this."  They are after all going to have to figure out what questions to ask on their own one day.  And of course I find this all very frustrating (as they do too).

to fossil: I don't see that I have to teach them everything there is to know about math or statistics.  What I am trying to do is to get them to recognize/understand some things and be able to perform a rudimentary set of statistical tests.  I show them the central limit theorem by giving them a bag of MnMs with half one color and half the other color.  They see the population balance, then they do a number of random selection draws to demonstrate that the sampling distribution really will cluster around the true population value.  This helps me help them understand the concept of a confidence interval, which in turn helps them understand the concept of sampling error. 

I tell them there are problems with assuming normality, but that wasn't what I was trying to test with that question.  And one cannot do everything in one course.  I am tasked by my department with demystifying basic statistics so they can design and carry out surveys for their Capstone classes and so that they can read published work in social science journals.  WE also want them to be more skeptical consumers of statistics generally.  Also, we do cover whether relationships are linear or curvilinear, as do most social scientists I know.

to daniel: I glanced through my book.  It seems to me it is written at an advanced high school level.  I'm no expert at assessing grade level of prose though.  I'm not really seeing any exclamation points and there are no color pics.  I do think that social science students are "word people" in the sense of being "not numbers people."  My mathematician students in the inter-disciplinary courses I teach do often have to adjust a bit to start providing full-fledged essays as they are often more "get it done and get it over with folks."  This is of course not meant to be a general claim as my sample is not representative :)







Title: Re: assuming too much math knowledge?
Post by: jonesey on April 23, 2008, 02:59:59 PM
(z= X - mean of X  /   standard deviation)

FWIW, I have no idea what this even means, and I'm in a doctoral program.  : )

I have a BA in English, which required one semester of math (IIRC, I took the lowest level of algebra requried, Math 101 or something like that, because I never took Algebra in HS: severe math-phobia) and one semester of an "advanced" math course, Trig for science majors, etc, or, for everyone else, Statistics.  I was a Business major for a bit, so I took "Business Stats" which required no actual math (grades were based on written papers evaluation business decisions that used rudimentary statistical analysis via a computer program). 

Now I'm in a doctoral program and terrified of taking Quantitative Analysis (although I've been told by others at the school that all anyone does is use a computer program for the actual math). 

Quote
As I was going over the answers in class the other day, I said "using simple algebra which you had in high school..." when one of my students said she had never had algebra.  I was so surprised I asked "then how did you get into college?"  I thought everyone had to have algebra 1 in order to graduate high school, much less qualify for college admission.  I guess not. 

No, they don't.  Two semesters of math, period.  In my case, General Math and Pre-Algebra.  I took Pre-Alg as a HS freshman, but it freaked me out so they put me in Bonehead General Math the following year.  Two years was the minimum requirement at my school, so I was done.  Now, four years were required for College Prep, but I wasn't going straight to college with my GPA (and attitude) anyway, so I didn't bother. 

I would expect to know math for a Data Analysis class, but if there isn't a math pre-req, you're going to get students who haven't done math of any kind for years.  For many people, math is something they dread like root canal and, as soon as the class is over, they dump that knowledge from their brains. 

Ask anyone whose taught an upper level math course in the Fall how much his/her student's retain from the Spring semester, three months earlier if you want an example. 


Title: Re: assuming too much math knowledge?
Post by: concordancia on April 23, 2008, 03:02:57 PM
It depends a lot on the state. I was in one that had "local" and "state" diplomas. If you expected to go to college, you were pushed into the state one, which included for years of math, named, creatively, math I, II, III and IV. As such, I had a strong grounding, but didn't know the difference between algebra and geometry.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 23, 2008, 03:56:53 PM
to daniel: I glanced through my book.  It seems to me it is written at an advanced high school level.  I'm no expert at assessing grade level of prose though.  I'm not really seeing any exclamation points and there are no color pics.

I wasn't talking specifically about stats texts when I mention a 'typical "math for nonscientists" college course', what I really meant was something like a Math 1 or "Math for Poets" type of course (probably Jonesey's "General Math" was of this variety).

Math and science students tend to be worse at writing essays/term papers than humanities and SS students at a comparable level simply because the latter have had much more practice, just as the math or physics student will have had more practice with formulaic problem solving.  I'm not sure this means that one group consists of "word people", the other of "number people", though sometimes people might self-identify one way or the other.    Any smart student should have no trouble with any math or social science or humanities course at the sophomore level or below, and in my experience the best social science and humanities majors are better than the average math and science students at math.

Jonesey, the problem with just relying on computer programs without some exposure to the formulas and how to manipulate them is that you will not know how to interpret the results, or to recognize errors. The reason students in a basic stats course should do at least a little of the algebra is that this helps you learn what the formulas mean. (For example: why is there a square root of n in some formulas?  We do we divide by n-1 instead of by n in such-and-such a formula?  When we call an estimator "unbiased", does that mean it has some sort of positive moral aspect?) - DvF





Title: Re: assuming too much math knowledge?
Post by: jonesey on April 23, 2008, 04:30:22 PM
Jonesey, the problem with just relying on computer programs without some exposure to the formulas and how to manipulate them is that you will not know how to interpret the results, or to recognize errors. The reason students in a basic stats course should do at least a little of the algebra is that this helps you learn what the formulas mean. (For example: why is there a square root of n in some formulas?  We do we divide by n-1 instead of by n in such-and-such a formula?  When we call an estimator "unbiased", does that mean it has some sort of positive moral aspect?) - DvF

I agree, which is why I'm going to do a little one-on-one remedial math with one of our profs here at my school prior to taking the quant course in the Fall.   


Title: Re: assuming too much math knowledge?
Post by: mended_drum on April 23, 2008, 06:18:42 PM

Math and science students tend to be worse at writing essays/term papers than humanities and SS students at a comparable level simply because the latter have had much more practice, just as the math or physics student will have had more practice with formulaic problem solving.

You know, this has not been my experience at my SLAC, at least not among freshmen and sophomores.  The students I have who claim to be scientifically or mathematically-oriented, are quite often doing badly in both their humanities and their science / math courses.  And the second-best Chaucer paper I ever received came from a physics major.  Maybe it's the SLAC itself--students who want to avoid humanities altogether don't usually come here.  But my best prepared students are usually quite well prepared in multiple disciplines, and writing essays requires at least as much logic and organization as verbal expressiveness.

Of course, as they enter their majors, they become more attuned to a particular discipline.


Title: Re: assuming too much math knowledge?
Post by: iomhaigh on April 23, 2008, 06:26:43 PM
I expect to have to review how to add & subtract fractions (Ex: 1 5/8" + 1 5/8"), but I regularly have to teach mine how to read a tape measure.

Tape measures, for those who have not opened one in a while, are generally BETTER marked than rulers when it comes to fractions of an inch and to having both inch (23") and foot/inch markings (1' 11")

Basics.  Basics.  Basics. 



Title: Re: assuming too much math knowledge?
Post by: jonesey on April 23, 2008, 06:57:27 PM
Maybe it's the SLAC itself--students who want to avoid humanities altogether don't usually come here. 

Funny.  I thought the humanities were precisely the reason one would attend a SLAC.  Isn't that what the "Liberal Art" are, largely?   

Don't mathematics majors gravitate towards, say, schools like MIT/Cal Poly/any school with an Engineering department?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 23, 2008, 07:28:55 PM
The students I have who claim to be scientifically or mathematically-oriented, are quite often doing badly in both their humanities and their science / math courses.

There are a lot of students who think they are scientifically or mathematically inclined, either because their K12 math was rather easy or because they really do enjoy the "gee whiz that's cool" aspect of science/math but haven't yet had to do any actual analysis. 

Quote
But my best prepared students are usually quite well prepared in multiple disciplines

I think that is right, and not inconsistent with what I wrote.  However, most of the best humanities undergraduates probably didn't shy away from taking 4 years of high school math, just as the best science students don't stop taking humanities courses in 10th grade.

Jonesey: You might want to check on what the seven "Liberal Arts" are!  At least 25% of my current department earned their undergraduate degrees from SLACs.   - DvF


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 23, 2008, 07:33:13 PM
Maybe it's the SLAC itself--students who want to avoid humanities altogether don't usually come here. 

Funny.  I thought the humanities were precisely the reason one would attend a SLAC.  Isn't that what the "Liberal Art" are, largely?   

Don't mathematics majors gravitate towards, say, schools like MIT/Cal Poly/any school with an Engineering department?

I don't agree with the equation that humanities = liberal arts.  Liberal arts include science and mathematics.



Title: Re: assuming too much math knowledge?
Post by: eulerian on April 23, 2008, 08:44:44 PM
(z= X - mean of X  /   standard deviation)

FWIW, I have no idea what this even means, and I'm in a doctoral program.  : )

I have a BA in English, which required one semester of math (IIRC, I took the lowest level of algebra requried, Math 101 or something like that, because I never took Algebra in HS: severe math-phobia) and one semester of an "advanced" math course, Trig for science majors, etc, or, for everyone else, Statistics.  I was a Business major for a bit, so I took "Business Stats" which required no actual math (grades were based on written papers evaluation business decisions that used rudimentary statistical analysis via a computer program). 

Now I'm in a doctoral program and terrified of taking Quantitative Analysis (although I've been told by others at the school that all anyone does is use a computer program for the actual math). 

Quote
As I was going over the answers in class the other day, I said "using simple algebra which you had in high school..." when one of my students said she had never had algebra.  I was so surprised I asked "then how did you get into college?"  I thought everyone had to have algebra 1 in order to graduate high school, much less qualify for college admission.  I guess not.

No, they don't.  Two semesters of math, period.  In my case, General Math and Pre-Algebra.  I took Pre-Alg as a HS freshman, but it freaked me out so they put me in Bonehead General Math the following year.  Two years was the minimum requirement at my school, so I was done.  Now, four years were required for College Prep, but I wasn't going straight to college with my GPA (and attitude) anyway, so I didn't bother. 

I would expect to know math for a Data Analysis class, but if there isn't a math pre-req, you're going to get students who haven't done math of any kind for years.  For many people, math is something they dread like root canal and, as soon as the class is over, they dump that knowledge from their brains. 

Ask anyone whose taught an upper level math course in the Fall how much his/her student's retain from the Spring semester, three months earlier if you want an example. 

jonesey, your post really makes me sad, because it shows a snapshot of the culture in this country where it is totally okay and acceptable to exhibit one's inability of mathematics. Please don't get me wrong; I'm not necessarily blaming on you. I am just pointing out that your post clearly describes how people think about math in this country. Imagine what it would be like if someone said something like your post where math is replaced by, say, music. "I hated music so much that I avoided taking music classes when I was in school..." I am sure that people are trying hard to improve math ed in the K-12 and college/university levels. But, I believe that it is also important to fight against such a culture where the math-phobic attitude is regarded as an acceptable thing.

A few years ago, at an annual math meeting, I saw a T-shirt which says "It is okay to like math."


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 23, 2008, 10:21:04 PM
Ask anyone whose taught an upper level math course in the Fall how much his/her student's retain from the Spring semester, three months earlier if you want an example. 

On this subject, correct grammar (contractions and plurals) is something else that doesn't seem to persist...

(Sorry jonesey, in the context the target was too inviting to resist!) - DvF


Title: Re: assuming too much math knowledge?
Post by: baka_janai on April 24, 2008, 02:49:52 AM
Students do a 20 point quiz and are then asked to figure out what percent they got correct.  Many can't seem to work this out.


Title: Re: assuming too much math knowledge?
Post by: kaysixteen on April 24, 2008, 04:04:10 AM
Random thoughts:

1)Math may be the subject field that is taught the most poorly, k-12, except perhaps for foreign languages (and foreign language avoidance is also very common amongst American college students, and, of course, most American adults cannot competently speak anything but English).

2)At least f.l.'s have a 'use' that is perceptible to kids.  Most hs/ undergrad students will be hard-pressed to know why anyone would need to know algebra, let alone any form of mathematics more advanced than this.  And, of course, most American adults never use algebra, let alone trigonometry, calculus, statistics, etc., in their daily personal or work lives.

3)Unlike when most of us forumites were hs kids, today's kids have been more or less fully calculatorized from early grade school.   Even the SAT permits their use nowadays.  Thus it should hardly surprise anyone that college kids lack fundamental understandings of mathematical concepts.

4)Most humanities PhDs, like it or not, never really use much math in their professional lives, and use no more math in their daily personal lives than any other American adult.  Many of us may well have been very successful at math courses in high school and even college, up to at least the level of 'AP calculus'.  However, such past successes, often 10+ years in the past, have little if any bearing on the amount of actual mathematics we recall from our school years.   Most could not even conceive of how to do a geometric proof, or a simple calculus integral, now, however well we did such things once.  This does not mean we could not quickly relearn these skills, but they are not there, right now.


Title: Re: assuming too much math knowledge?
Post by: eulerian on April 24, 2008, 09:05:24 AM
Random thoughts:

1)Math may be the subject field that is taught the most poorly, k-12, except perhaps for foreign languages (and foreign language avoidance is also very common amongst American college students, and, of course, most American adults cannot competently speak anything but English).

2)At least f.l.'s have a 'use' that is perceptible to kids.  Most hs/ undergrad students will be hard-pressed to know why anyone would need to know algebra, let alone any form of mathematics more advanced than this.  And, of course, most American adults never use algebra, let alone trigonometry, calculus, statistics, etc., in their daily personal or work lives.

3)Unlike when most of us forumites were hs kids, today's kids have been more or less fully calculatorized from early grade school.   Even the SAT permits their use nowadays.  Thus it should hardly surprise anyone that college kids lack fundamental understandings of mathematical concepts.

4)Most humanities PhDs, like it or not, never really use much math in their professional lives, and use no more math in their daily personal lives than any other American adult.  Many of us may well have been very successful at math courses in high school and even college, up to at least the level of 'AP calculus'.  However, such past successes, often 10+ years in the past, have little if any bearing on the amount of actual mathematics we recall from our school years.   Most could not even conceive of how to do a geometric proof, or a simple calculus integral, now, however well we did such things once.  This does not mean we could not quickly relearn these skills, but they are not there, right now.

I'm sure that, if you did well in high school and college math courses, that must have helped building your analytical skills.

I do agree with some of your points (such as, math is taught very poorly in high schools..). But, I have some serious issues with others. Especially, the statement "most American adults never use algebra, let alone trigonometry, calculus, statistics, etc., in their daily personal or work lives."

I don't know how you define your "daily personal or work lives". When I lament the lack of mathematical skills, I usually tend to think more of quantitative literacy, rather than knowledge in, say, calculus. Here are some concrete examples I have encountered:

1. When I taught a 'liberal arts math' course, mostly for humanities and soc sci majors, I had a question in an exam that contains a histogram which looks, roughly, like this: (I wish I can include graphics here. The x- and y- axes are inverted here for the sake of typography..)

Musician's salary;

$20k - $30k : XX
$30k - $40k : XXXX
$40k - $50k : XXXXX
$50k - $60k : XX
$60k - $70k : X

A surprisingly large number of students couldn't find mean, 25 percentile etc,. Also, many of them were unable to answer questions like "How many musicians make more than $50k?" I should say that they were able to compute mean, 25 percentiles, etc, when I presented the data set using numbers. So, the problem with the above question was that they were unable to "read" the histogram. In my question, all the numbers were 'kind', that is, all the answers worked out to be whole numbers (no fractions or decimals) and it was a multiple choice question. I had to wonder what they would think when they read newspapers and graphs therein. (I know. they don't read newspapers...)

2. As reported in this forum, many students can't compute their averages.

3. A colleague of mine described to me a committee meeting she was in. They were discussing how we ought to interpret students evaluation results. One argument there was that we have to consider both mean and standard deviation together. One person in the committee (in a humanity department) insisted that we cannot include the word "standard deviation" in the committee report because "no one knows what that term means". To me, this sounds like, you gotta talk about apples, but, you can't use the word "apple", because no one knows what "apple" means. If you have to use the concept of standard deviation, you better know what standard deviation is.

I think of this like a pandemic in the US. Many people lack the most basic quantitative literacy skills and they feel it's okay because "we don't use those in everyday lives". Well, if you don't have those skills, obviously you can't use them, therefore, don't need them in your everyday lives! You can get by a 5th-grade level of vocabulary in our daily lives, so why bother to learn difficult words?

The reality is, though, that the demand for this quantitative literacy skill is nowadays increasing more than ever in order to become an informed consumer and citizen. And, we're falling more and more behind on this front. And people say it's okay because "we don't need them in everyday lives".


Title: Re: assuming too much math knowledge?
Post by: jonesey on April 24, 2008, 09:20:27 AM
On this subject, correct grammar (contractions and plurals) is something else that doesn't seem to persist...

(Sorry jonesey, in the context the target was too inviting to resist!) - DvF

I knew I'd get caught on this.  : )

FWIW, I take full responsibility for my lack of math knowledge.  I didn't like math, took the easy way out, and that's that. 

I agree with K16's post 100%.  Unless you're going to med school, or teaching math, or, perhaps, working in finance (and even those people use computers to compute their formulas), you just aren't using anything beyond basic computational skills.  Algebra?  No.  Calculus?  Most HS don't require Calc.  Many only require up to Trig, and only then for College Prep programs.

FWIW, I teach freshmen CC students, many of whom aced their Calc classes in HS, but are in remedial math at the CC level due to (I assume) lack or retention or easy grading at the HS level. 

I can relate to math profs because I teach Freshman (and developmental) English.  My classes are full of the "I hate English" variety of students. 

IME, Math and English bear the brunt of the "I hate this subject" crowd.  Sure, some people hate science classes, but, unless you're majoring in it, most students can get away with only one general survey science course on their way to a BA. 

I know the vast majority of posters have PhDs, and, it seems, most of those PhDs are in scientific fields and/or are from big, R1-type universities.  Take a moment and think, however, about how easy it is to get a BA in, say, Communications (or Criminal Justice, or Rec and Leisure Studies) if you a)don't plan on going to grad school, so you don't take any difficult courses (i.e. math) that you'd need at the grad school level and b) you don't care about your GPA for the same reason.

Getting a BA with a 2.0 GPA in many fields is pretty darn easy.  This is what a lot of my students are aiming for, and often make comments like "Well, after your class I've only got one more lousy English class to go.  I hope their isn't too much reading in it." etc, etc.  : )

I think we (as profs) tend to view our student's undergrad experience through the lens of our own, which were, for most of you, filled with A grades and weekends of studying and killing yourselves over that next paper.  For much of America, college is four more years of partying and scraping by before having to go out and face the real world. 


Title: Re: assuming too much math knowledge?
Post by: momto2 on April 24, 2008, 09:38:24 AM
In Eulerian's histogram, you can't tell how many make more than $50k, given that the 2 x-s in that row could be people who make exactly $50k.  Or am I wrong about this?


Title: Re: assuming too much math knowledge?
Post by: kaysixteen on April 24, 2008, 10:38:55 AM
OK, lemme ask it more directly: how many American adults use calculus in their professional lives?  I could probably count the professions doing so on both sets of fingers and toes, being generous.  As to how many ever use it in their daily personal lives....


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 10:55:13 AM
OK, lemme ask it more directly: how many American adults use calculus in their professional lives?  I could probably count the professions doing so on both sets of fingers and toes, being generous.  As to how many ever use it in their daily personal lives....

The argument that subject X is not used in your professional life can probably be made about any academic subject.  It is a common argument amongst grade-school children.

If you had read the thread, you would know that the original question was about statistics, not calculus.  Clearly, statistics is widely used in the social sciences, as well as all of the hard sciences.


Title: Re: assuming too much math knowledge?
Post by: fossil on April 24, 2008, 11:04:37 AM
OK, lemme ask it more directly: how many American adults use calculus in their professional lives?  I could probably count the professions doing so on both sets of fingers and toes, being generous.  As to how many ever use it in their daily personal lives....

OK, let me pose a question that seems eminently practical to me:  Your establish a 401(k) with an initial deposit of $50,000 and contribute, say, $6,000/year in bi-monthly installments.  The account yields a constant 7%, compounded continuously.  How much money will be in that account in 25 years?

How would you go about computing this?


Title: Re: assuming too much math knowledge?
Post by: eulerian on April 24, 2008, 11:11:47 AM
OK, lemme ask it more directly: how many American adults use calculus in their professional lives?  I could probably count the professions doing so on both sets of fingers and toes, being generous.  As to how many ever use it in their daily personal lives....

Well, I can answer that directly: probably not many American adults use calculus in their professional and personal lives. And, I have no problem with that. What I do claim is that many Americans don't have basic arithmetic skills and elementary math concepts, which I generally call quantitative skills (the examples I quoted in my previous post), and they should have those skills. These are different from calculus because it's something an informed citizen ought to have.

Imagine how you would feel if you were in a society where majority of the people don't use anything higher than the 5th-grade level vocabulary.

That's exactly how I felt when I came to the US (from another country) to begin my PhD in math. I've seen an apartment manager, who was struggling to find out how much he needs to return from my security deposit of $550 minus the cleaning cost of $75. When I told him I needed to get $475, he didn't believe me initially. After checking it with his calculator, he looked at me like I am an alien... (I was, for the visa/tax purpose.) I had to wonder how many graphs/pictures in NY times he would correctly understand.


Title: Re: assuming too much math knowledge?
Post by: iomhaigh on April 24, 2008, 11:13:50 AM
I have a humanities PhD, and while I know I have an odd job, I still have to use and teach math, statistics and physics on a regular basis.

Physics:  It's what stagehands and designers use to prevent the speakers from falling on your head at rock concerts.


Title: Re: assuming too much math knowledge?
Post by: kaysixteen on April 24, 2008, 11:27:42 AM
You must have an odd job indeed.  Most humanities PhDs never took a statistics class, let alone have ever been asked to teach it.  Of course, it makes no difference whether I can compute the question involved, about the retirement fund.  I would have an accountant do so for me, as would most adults, rather than trying to remember vaguely understood calculus topics from 25 years removed.  My point is simple enough, boiled down-- calculus is an irrelevance for most American adults, and I do not think high schools should teach it.  There are better, more useful aspects of mathematics (such as for instance, statistics) that could occupy those senior years.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 11:33:31 AM

My point is simple enough, boiled down-- calculus is an irrelevance for most American adults, and I do not think high schools should teach it. 

If that is your point, to teach only what is relevant to most American adults, then most academic subjects can be eliminated.


Title: Re: assuming too much math knowledge?
Post by: conjugate on April 24, 2008, 12:56:53 PM
Oh, good; I get to jump back in.  First of all, I will observe that K16 has a typo (or else I'm being snarky; which is the case? Left as an exercise to the reader):


1)Math may be the subject field that is taught the most poorly, k-12, except perhaps for foreign languages (and foreign language avoidance is also very common amongst American college students, and, of course, most American adults cannot competently speak anything but English).


Not sure why the two unneeded words were included.  Now, that said, I have to agree with K16 here, at least to a point, and possible for reasons other than the ones he uses.

My point is simple enough, boiled down-- calculus is an irrelevance for most American adults, and I do not think high schools should teach it.  There are better, more useful aspects of mathematics (such as for instance, statistics) that could occupy those senior years.
 

I will agree that HS calculus is not, in general, a good thing.  Partly this is because it has happened that a student gets a passing grade in HS AP Calc and finds he or she cannot succeed at a college-level Calc II owing to any number of reasons (poor articulation, lower standards of success) leaving the student stuck and unable to go on to get a degree in a technical field.  Also, as K16 points out, many students don't use math past a certain point. 

OK, let me pose a question that seems eminently practical to me:  Your establish a 401(k) with an initial deposit of $50,000 and contribute, say, $6,000/year in bi-monthly installments.  The account yields a constant 7%, compounded continuously.  How much money will be in that account in 25 years?

How would you go about computing this?

K16 also has a good point here; there are numerous on-line calculators that will do these problems automatically (and I suspect almost every financial institution has one.  However, let me add a personal experience.

When I went to buy a new car (my first really new car ever, in fact) I carefully thought about the interest rate, the price I was paying, and the monthly payments.  Something seemed wrong to me, so I tried to get a fast approximation.  Sure enough, I found that I seemed to be paying significantly more than I should have been.

I talked to the car salesman, who told me that he was not qualified to say, because the numbers came out of the computer and he more or less had to do what the computer said.  But he went away and came back to tell me that apparently by accident a $100 fee (for some stupid thing like a stripe or something — I don't remember what) had been entered as a $1000 fee.  He assured me that in all likelihood, the error would have been caught by someone else before the final papers were issued.

That's not entirely to the point, since the compound interest formulas and such are often taught as pre-calculus; I learned them in high school, and they are taught at my current school at the pre-calculus level.  But it shows that this stuff can be useful sometimes, even in unexpected ways.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 01:02:07 PM

I will agree that HS calculus is not, in general, a good thing.  Partly this is because it has happened that a student gets a passing grade in HS AP Calc and finds he or she cannot succeed at a college-level Calc II owing to any number of reasons (poor articulation, lower standards of success) leaving the student stuck and unable to go on to get a degree in a technical field.  Also, as K16 points out, many students don't use math past a certain point. 


What is the logic here ?  This seems to be mainly an argument about the use of AP courses, not whether calculus should be taught in HS.

Again, many students don't use most academic subjects past a certain point.



Title: Re: assuming too much math knowledge?
Post by: conjugate on April 24, 2008, 01:24:58 PM

I will agree that HS calculus is not, in general, a good thing.  Partly this is because it has happened that a student gets a passing grade in HS AP Calc and finds he or she cannot succeed at a college-level Calc II owing to any number of reasons (poor articulation, lower standards of success) leaving the student stuck and unable to go on to get a degree in a technical field.  Also, as K16 points out, many students don't use math past a certain point. 


What is the logic here ?  This seems to be mainly an argument about the use of AP courses, not whether calculus should be taught in HS.

Again, many students don't use most academic subjects past a certain point.

Well, let me clarify.  First of all, as far as I am aware the only HS calculus courses taught where I am are in fact AP Calculus, so I apparently conflated the two ideas.  Second of all, I suppose we should ask what "should" be taught in HS.  If students don't use most academic subjects past a certain point, should we be teaching them at all?  I think the idea of high school is that students learn the basic skills that they need to be productive successful citizens (and I will set aside the question of whether or not, or to what degree, high schools accomplish this, and duck the question of what "productive" or "successful" mean). 

Thus, even if the student forgets how correctly to pronounce the prologue to Chaucer's Canterbury Tales or remember offhand the text of the 7th Amendment to the Constitution of the United States (both of which were required at my high school, and both of which I have forgotten, though I think it has something to do with Aprille's souete shoures getting a jury trial), they should retain enough of the basic ideas that they can, for instance, understand some of the issues behind rendition or realize that English is not a uniquely American language¹.

So my feeling is that whatever benefit could come of a high school calculus class might come as well or better from a HS geometry, analytical geometry, or pre-calculus class.  While no one believes in the sheer power and beauty of calculus more than I, it seems one can be a good and productive citizen without being able to find the area of the bounded region between two plane curves (for instance).  Do you feel that calculus should be taught in high school?  Should it be mandatory, optional, or available only via a partnership with a college or university?  Just curious.


¹In another thread, a poster complains of a student who asserted that God wrote the Bible in English to show that America was the greatest country on Earth, or something like that.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 01:35:48 PM

My personal experience of high school was tiered into "tracks".  Calculus (and other AP subjects), where the top tier.  In other words, most students did not take calculus, and it would not have been an option for those below track 1, because they would not have had the prerequisites.

Of course all students should not take calculus.  I can't imagine that it is the case anywhere that all students in a HS would be taking calculus (except perhaps in schools such as Bronx Science).

The purpose of HS does not have to be universal.  For some students, the purpose is to graduate and work.  For others, the purpose is to graduate and get into any college.  For others, it is to graduate and go to an elite university.  It is not clear why all of these purposes cannot be accomadated in a single HS institution.  There is no need to treat all students identically.



Title: Re: assuming too much math knowledge?
Post by: kaysixteen on April 24, 2008, 01:46:35 PM
My point is that, regardless of the math skills of the hs student (with the handful of exceptions for the truly mathematically gifted and precocious) there are better 'math' classes for high school than calc, areas of math that are worthy, far more useful for the average kid, and tend never to get covered (at least not in the last thirty years or so) owing to a desire of hss to please college admissions offices with 'calculus' on the transcripts of hs kids.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 01:52:05 PM
My point is that, regardless of the math skills of the hs student (with the handful of exceptions for the truly mathematically gifted and precocious) there are better 'math' classes for high school than calc, areas of math that are worthy, far more useful for the average kid, and tend never to get covered (at least not in the last thirty years or so) owing to a desire of hss to please college admissions offices with 'calculus' on the transcripts of hs kids.

We don't need to lump all of the students together with the "average kid".


Title: Re: assuming too much math knowledge?
Post by: jonesey on April 24, 2008, 02:20:41 PM
Imagine how you would feel if you were in a society where majority of the people don't use anything higher than the 5th-grade level vocabulary.

The majority of Americans don't use anything higher than a 5th grade level vocab; newspapers are written at the 4th grade level.  You're taught that in Journalism 101.  How many four-syllable words are in your daily paper? 



Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 02:24:44 PM
Imagine how you would feel if you were in a society where majority of the people don't use anything higher than the 5th-grade level vocabulary.

The majority of Americans don't use anything higher than a 5th grade level vocab; newspapers are written at the 4th grade level.  You're taught that in Journalism 101.  How many four-syllable words are in your daily paper? 



So you are also making the least common denominator argument ?



Title: Re: assuming too much math knowledge?
Post by: jonesey on April 24, 2008, 02:28:34 PM
Imagine how you would feel if you were in a society where majority of the people don't use anything higher than the 5th-grade level vocabulary.

The majority of Americans don't use anything higher than a 5th grade level vocab; newspapers are written at the 4th grade level.  You're taught that in Journalism 101.  How many four-syllable words are in your daily paper? 

So you are also making the least common denominator argument ?

No, not at all.  I've explained to my students that learning math isn't just about whether or not you'll ever use it "in real life."  Learning math changes the way students look at things.  It enables more advanced analytical thinking and problem solving skills across the board. 

As far as English goes, I think most newspaper writing is criminally lowbrow.  But then, I'm a snob.  : )


Title: Re: assuming too much math knowledge?
Post by: fossil on April 24, 2008, 02:58:51 PM
The idea that "it's in a table that the bank provides" is reassuring only up to a point.  How are you going to detect an error, for instance?  What method do you have for eyeballing an answer to see whether it's reasonable.  For that matter, can you tell me why the APR on an account is higher than the nominal interest rate?  How would you handle an account where the interest rate is changeable?  Any ideas?

While we're on the subject, which is more radioactive; a substance with a half-life of 5 days or one with a half-life of 5,000,000 years?  How do you recognize that the growth of a population is most likely malthusian?  How do you recognize that growth will stop short of some limit?  Do you know how to turn common-sense assumptions into mathematical form accurately enough to make asessments like these?

People stink (generally speaking) at calculus not because they're bad at memorizing formulas but because they are resistant to thinking things through while they're learning them.  It's a deficiency of logical reasoning, not of rote memorization, that cripples most people mathematically.

BTW, there's no such subject as "AP calculus"; either you're learning calculus or yu're not.  In the same fashion, there's no such thing as "pre-calculus", let alone "pre-algebra".


Title: Re: assuming too much math knowledge?
Post by: jonesey on April 24, 2008, 03:31:39 PM
BTW, there's no such subject as "AP calculus"; either you're learning calculus or yu're not.  In the same fashion, there's no such thing as "pre-calculus", let alone "pre-algebra".

Tell that to the state department of education:

Quote
The major topics covered in High School Pre-Algebra are: Expressions, Order of Operations, Integers, Pattern Recognition, Ratio, Proportion, Percent, Equations, Inequalities and Functions, Graphing One Variable Equations, Solving One Variable Equations.

Also, you might want to read the Chicago Public Schools Structure Curriculum: Pre-Calculus (http://intranet.cps.k12.il.us/Lessons/StructuredCurriculumTOC/SCMathematics/HS_PreCalculus_Daily_Lessons_/SCMAPC1/MAPC_Overview_.pdf)


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 24, 2008, 03:38:36 PM
I think that the soundest argument for teaching the Calculus widely is not for its applications, but that it is one of the most profound intellectual achievements of the last millenium.  Just as any member of our cultural community should have exposure to Shakespeare and Mozart and da Vinci, so should they have exposure to Newton and Leibniz.  The fact that we do not teach it well in high schools, and certainly do not teach it as an object of cultural importance at any level, is not an argument that it should not be taught.

During WWII the Army printed a very small number of books they deemed of intrinsic value in a special format ("Armed Services Edition") that would fit in a GI's trouser pocket.  One of these was The Education of T.C. MITS, by Lillian Lieber (a mathematician) and Hugh Lieber (an artist).  This book argues - in the form of free verse and modern art - that mathematics in general, and pure math in particular, are important tools for a genuine understanding of abstract concepts like "justice" and "freedom".   The book is remarkable in that it starts with some arithmetic puzzles and makes it through Calculus and non-Euclidean geometry, managing to tie it all together with their underlying nonmathematical message.

This book was very influential among mathematical scientists of my generation (and the generation before, I'm not that old!), and makes a much better argument than I could here why humanities people should know some pure mathematics completely aside from the practical question of how to understand amortization tables, survey data, and load diagrams for building a deck.

(Jonesey, I think you in particular would really enjoy this; it has recently been rereleased in an inexpensive paperback edition.) - DvF


Title: Re: assuming too much math knowledge?
Post by: kaysixteen on April 24, 2008, 05:11:32 PM
Precisely because calc is so profound makes it a waste in high school.  Too many students lack the intellectual maturity to study it competently yet, and if they are forced to attempt it nonetheless, they may well do less than well, and, then, develop a hostility towards it (and math in general) that we would not want them to harbor.


Title: Re: assuming too much math knowledge?
Post by: jonesey on April 24, 2008, 05:21:54 PM
Precisely because calc is so profound makes it a waste in high school.  Too many students lack the intellectual maturity to study it competently yet, and if they are forced to attempt it nonetheless, they may well do less than well, and, then, develop a hostility towards it (and math in general) that we would not want them to harbor.

Or, at many colleges, HS Calculus is sufficient enough to preclude students from taking any math courses in college, exacerbating the problem the OP has.


Title: Re: assuming too much math knowledge?
Post by: math_prof on April 24, 2008, 08:14:19 PM
Precisely because calc is so profound makes it a waste in high school.  Too many students lack the intellectual maturity to study it competently yet, and if they are forced to attempt it nonetheless, they may well do less than well, and, then, develop a hostility towards it (and math in general) that we would not want them to harbor.

Who is being forced to attempt calculus in high school?  Have things changed that much since I went to high school several years ago?  As far as I knew, the only students that took calculus were those who tested into it and who planned to major in engineering or science-related fields at the university level.  Those who weren't up to it were on a track that took them only as high as Algebra II.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 24, 2008, 08:47:16 PM
Who is being forced to attempt calculus in high school?  Have things changed that much since I went to high school several years ago?

At high schools with large numbers of college-bound students, students are strongly encouraged to take Calculus because (a) it will look good on their college application portfolio, and (b) all the "good" students take it.  Then, the course itself is dumbed down so that weaker students handle take it, and grades are inflated so that parents won't complain about their child's grade  (college entrance again). - DvF


Title: Re: assuming too much math knowledge?
Post by: eulerian on April 24, 2008, 09:06:24 PM
Precisely because calc is so profound makes it a waste in high school.  Too many students lack the intellectual maturity to study it competently yet, and if they are forced to attempt it nonetheless, they may well do less than well, and, then, develop a hostility towards it (and math in general) that we would not want them to harbor.

Wow. I'm constantly amazed by K16's posts..

So, calc is so profound for our high school students, that we shouldn't teach it any more. Other subjects (presumably humanities and social sciences), then, are shallow enough that it is safe to teach those subjects in high schools. Oh, what about those students in Europe and Asia, who certainly learn that 'profound' calculus and even more advanced math in high school?

Again, calculus is so profound that we shouldn't teach it in high schools... Wow..



Title: Re: assuming too much math knowledge?
Post by: kraken on April 24, 2008, 09:06:53 PM
So...it doesn't sound as though Calculus in High School is the problem.  Rather, it is the context in which it is taught that is problematic.  None of this is new.  We all know the devastating impact of grade inflation and the conceptualization of college degrees as mere credentials leading to jobs.


Title: Re: assuming too much math knowledge?
Post by: kraken on April 24, 2008, 09:08:07 PM
Of course not.  It would be a shame if they had to go beyond calculating proportions and percentages.  At this point, sadly, I'd be happy if they could do that reliably.


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 09:08:47 PM
Precisely because calc is so profound makes it a waste in high school.  Too many students lack the intellectual maturity to study it competently yet, and if they are forced to attempt it nonetheless, they may well do less than well, and, then, develop a hostility towards it (and math in general) that we would not want them to harbor.

Nobody is arguing that all students should take calculus.  This has been pointed out multiple times to you on this thread.  Sorry if you cannot understand this.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on April 24, 2008, 09:57:39 PM
Nobody is arguing that all students should take calculus.  This has been pointed out multiple times to you on this thread.  Sorry if you cannot understand this.

I think he might be replying to my post, where I give an argument as to why it should be widely taught, by which I really meant simply more widely than to just STEM professionals.  While I wouldn't argue that everyone needs calculus, I would argue that some exposure to it is as much part of a basic Western education as is comparable exposure to the great art, music, and literature of the last 500 years.  - DvF


Title: Re: assuming too much math knowledge?
Post by: iomhaigh on April 24, 2008, 10:12:59 PM
Nobody is arguing that all students should take calculus.  This has been pointed out multiple times to you on this thread.  Sorry if you cannot understand this.

I think he might be replying to my post, where I give an argument as to why it should be widely taught, by which I really meant simply more widely than to just STEM professionals.  While I wouldn't argue that everyone needs calculus, I would argue that some exposure to it is as much part of a basic Western education as is comparable exposure to the great art, music, and literature of the last 500 years.  - DvF

Seriously.  A liberal arts education is as much about, if not more about, learning critical thinking and reasoning skills in a variety of fields, not about the actual information that you learn.  Exposure is good, but the process of learning new material and learning to think is what will serve you in your life. 
   
Bad humanities prof talking!  You're not supposed to admit that content is largely irrelevant and the skills and process are what matter much more in the long run!

Oops... sorry... I meant... yeah, teaching hard things and challenging students with material that might be beyond them is a bad idea and a waste of time, especially if they might never use it again. 

Math is hard 'cuz my Barbie said so. 


Title: Re: assuming too much math knowledge?
Post by: stringyone on April 24, 2008, 11:36:06 PM
Precisely because calc is so profound makes it a waste in high school.  Too many students lack the intellectual maturity to study it competently yet, and if they are forced to attempt it nonetheless, they may well do less than well, and, then, develop a hostility towards it (and math in general) that we would not want them to harbor.

Nobody is arguing that all students should take calculus.  This has been pointed out multiple times to you on this thread.  Sorry if you cannot understand this.

K16 is merely pointing out the fact that it is widely accepted by students, parents, HS teachers, and the like that the failure to take Calculus in HS essentially demolishes any chances of gaining admission to any ''good'' college.  As such, students are introduced to significant mathematical ideas long before they have the mathematical maturity to grasp these concepts.  In particular, students are required to use calculators as early
as the third grade and Algebra I is now commonly taught in the 7th and 8th grades by teachers who are much stronger in the art of discipline than they are in the art of mathematics (this is not meant to be disrespectful of Middle School teachers in any way).  In HS, the problem is exasperated by the fact that disillusioned and/or overworked HS teachers essentially push students through the curriculum by teaching rote learning instead of good problem solving skills.   

Whenever I teach Calculus (and some pre-Calculus courses) in the Fall term, I always have 2 or 3 freshmen approach me during the term completely distraught by the fact that they are failing the course, in spite of having gotten an ''A'' in AP Calculus/gotten a 5 on the AP Calculus exam(if they are taking Calculus II or III).  After inspecting their work, I find a random smattering of incoherent thoughts followed by an answer that is miraculously correct. 

In HS, students learn how to survive mathematics but they don't learn mathematics. 


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 24, 2008, 11:50:05 PM
Precisely because calc is so profound makes it a waste in high school.  Too many students lack the intellectual maturity to study it competently yet, and if they are forced to attempt it nonetheless, they may well do less than well, and, then, develop a hostility towards it (and math in general) that we would not want them to harbor.

Nobody is arguing that all students should take calculus.  This has been pointed out multiple times to you on this thread.  Sorry if you cannot understand this.

K16 is merely pointing out the fact that it is widely accepted by students, parents, HS teachers, and the like that the failure to take Calculus in HS essentially demolishes any chances of gaining admission to any ''good'' college. 

Then argue against this trend, not against teaching calculus.  Your battle is pitched against the wrong enemy.

Quote
As such, students are introduced to significant mathematical ideas long before they have the mathematical maturity to grasp these concepts.  In particular, students are required to use calculators as early
as the third grade and Algebra I is now commonly taught in the 7th and 8th grades by teachers who are much stronger in the art of discipline than they are in the art of mathematics (this is not meant to be disrespectful of Middle School teachers in any way).  In HS, the problem is exasperated by the fact that disillusioned and/or overworked HS teachers essentially push students through the curriculum by teaching rote learning instead of good problem solving skills.   

I think you mean exacerbated, rather than exasperated.  I'm exasperated.

Quote
Whenever I teach Calculus (and some pre-Calculus courses) in the Fall term, I always have 2 or 3 freshmen approach me during the term completely distraught by the fact that they are failing the course, in spite of having gotten an ''A'' in AP Calculus/gotten a 5 on the AP Calculus exam(if they are taking Calculus II or III).  After inspecting their work, I find a random smattering of incoherent thoughts followed by an answer that is miraculously correct. 

Two or three ?  You are going to have two or three students that have problems in any course.

Quote
In HS, students learn how to survive mathematics but they don't learn mathematics. 

This is a gross generalization.  Can we refrain from penalizing bright students, and competant teachers ?



Title: Re: assuming too much math knowledge?
Post by: stringyone on April 25, 2008, 01:44:39 AM
Then argue against this trend, not against teaching calculus.  Your battle is pitched against the wrong enemy.

SciencephD,

I believe that you are being far too literal here. Since this is a community of educators, K16 most likely assumed that we could infer that she was referring to the systemic problems of HS math programs.  Its possible that she couldn't articulate these problems (particularly if she is not in the sciences), but her argument acknowledges the existence of these problems.


Quote

Two or three ?  You are going to have two or three students that have problems in any course.

I think you missed my point entirely.  I never said that I have 2-3 struggling students.  I said that I have 2-3 struggling freshmen  who can't understand why they are struggling because of their previous experience in AP Calculus.   

Quote
This is a gross generalization.  Can we refrain from penalizing bright students, and competant teachers ?

Whenever you are referring to issues of this nature you can only speak in generalities.  That is, you are referring to the general student, the general teacher, the general school, etc.  Where people are involved, you can find a counterexample to any statement made.  One of my best students to date had taken AP Calculus in HS.  I first met him when he took my Calculus III course as a freshman and he was later a student in my Differential Equations and Complex Analysis courses.  When I was in HS, I had an extremely competent teacher for Pre-calculus and AP Calculus.  He was difficult, but I learned the material very well.  Do I ignore these experiences when considering the HS math education problem? Of course not.  But I would be remiss not to acknowledge that there is overwhelming evidence to support a claim that these experiences are exceptions to a general trend.



BTW...I think that, after midnight, I am entitled to mistype a word or two (or perhaps it was a bit of a Freudian slip...).


Title: Re: assuming too much math knowledge?
Post by: king_ghidorah on April 25, 2008, 02:01:22 AM
I grew up when the country was paranoid that the Rooskies were producing more scientists and thus would take over the world.  Science and math were highly "encouraged" for school kids.  I cannot tell how many times I heard "You will use this for the rest of your life."  Oh man what BS!!  I suppose that I fall into that category of poorly taught math students (although I might argue English is the most poorly taught discipline in lower education), but I have resented the fact that I "had" to take math ever since - subject that embarrassed and frustrated me no end and which I really doubt did me much good in the big picture. 

Sorry, not really on subject, but I just had to vent.


Title: Re: assuming too much math knowledge?
Post by: poiuy on April 25, 2008, 03:34:24 AM
To revive the sub-thread about teaching math, here is a gem from today's NYT:  http://www.nytimes.com/2008/04/25/science/25math.html

It's the report of a study by researchers at OSU, throwing doubt on the idea that using real world examples leads to better math learning. 

Quote:
"In the experiment, the college students learned a simple but unfamiliar mathematical system, essentially a set of rules. Some learned the system through purely abstract symbols, and others learned it through concrete examples like combining liquids in measuring cups and tennis balls in a container.
Then the students were tested on a different situation — what they were told was a children’s game — that used the same math.
....
The students who learned the math abstractly did well with figuring out the rules of the game. Those who had learned through examples using measuring cups or tennis balls performed little better than might be expected if they were simply guessing. Students who were presented the abstract symbols after the concrete examples did better than those who learned only through cups or balls, but not as well as those who learned only the abstract symbols.
The problem with the real-world examples, Dr. Kaminski said, was that they obscured the underlying math, and students were not able to transfer their knowledge to new problems."

I have not read the actual study, but I find the experiment as reported incomplete (there is no comparison group of students who learnt abstract symbols first, then widely varied concrete examples, iteratively). 

Some other mathematicians have raised the point that not all students learn the same way. 

It's anecdotal, but based on my own learning style, and watching so many children I know, I just don't buy Kaminski's conclusions.  Some math-talented kids will learn easily through abstractions and be able to apply them.  The rest of us have to go back and forth between  abstractions and applications, and practice a lot, and keep at it lifelong.  What emerges is a recognition of the importance of math skills, even if we can't apply as easily and quickly as others. 

Poiuy





Title: Re: assuming too much math knowledge?
Post by: kaysixteen on April 25, 2008, 10:06:04 AM
One more time, simply laid out, hopefully sufficiently simply even for scientists:

1)calculus is not the best use of math class for the vast majority of HS students, since the vast majority of them are not really prepared to study it then
2)there will always be a handful of exceptions, and these kids can be accomodated
3)Most college kids can get a calc class, if it is important enough to  expose 'well educated' kids to this subject, though that is probably a debatable point too


Title: Re: assuming too much math knowledge?
Post by: stringyone on April 25, 2008, 11:24:17 AM
One more time, simply laid out, hopefully sufficiently simply even for scientists:

1)calculus is not the best use of math class for the vast majority of HS students, since the vast majority of them are not really prepared to study it then
2)there will always be a handful of exceptions, and these kids can be accomodated
3)Most college kids can get a calc class, if it is important enough to  expose 'well educated' kids to this subject, though that is probably a debatable point too

hmmm.... I misunderstood your original meaning.  In light of this post, I must respectfully disagree with your opinion and side with sciencephd here (though I still believe hu to be a bit too literal).  By your logic, half of the courses offered in HS (e.g, World History, US History, American government, all science and literature courses) shouldn't be offered. 

The course isn't the problem rather its the preparation for and/or teaching of the course that is problematic.  It is common belief that Calculus is this mysterious creature that teaches you to calculate even more mysterious beings like derivatives and integrals.  Calculus is not about calculating anything.  In Calculus students learn to use the basic  principles from prerequisite courses to study the behavior of functions.  The analytical skills learned in Calculus are the ''math skills'' that are most transferable to adulthood ( (everyone uses these analytical skills - whether they like it/know it or not). 

The problem is that the prerequisites (and sometimes the actual course) are not taught properly so by the time students finish the course, they have no true understanding of Calculus' purpose.  Calculus is no less relavant than a US History course nor are HS students any more prepared to take said US History course than they are prepared to a Calculus course (have you seen how poorly most college students write - not to mention the egregious lack of reading comprehension skills?).


Title: Re: assuming too much math knowledge?
Post by: sciencephd on April 25, 2008, 11:26:18 AM
One more time, simply laid out, hopefully sufficiently simply even for scientists:


1)calculus is not the best use of math class for the vast majority of HS students, since the vast majority of them are not really prepared to study it then

Most HS students probably shouldn't even go to college.  Wal-mart does not require a college degree, as you probably have figured out by now.

Quote
2)there will always be a handful of exceptions, and these kids can be accomodated

It's not a "handfull".  Math, engineering, and science majors, plus non-science majors entering medicine and allied health, represents a large fraction of students.  It's pretty ironic that you're trying to make a utilitarian argument in education here.  What are you going to compare, classics vs. chemistry ? 

Quote
3)Most college kids can get a calc class, if it is important enough to  expose 'well educated' kids to this subject, though that is probably a debatable point too

You don't start with this stuff in college.  Otherwise it would take six years to get a good degree in science, math, or engineering.  In any good university, the calculus is quite heavy in first year physics.


Title: Re: assuming too much math knowledge?
Post by: kaysixteen on April 26, 2008, 11:49:44 PM
I suppose I ought to say something, like it is ludicrous to compare the intellectual maturity needed for a hs kid to take a US history class vs. a calc class, or that most kids aren't going to be physics majors in college, but I do not think I will bother.  I have made my point.  I stand by it.  Every thing we do or do not teach in hs requires choices.   Some choices are more reasonable than others.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 11, 2008, 01:14:42 AM
Agreed.  The problem of lack of interest in math education doesn't seem to exist in all countries, though.  For example, TIMSS shows that at the 12th grade level, whose scores are very different from the 8th grade level in both directions (up for most countries, VERY much down for the US), Norwegian boys scored 2 standard deviations higher than Swiss boys (589 vs. 519).  But Swiss boys scored 2 standard deviations higher than Swiss girls (519 vs. 444).  And Swiss girls scored another standard deviation higher than American girls (444 vs. 393), for a total of 5 standard deviations of separation between American girls and Norwegian boys. 

SAT scores for 12th graders show that boys in Catholic states score almost two standard deviations lower than boys in Protestant states.  And girls in Catholic states score another two standard deviations lower than boys in Catholic states, for a total of 4 standard deviations of separation between Protestant boys and Catholic girls.  They also show that two thirds of those who score over 600 in SAT math are boys and only one third are girls. 

NAEP confirms the phenomena, plus provides the additional insight that blacks score another 5-9 standard deviations lower than Whites, and that blacks in the District of Columbia have an IQ which is 4 IQ points lover than the average for American blacks, another half of a standard deviation.  

While not every step along the way is necessarily cumulative, it's not impossible that the total number of standard deviations of separation between American black females in DC and boys in Norway is a total of 14 to 18.5, something we might be more concerened about if the quality of our students' math education was on par with Norway's.


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on December 11, 2008, 01:53:37 AM
I'll admit, I haven't read all 6 pages of the thread.  Maths terrify me.  I fell off the truck back in 5th grade.  I'm a member of the early "new" math generation, and I went to a private lower school where some teachers liked math and taught it the "old" way, some decided to teach it the "new" way, and some didn't like teaching it so it wasn't emphasised.

I did okay in algebra, as long as we were talking theory.  Calculators were banned, and to this day I still sometimes mentally count on my fingers, so arithmetically I'd sometimes fail getting an answer (which was a fail--loic didn't count for points). 

I really liked, and did well at, geometry for some reason now lost to me in the midst of time and maths fear.  While I was otherwise a good good chemestry student that loved the sciences, I lost it when I had a HS instructor that insisted on starting every class with a graded quiz of 10 questions that stretched across the full front of the room blackboard which had to be answered in 5 minutes using a slide rule.  In that entire year I think I might have managed to get one of those damned questions finished before the time was up.  Other than that my understanding of the science was sound, and I absolutely loved biology, but those damned quizzes cost me my grade--and any confidence I had.  I barely passed that class. 

I've avoided taking any maths and sciences since, although at the zoo I teach basic science, including chemestry, biology, geology, and ecology--and do it very well from what I'm told by teachers bringing in their classes, and by other volunteers that have taught the subjects, some professionally, for far longer than I.

My late husband, who was a math whiz, insisted that, based upon what he'd seen of my interests and abilities, I'd enjoy and do quite well in physics--but the entire idea scares the pants off of me.  In order to eventually graduate from any program I have to have my math requirement satisfied.  I've avoided taking it formally for 36 years (oddly, the older I get, and the more I avoid it formally, the more it makes sense to me in an informal setting).  But, I also haven't graduated in 36 years; I sure as heck have enjoyed all the other courses--mostly, from year 1, upper level-- I've taken in that time, though. 

I sometimes think I'm the personification of Zonker from Doonsbury, except for our different motivations for not graduating.  I'm a fairly strong person, but I actually panic and break down crying at the idea of having to take a math class for a grade.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 11, 2008, 02:08:31 AM
I'll admit, I haven't read all 6 pages of the thread.  Maths terrify me.  I fell off the truck back in 5th grade.  I'm a member of the early "new" math generation, and I went to a private lower school where some teachers liked math and taught it the "old" way, some decided to teach it the "new" way, and some didn't like teaching it so it wasn't emphasised.

I did okay in algebra, as long as we were talking theory.  Calculators were banned, and to this day I still sometimes mentally count on my fingers, so arithmetically I'd sometimes fail getting an answer (which was a fail--loic didn't count for points). 

I really liked, and did well at, geometry for some reason now lost to me in the midst of time and maths fear.  While I was otherwise a good good chemestry student that loved the sciences, I lost it when I had a HS instructor that insisted on starting every class with a graded quiz of 10 questions that stretched across the full front of the room blackboard which had to be answered in 5 minutes using a slide rule.  In that entire year I think I might have managed to get one of those damned questions finished before the time was up.  Other than that my understanding of the science was sound, and I absolutely loved biology, but those damned quizzes cost me my grade--and any confidence I had.  I barely passed that class. 

I've avoided taking any maths and sciences since, although at the zoo I teach basic science, including chemestry, biology, geology, and ecology--and do it very well from what I'm told by teachers bringing in their classes, and by other volunteers that have taught the subjects, some professionally, for far longer than I.

My late husband, who was a math whiz, insisted that, based upon what he'd seen of my interests and abilities, I'd enjoy and do quite well in physics--but the entire idea scares the pants off of me.  In order to eventually graduate from any program I have to have my math requirement satisfied.  I've avoided taking it formally for 36 years (oddly, the older I get, and the more I avoid it formally, the more it makes sense to me in an informal setting).  But, I also haven't graduated in 36 years; I sure as heck have enjoyed all the other courses--mostly, from year 1, upper level-- I've taken in that time, though. 

I sometimes think I'm the personification of Zonker from Doonsbury, except for our different motivations for not graduating.  I'm a fairly strong person, but I actually panic and break down crying at the idea of having to take a math class for a grade.


95% of Japanesse, Korean, and Chinese students, and 65% of German students, graduate from high school after having *passed* calculus, compared to less than 5% of ours who take (not necessarily pass) calculus or "pre-calculus".

At that rate, how long can we expect to be referred to as a "technological society"?


Title: Re: assuming too much math knowledge?
Post by: cc_alan on December 11, 2008, 02:15:42 AM
95% of Japanesse, Korean, and Chinese students, and 65% of German students, graduate from high school after having *passed* calculus, compared to less than 5% of ours who take (not necessarily pass) calculus or "pre-calculus".

At that rate, how long can we expect to be referred to as a "technological society"?

Hang on... I'm texting you my response...

Alan


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 11, 2008, 03:00:00 AM
DNFTT - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 12, 2008, 01:42:01 AM
95% of Japanese, Korean, and Chinese students, and 65% of German students, graduate from high school after having *passed* calculus, compared to less than 5% of ours who take (not necessarily pass) calculus or "pre-calculus".

At that rate, how long can we expect to be referred to as a "technological society"?

Hang on... I'm texting you my response...

Alan

This is about how I summarize our position in the world now:


TIMSS shows that 12th graders, whose scores are very different from
8th graders in both directions (up for most countries, VERY much down
for the US), Norwegian boys scored 2 standard deviations higher than
Swiss boys (589 vs. 519).  But Swiss boys scored 2 standard deviations
higher than Swiss girls (519 vs. 444).  And Swiss girls scored another
standard deviation higher than American girls (444 vs. 393), for a
total of 5 standard deviations of separation between American girls
and Norwegian boys.

SAT scores for 12th graders show that boys in Catholic states score
almost two standard deviations lower than boys in Protestant states.
And girls in Catholic states score another two standard deviations
lower than boys in Catholic states, for a total of 4 standard
deviations of separation between Protestant boys and Catholic girls.
They also show that two thirds of those who score over 600 in SAT Math
are boys and only one third girls.

Even though the GRE (Graduate Record Examination) is not a
representative cross-section of the American population, as it's taken
mostly by college graduates hoping to go to graduate school and thus
represents a small, elite crowd, it still confirms the phenomena
closely enough.  Not only does it show that the standard deviation for
males of every race in every GRE subject is higher than for females of
those respective races and topics, but it too shows that the gender
gap for Whites and Hispanics is two thirds of a standard deviation,
hardly a "statistically insignificant" difference as the news media
expounds.  Even the smaller standard deviations of .6 for "other"
races, .59 for Mexicans, .56 for Asians, .5 for Puerto Ricans, .47 for
Indians, and .4 for Blacks can hardly be characterized as
"statistically insignificant".

NAEP also confirms the phenomena, plus provides the additional insight
that Blacks score another 5-9 standard deviations lower than Whites,
and that Blacks in the District of Columbia have an IQ which is 4 IQ
points lover than the average for American Blacks, another half of a
standard deviation.

While egalitarians delight in proclaiming that the gender gap in NAEP
math decreased from 7 points to only 3 points and the White/Black race
gap decreased from 38 points to only 28 points just in the last three
decades, the most casual observation of the data will prove to you
otherwise.  Is it really possible that our education system managed to
alter God's Design by narrowing race and gender gaps which have
existed for millennia--in only a few short decades?  No.  Is it
possible that, given such huge gender and race gaps in other
standardized tests, that NAEP managed to produce a test which
illustrates no gender and lower race gaps?  No.  What did happen is
the way the standard deviation was changed in the reporting of the
data.  The most optimistic assessment of how this standard deviation
was changed shows that this supposed decrease in the race gap from 38
to 28 points was actually an increase in the standard deviation from
5.4 to 9.3.  Is that possible? Could this dumbing down of America as
reflected in the 135 SAT point decrease just in the last four decades
and our scoring dead last in 17 of 34 TIMSS subjects have resulted in
the dumbing down of Blacks even more?

That's actually not impossible, because the experts who've manipulated
this test data have managed to remove it from our public consciousness
and from all political debate.

Not every step along the way is necessarily cumulative, but it's also
not impossible that the total number of standard deviations of
separation between American black females in DC and boys in Norway is
a total of 14 to 18.5 standard deviations.


Title: Re: assuming too much math knowledge?
Post by: conjugate on December 12, 2008, 01:47:20 AM

Not every step along the way is necessarily cumulative, but it's also
not impossible that the total number of standard deviations of
separation between American black females in DC and boys in Norway is
a total of 14 to 18.5 standard deviations.

It is if we're assuming anything even remotely like a normal distribution.  Getting outside of three standard deviations is very unlikely (three-tenths of a percent); getting outside of 10 or 12 is a miracle of Biblical proportions.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 12, 2008, 03:03:15 AM

Not every step along the way is necessarily cumulative, but it's also
not impossible that the total number of standard deviations of
separation between American black females in DC and boys in Norway is
a total of 14 to 18.5 standard deviations.

It is if we're assuming anything even remotely like a normal distribution.  Getting outside of three standard deviations is very unlikely (three-tenths of a percent); getting outside of 10 or 12 is a miracle of Biblical proportions.

True, especially when comparing different types of tests with different standard deviations, and when you don't even know what the standard deviation is for some tests and have to guess.  The open nature of TIMSS is what makes it so valuable compared to, say, NAEP.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 12, 2008, 04:00:59 AM
You're not considering trends and cohorts when reading the surveys.  In 2003 Norway's 8th graders were ahead of their US counterparts, now they are behind; the US students gained 11 points in that period.  Some of this might be noise, but this most likely reflects the greatly improved K-12 mathematics standards that have recently been implemented in many states (see Fordham Foundation reports, especially on the California curriculum).  The 12 graders in 2007 were the 8th graders from 2003.  There is every reason to believe that the 2011 figures will show the US ahead of Norway (especially since the out-of-control cost-of-living in Norway is hurting their per-pupil expenditures in real Kroner).

As for performance differences by race in the US, I would guess that the average African-American at New Trier High has better math scores than the average white student at Henry Ford High in Detroit. - DvF


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on December 12, 2008, 04:44:19 AM
Is it really possible that our education system managed to
alter God's Design by narrowing race and gender gaps which have
existed for millennia--in only a few short decades?


God has an education system design and s/he has gender/race preferences?  Who knew?  Not me. 

I may be a bit math phobic, but I'm not stupid.  I understand statistics, and I understand picking and choosing numbers that fit whatever mold you'd like them to fit.  Not that I read much of your post following the sentance I quoted.  You may be free to peddle your beliefs wherever you'd like to, but, in the future, please refrain from quoting me in any way whatsoever, thank you very much. 


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 13, 2008, 01:34:07 AM
You're not considering trends and cohorts when reading the surveys.  In 2003 Norway's 8th graders were ahead of their US counterparts, now they are behind; the US students gained 11 points in that period.  Some of this might be noise, but this most likely reflects the greatly improved K-12 mathematics standards that have recently been implemented in many states (see Fordham Foundation reports, especially on the California curriculum).  The 12 graders in 2007 were the 8th graders from 2003.  There is every reason to believe that the 2011 figures will show the US ahead of Norway (especially since the out-of-control cost-of-living in Norway is hurting their per-pupil expenditures in real Kroner).

As for performance differences by race in the US, I would guess that the average African-American at New Trier High has better math scores than the average white student at Henry Ford High in Detroit. - DvF

Good points.

It's what happens to our scores between 8th and 12th grade which is the question, though.  How much will an 11 point gain at the 8th grade level (even if it's real and not noise, as you suggest) compensate for the drop in scores between 8th and 12th grade by US girls of 112 points and boys of 58 points?  Especially when at the same time, in Norway, scores for girls increased 22 points and boys 84 points?

On Dec 11, 10:06 pm, RichAsianKid <richasian...@hotmail.com> wrote:
> With bated breath, the world awaited for close to a year for the
> release of the latest benchmarkTIMSSstudy from 2007 which involved
> more than 60 participant countries and 425,000 students from round the
> globe. At that sample size,TIMSS2007 is the largest study of student
> math and science achievement in the world. And the results were
> finally just released couple days ago.
>
> You can read the details below, but as usual, average scores way way
> *underestimate* real differences between countries. So let
> RichAsianKid post just one additional bit of data here to clarify what
> he means:
>
> (1) First, math achievement
>
>      http://i36.tinypic.com/28b5uzp.jpg
>
> Wow! some Asian country countries have kids where upwards of 40% have
> reached the advanced level - while many countries only have single
> digits, sometimes 1 or 2 %, and many countries have zero percent. No
> much of a right-end of the bell curve is there? Now, what does
> advanced level mean in math (You can read it on your own and save me
> some typing....)
>
>      http://i36.tinypic.com/2up8zlj.jpg
>
> (2) Now we go to science achievement
>
>      http://i38.tinypic.com/jqhu2r.jpg
>
> Here the results are slightly closer, but still grossly
> disproportionate. And what does "advanced" mean in science?
>
>      http://i33.tinypic.com/jj1z49.jpg
>
> (3) And finally, don't forget this. The so-called g-factor, i.e.
> intelligence, correlates at over 0.90 level with the previousTIMSS
> results (1995, 1999, 2003) at the national level, as shown.
>
>      http://i26.tinypic.com/znanh1.jpg
>
> Yup.
>
> Yet the latest proof that human groups do not achieve equally.
>
> * * * Featured Article * * *
>
> http://www.sciencedaily.com/releases/2008/12/081210171906.htm
>
> Asian Students Top Latest Global Math, Science Study
>
> ScienceDaily (Dec. 11, 2008) — Students from Asian countries were top
> performers in math and science at both the fourth and eighth grade
> levels, according to the most recent reports of the Trends in
> International Mathematics and Science Study (TIMSS), released by the
> study's directors Michael O. Martin and Ina V.S. Mullis of Boston
> College.
>
> In mathematics, at the fourth grade level, Hong Kong SAR and Singapore
> were the top performing countries, followed by Chinese Taipei and
> Japan. Kazakhstan, the Russian Federation, England, Latvia, and the
> Netherlands also performed very well. In mathematics achievement at
> the eighth grade, Chinese Taipei, Korea, and Singapore were followed
> by Hong Kong SAR and Japan. There was a substantial gap in average
> mathematics achievement between the five Asian countries and the next
> group of four similarly performing countries, including Hungary,
> England, the Russian Federation, and the United States.
>
> In science, students from Singapore and Chinese Taipei were top
> performers at both grade levels. In science achievement at the fourth
> grade, Singapore was the top performing country, followed by Chinese
> Taipei and Hong Kong SAR. Japan, the Russian Federation, Latvia,
> England, the United States, Hungary, Italy, and Kazakhstan also
> performed very well. At the eighth grade in science, Singapore and
> Chinese Taipei again had the highest average achievement, followed by
> Japan and Korea. England, Hungary, the Czech Republic, Slovenia, Hong
> Kong SAR, and the Russian Federation also performed well. Countries
> and scores are listed below.
>
> TIMSSis one of the world's most influential global assessments of
> student achievement in math and science. With more than 60
> participants and 425,000 students assessed,TIMSS2007 also is the
> largest study of student math and science achievement in the world.
> Each country sampled approximately 4,000 students in 150 schools.
>
> TheTIMSS2007 report also provides data at the fourth and eighth
> grades for those countries that also participated inTIMSS1995, 1999
> and 2003.
>
> "One of the great strengths ofTIMSSis the ability to monitor
> progress in educational improvement over time," saidTIMSSDirectors
> Michael O. Martin and Ina V.S. Mullis of Boston College. "Such trend
> information is crucial in helping policy makers understand the impact
> of decisions about investment in education, curricular reform, and
> initiatives to improve instruction."
>
> As with previousTIMSSreports,TIMSS2007 data provide invaluable
> international benchmarks that can be used to help define world-class
> performance in mathematics and science at the middle or lower-
> secondary school level. Beyond comparisons in mathematics and science
> test scores, they said, the reports provide a wealth of information on
> educational policies and practices around the world, as well as on
> gender performance, home environment, curriculum and instructional
> approaches and teacher preparation in math and science.
>
> AboutTIMSS
>
> TIMSS, the Trends in International Mathematics and Science Study, is
> the largest assessment of international student achievement in the
> world and was the first to provide data about trends in math and
> science achievement over time.
>
> TIMSSis a project of the International Association for the Evaluation
> of Educational Achievement (IEA) headquartered in Amsterdam, and is
> directed by theTIMSS& PIRLS International Study Center at Boston
> College in collaboration with a worldwide network of organizations and
> representatives from the participating countries.
>
> TIMSS2007 is the fourth in a continuing cycle of international
> mathematics and science assessments conducted every four years.TIMSS
> assesses achievement in countries around the world and collects a rich
> array of information about the educational contexts for learning
> mathematics and science.
>
> TheTIMSS2007 report involved more than 60 participants: it contains
> science results for 37 countries and 7 benchmarking participants at
> the fourth grade and for 50 countries and 7 benchmarking participants
> at the eighth grade. Each country sampled approximately 4,000 students
> in 150 schools. Trend data are provided at the fourth and eighth
> grades for those countries that also participated in 1995, 1999, and
> 2003.
>
> To inform educational policy in the participating countries,TIMSS
> also routinely collects extensive background information that
> addresses concerns about the quantity, quality and content of
> instruction.TIMSS2007 offers detailed information about mathematics
> and science curriculum coverage and implementation, as well as teacher
> preparation, resource availability and the use of technology.
>
> TIMSS2007 Participants
>
> Participating countries: Algeria, Armenia, Australia, Austria,
> Bahrain, Bosnia and Herzegovina, Botswana, Bulgaria, Chinese Taipei,
> Colombia, Cyprus, Czech Republic, Denmark, Egypt, El Salvador,
> England, Georgia, Germany, Ghana, Hong Kong, Hungary, Indonesia, Iran,
> Israel, Italy, Japan, Jordan, Kazakhstan, Korea, Republic of Kuwait,
> Latvia, Lebanon, Lithuania, Malaysia, Malta, Mongolia, Morocco,
> Netherlands, New Zealand, Norway, Oman, Palestinian National
> Authority, Qatar, Romania, Russian Federation, Saudi Arabia, Scotland,
> Serbia, Singapore, Slovak Republic, Slovenia, Sweden, Syrian Arab
> Republic, Thailand, Tunisia, Turkey, Ukraine, United States, Yemen.
> Benchmarking entities include the provinces of Alberta, British
> Columbia, Ontario and Quebec in Canada; Dubai (United Arab Emirates);
> Basque Country in Spain, and Massachusetts and Minnesota in the United
> States.
>
> The fullTIMSS2007 reports are available on-line attimss.bc.eduTIMSS2007 Data Exhibits Summarizing Principal Achievement Results
> (Trends in International Mathematics and Science Study)
>
> Mathematics Achievement at the 4th Grade
>
> Country Average Scale Score (TIMSSScale Average 500)
>
>    1. Hong Kong SAR 607
>    2. Singapore 599
>    3. Chinese Taipei 576
>    4. Japan 568
>    5. Kazakhstan 549
>    6. Russian Federation 544
>    7. England 541
>    8. Latvia 537
>    9. Netherlands 535
>   10. Lithuania 530
>   11. United States 529
>   12. Germany 525
>   13. Denmark 523
>   14. Australia 516
>   15. Hungary 510
>   16. Italy 507
>   17. Austria 505
>   18. Sweden 503
>   19. Slovenia 502
>   20. Armenia 500
>   21. Slovak Republic 496
>   22. Scotland 494
>   23. New Zealand 492
>   24. Czech Republic 486
>   25. Norway 473
>   26. Ukraine 469
>   27. Georgia 438
>   28. Iran, Islamic Rep. of 402
>   29. Algeria 378
>   30. Colombia 355
>   31. Morocco 341
>   32. El Salvador 330
>   33. Tunisia 327
>   34. Kuwait 316
>   35. Qatar 296
>   36. Yemen 224
>   37. Benchmarking Participants
>   38. Massachusetts, US 572
>   39. Minnesota, US 554
>   40. Quebec, Canada 519
>   41. Ontario, Canada 512
>   42. Alberta, Canada 505
>   43. British Columbia, Canada 505
>   44. Dubai, UAE 444
>
> Science Achievement at the 4th Grade
>
> Country Average Scale Score (TIMSSScale Average 500)
>
>    1. Singapore 587
>    2. Chinese Taipei 557
>    3. Hong Kong SAR 554
>    4. Japan 548
>    5. Russian Federation 546
>    6. Latvia 542
>    7. England 542
>    8. United States 539
>    9. Hungary 536
>   10. Italy 535
>   11. Kazakhstan 533
>   12. Germany 528
>   13. Australia 527
>   14. Slovak Republic 526
>   15. Austria 526
>   16. Sweden 525
>   17. Netherlands 523
>   18. Slovenia 518
>   19. Denmark 517
>   20. Czech Republic 515
>   21. Lithuania 514
>   22. New Zealand 504
>   23. Scotland 500
>   24. Armenia 484
>   25. Norway 477
>   26. Ukraine 474
>   27. Iran, Islamic Rep. of 436
>   28. Georgia 418
>   29. Colombia 400
>   30. El Salvador 390
>   31. Algeria 354
>   32. Kuwait 348
>   33. Tunisia 318
>   34. Morocco 297
>   35. Qatar 294
>   36. Yemen 197
>
> Benchmarking Participants
>
>    1. Massachusetts, US 571
>    2. Minnesota, US 551
>    3. Alberta, Canada 543
>    4. British Columbia, Canada 537
>    5. Ontario, Canada 536
>    6. Quebec, Canada 517
>    7. Dubai, UAE 460
>
> Mathematics Achievement at the 8th Grade
>
> Country Average Scale Score (TIMSSScale Average 500)
>
>    1. Chinese Taipei 598
>    2. Korea, Rep. of 597
>    3. Singapore 593
>    4. Hong Kong SAR 572
>    5. Japan 570
>    6. Hungary 517
>    7. England 513
>    8. Russian Federation 512
>    9. United States 508
>   10. Lithuania 506
>   11. Czech Republic 504
>   12. Slovenia 501
>   13. Armenia 499
>   14. Australia 496
>   15. Sweden 491
>   16. Malta 488
>   17. Scotland 487
>   18. Serbia 486
>   19. Italy 480
>   20. Malaysia 474
>   21. Norway 469
>   22. Cyprus 465
>   23. Bulgaria 464
>   24. Israel 463
>   25. Ukraine 462
>   26. Romania 461
>   27. Bosnia and Herzegovina 456
>   28. Lebanon 449
>   29. Thailand 441
>   30. Turkey 432
>   31. Jordan 427
>   32. Tunisia 420
>   33. Georgia 410
>   34. Iran, Islamic Rep. of 403
>   35. Bahrain 398
>   36. Indonesia 397
>   37. Syrian Arab Republic 395
>   38. Egypt 391
>   39. Algeria 387
>   40. Colombia 380
>   41. Oman 372
>   42. Palestinian Nat'l Auth. 367
>   43. Botswana 364
>   44. Kuwait 354
>   45. El Salvador 340
>   46. Saudi Arabia 329
>   47. Ghana 309
>   48. Qatar 307
>   49. Morocco 381
>
> Benchmarking Participants
>
>    1. Massachusetts, US 547
>    2. Minnesota, US 532
>    3. Quebec, Canada 528
>    4. Ontario, Canada 517
>    5. British Columbia, Canada 509
>    6. Basque Country, Spain 499
>    7. Dubai, UAE 461
>
> Science Achievement at the 8th Grade
>
> Country Average Scale Score (TIMSSScale Average 500)
>
>    1. Singapore 567
>    2. Chinese Taipei 561
>    3. Japan 554
>    4. Korea, Rep. of 553
>    5. England 542
>    6. Hungary 539
>    7. Czech Republic 539
>    8. Slovenia 538
>    9. Hong Kong SAR 530
>   10. Russian Federation 530
>   11. United States 520
>   12. Lithuania 519
>   13. Australia 515
>   14. Sweden 511
>   15. Scotland 496
>   16. Italy 495
>   17. Armenia 488
>   18. Norway 487
>   19. Ukraine 485
>   20. Jordan 482
>   21. Malaysia 471
>   22. Thailand 471
>   23. Serbia 470
>   24. Bulgaria 470
>   25. Israel 468
>   26. Bahrain 467
>   27. Bosnia and Herzegovina 466
>   28. Romania 462
>   29. Iran, Islamic Rep. of 459
>   30. Malta 457
>   31. Turkey 454
>   32. Syrian Arab Republic 452
>   33. Cyprus 452
>   34. Tunisia 445
>   35. Indonesia 427
>   36. Oman 423
>   37. Georgia 421
>   38. Kuwait 418
>   39. Colombia 417
>   40. Lebanon 414
>   41. Egypt 408
>   42. Algeria 408
>   43. Palestinian Nat'l Auth. 404
>   44. Saudi Arabia 403
>   45. El Salvador 387
>   46. Botswana 355
>   47. Qatar 319
>   48. Ghana 303
>   49. Morocco 402
>
> Benchmarking Participants
>
>    1. Massachusetts, US 556
>    2. Minnesota, US 539
>    3. Ontario, Canada 526
>    4. British Columbia, Canada 526
>    5. Quebec, Canada 507
>    6. Basque Country, Spain 498
>    7. Dubai, UAE 489
 


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 13, 2008, 03:41:30 AM
You still don't get it.  There was no drop in US scores between 8th and 12th grade; there was a difference in cohort.

I find this kind of hysterical metrology uninteresting and counterproductive.  It leads some people to imagine there's a significant racial or sexual component to mathematical ability when that's not what the data really shows, and merely serves to fuel baser worldviews. More importantly, it doesn't suggest any constructive policy other than institutional hand-wringing. It makes sense to ask if (for example) increasing the dollars spent per student increases mathematics achievement, since a positive answer would support a policy of increased STEM funding in schools; it makes no sense to ask if increasing the Norwegian fraction of a student's DNA increases their achievement, as there is nothing we can do if the answer is "yes". - DvF


Title: Re: assuming too much math knowledge?
Post by: kiana on December 13, 2008, 11:15:36 AM
We could all run out and make babies with Norwegians to improve the % Norwegian in the general population!

(:


Title: Re: assuming too much math knowledge?
Post by: christianp on December 16, 2008, 03:17:20 PM
As for performance differences by race in the US, I would guess that the average African-American at New Trier High has better math scores than the average white student at Henry Ford High in Detroit. - DvF

Why would you believe that?

Do you have some kind of evidence to support that belief?


Title: Re: assuming too much math knowledge?
Post by: christianp on December 16, 2008, 03:20:51 PM
You still don't get it.  There was no drop in US scores between 8th and 12th grade; there was a difference in cohort.

I find this kind of hysterical metrology uninteresting and counterproductive.  It leads some people to imagine there's a significant racial or sexual component to mathematical ability when that's not what the data really shows, and merely serves to fuel baser worldviews. More importantly, it doesn't suggest any constructive policy other than institutional hand-wringing. It makes sense to ask if (for example) increasing the dollars spent per student increases mathematics achievement, since a positive answer would support a policy of increased STEM funding in schools; it makes no sense to ask if increasing the Norwegian fraction of a student's DNA increases their achievement, as there is nothing we can do if the answer is "yes". - DvF

Could you explain what you mean by that?


Title: Re: assuming too much math knowledge?
Post by: concerned_parent on December 16, 2008, 03:27:37 PM
 

I am assuming your college does not have basic skills testing for incoming students and if so, you will continue to have this problem. The basic skills testing is used for math and English placement, and includes proficiency in Algebra.
It is disheartening but a reality that students have to learn Algebra in college.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 16, 2008, 04:07:15 PM
As for performance differences by race in the US, I would guess that the average African-American at New Trier High has better math scores than the average white student at Henry Ford High in Detroit. - DvF

Why would you believe that?

Because I've taught mathematics to minority students from good high schools, and to white kids from bad ones, and the former perform better than the latter in my experience.

Quote
Could you explain what you mean by that?

I think it is pretty self-explanatory.

Am I right in assuming you are jacobisrael under a new login name? - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 16, 2008, 04:10:44 PM
You still don't get it.  There was no drop in US scores between 8th and 12th grade; there was a difference in cohort.

I find this kind of hysterical metrology uninteresting and counterproductive.  It leads some people to imagine there's a significant racial or sexual component to mathematical ability when that's not what the data really shows, and merely serves to fuel baser worldviews. More importantly, it doesn't suggest any constructive policy other than institutional hand-wringing. It makes sense to ask if (for example) increasing the dollars spent per student increases mathematics achievement, since a positive answer would support a policy of increased STEM funding in schools; it makes no sense to ask if increasing the Norwegian fraction of a student's DNA increases their achievement, as there is nothing we can do if the answer is "yes". - DvF

Are you sure that you've read that TIMSS study about our 12th grade scores?  The methodology for picking the cohorts was the same in both the 8th and 12th grade and many of the same countries took both tests so that such comparisons can be made.  If by "racial component" you refer to the literal standard deviation gaps between countries, then TIMSS is clear evidence that there IS a "racial component" and in particular a "sexual component", to math scores--as well as all the other subjects tested in TIMSS.

This might not be what we teach in our schools, but when 12th grade boys in the US scored a standard deviation lower than 8th grade US boys, whereas 12th grade boys in Cyprus, Norway, and Sweden scored a standard deviation higher than their 8th grade boys, it SHOULD be well known throughout the universe. 

Why should we ignore that 12th grade girls in the US scored TWO standard deviations lower than 8th grade US girls, whereas 12th grade girls in Cyprus, Greece, and Norway scored higher than their 8th grade girls.





Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 16, 2008, 04:18:36 PM
Are you sure that you've read that TIMSS study about our 12th grade scores?  The methodology for picking the cohorts was the same in both the 8th and 12th grade

They nevertheless are not the same cohort.  The reason is that the 8th graders were in 8th grade that year, and the 12th graders were in 12th grade that year.  In many cases, when the 12th graders were in middle school they had different curricula than the 8th graders did when they were in middle school.

This is not complicated stuff.  Really. - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 16, 2008, 04:31:35 PM
As for performance differences by race in the US, I would guess that the average African-American at New Trier High has better math scores than the average white student at Henry Ford High in Detroit. - DvF

Why would you believe that?

Because I've taught mathematics to minority students from good high schools, and to white kids from bad ones, and the former perform better than the latter in my experience.

Quote
Could you explain what you mean by that?

I think it is pretty self-explanatory.

Am I right in assuming you are jacobisrael under a new login name? - DvF

Correct.  It turns out the problem was an update from IE7 to IE8, since a different system that hadn't been updated didn't have that problem.

Even the folks at NAEP believe their recent monumental attempts at education in DC (per student expenditures 6 times greater than some other states) has been a success.  But their own 8th grade math scores still show that blacks in DC score the equivalent of 4 IQ points lower than the national average for blacks.  Clearly something didn't work the way they thought it would.  Even though NAEP doesn't have math scores at the 12th grade level by state and DC, TIMSS 12th grade shows that the situation deteriorates significantly between 8th and 12th grade.  Your anecdote might be honest and accurate, but that and $3 won't buy you a cup of coffee, much less raise test scores in DC.

Since you raise the subject, how many American students do you believe score in the same range as Norway? Do you believe American students of purely Norwegian ancestry score that high?  Or do you think they score lower because of the way they're educated here?  The reason I ask is that I was educated in the US, Norway, and Germany and might be able to help fill in some of the missing gaps in the stats.

That wasn't a rhetorical question about sample sizes, subsets, and cohorts.  Having discussed this with the director of NAEP illustrated that his definition is completely different from other sources.  So it would be greatly appreciated if you would provide your definition so your point can be better understood.



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 16, 2008, 04:37:21 PM
You are reading my answer above as saying that the solution is throwing money at the problem.  I never said that at all.

I do not know what your point is.  Let us suppose for the sake of argument that you are right and American students of color are structurally inferior in mathematical ability to Northern European students of pallidness.  Now what? - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 16, 2008, 05:08:47 PM
Are you sure that you've read that TIMSS study about our 12th grade scores?  The methodology for picking the cohorts was the same in both the 8th and 12th grade

They nevertheless are not the same cohort.  The reason is that the 8th graders were in 8th grade that year, and the 12th graders were in 12th grade that year.  In many cases, when the 12th graders were in middle school they had different curricula than the 8th graders did when they were in middle school.

This is not complicated stuff.  Really. - DvF

Now I understand your point.  Thank you very much for clarifying it.

Please point me to the evidence that there was a national, across the board, change in the curricula between 1991 and 1995 if you believe this to be a possible explanation.  Can the same be said for all of the other countries which took TIMSS?

If anything DID change (and this is not to even hint that anything changed) then would you not agree that our change was clearly for the worse and theirs was for the better?

Austria's scores were an exception in Europe, as they followed a similar pattern to the US, only more extreme.  While our boys' scores decreased 56 points, theirs decreased 85 points.  And while our girls' scores decreased 104 points, their decreased 137 points.  So while just the increase in the gender gap was 48 points in the US, it was 52 points in Austria.  This is not an insignificant decrease, since the standard deviation for US girls was 53, making this 0.91 S.D.  Since the standard deviation for Austrian girls was larger, at 71, the increase in their gender gap was smaller, at 0.73 S.D.

But there was already an 8 point gender gap in Austrian 8th graders, making their total gender gap by 12th grade 0.85 S.D.

I'm not clear on how changes in the curricula could have affected any of this.  I don't even know what can be changed to cause such huge race and sex gaps, or to make them bigger or smaller.  So it would be greatly appreciated if you'd provide an example.

Actually, I can think of one small example.  Not too long ago, Chinese educators were invited to visit the US to study our education system.  They asked many great questions, and my input was they should implement calculus in high school as Japan had.  They did that, and now 95% of Chinese students complete calculus before they graduate from high school.

Pretty smart, eh?  What have our educators done lately to top that?



Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 16, 2008, 05:34:22 PM
You are reading my answer above as saying that the solution is throwing money at the problem.  I never said that at all.

I do not know what your point is.  Let us suppose for the sake of argument that you are right and American students of color are structurally inferior in mathematical ability to Northern European students of pallidness.  Now what? - DvF

Well, please permit me first to answer my own question about American boys of Norwegian ancestry, versus boys in Norway.

My anecdotal evidence is that they're equal.  I've met both and personally think that those in the US have a slightly better opportunity for education than those in Norway. But like yours, this is simply an anecdote.

What do the statistics say?  We don't have TIMSS scores broken down by race or state, but SAT math shows that Whites in states like North Dakota score 154 points higher than "Whites" in states like New York and New Jersey, and these two different tests correlate very well.  Clearly there's a race gap within Whites in the US.  But not even this completely explains how Norwegian boys managed to score 155 points or 2.5 S.D. higher than American boys.  As none of the 85 African nations were represented in this part of TIMSS, we really have no idea what their scores are.

Maybe a reliable estimate can be achieved by breaking down our TIMSS score into race and sex categories to assess the validity of your anecdote?

This hasn't been done yet, so perhaps now is the time to do so?



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 16, 2008, 09:13:49 PM
Please point me to the evidence that there was a national, across the board, change in the curricula between 1991 and 1995 if you believe this to be a possible explanation. 

I don't know why you are bringing up 1991-5; I am talking about much more recent changes in curricula, tied to changes in state standards.  I already gave you a reference above. 

Quote
I'm not clear on how changes in the curricula could have affected any of this.  I don't even know what can be changed to cause such huge race and sex gaps, or to make them bigger or smaller. 

It is increasingly clear that your (mis)understanding of all the arguments above are brightly colored by your deeply-held belief that these structural differences exist.  We have these these "discussions" on this forum with tedious regularity, and I do not care to participate any longer.  If you want to believe that you have, by virtue of your sex or ethnicity, greater potential to do good math and science, then by all means go for it.  However, if you are of student age, please don't become a TA for me.  The last time I had a TA who believed that he was smarter than his students by virtue of his ethnicity and superior national training, he was a disaster. - DvF


Title: Re: assuming too much math knowledge?
Post by: history_grrrl on December 16, 2008, 09:19:07 PM
Wow, Charles Murray reads the Chronicle fora. Who knew?


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 17, 2008, 12:41:28 PM
Are you sure that you've read that TIMSS study about our 12th grade scores?  The methodology for picking the cohorts was the same in both the 8th and 12th grade

They nevertheless are not the same cohort.  The reason is that the 8th graders were in 8th grade that year, and the 12th graders were in 12th grade that year.  In many cases, when the 12th graders were in middle school they had different curricula than the 8th graders did when they were in middle school.

This is not complicated stuff.  Really. - DvF

Now I understand your point.  Thank you very much for clarifying it.

Please point me to the evidence that there was a national, across the board, change in the curricula between 1991 and 1995 if you believe this to be a possible explanation.  Can the same be said for all of the other countries which took TIMSS?

If anything DID change (and this is not to even hint that anything changed) then would you not agree that our change was clearly for the worse and theirs was for the better?

Austria's scores were an exception in Europe, as they followed a similar pattern to the US, only more extreme.  While our boys' scores decreased 56 points, theirs decreased 85 points.  And while our girls' scores decreased 104 points, their decreased 137 points.  So while just the increase in the gender gap was 48 points in the US, it was 52 points in Austria.  This is not an insignificant decrease, since the standard deviation for US girls was 53, making this 0.91 S.D.  Since the standard deviation for Austrian girls was larger, at 71, the increase in their gender gap was smaller, at 0.73 S.D.

But there was already an 8 point gender gap in Austrian 8th graders, making their total gender gap by 12th grade 0.85 S.D.

I'm not clear on how changes in the curricula could have affected any of this.  I don't even know what can be changed to cause such huge race and sex gaps, or to make them bigger or smaller.  So it would be greatly appreciated if you'd provide an example.

Actually, I can think of one small example.  Not too long ago, Chinese educators were invited to visit the US to study our education system.  They asked many great questions, and my input was they should implement calculus in high school as Japan had.  They did that, and now 95% of Chinese students complete calculus before they graduate from high school.

Pretty smart, eh?  What have our educators done lately to top that?



I've tried to stay out of this one as DvF has done an admirable job of presenting the points I wanted to make. However, please allow me to add my two cents' worth. First, you are comparing different systems that do different things. You are comparisons are being made between countries where there are NATIONAL curricula, those where there are STATE curricula, and at least one where it is a hodgepodge of STATE and LOCAL curricula. So, we are comparing apples to oranges to pears

Also, we need to address the differences in systemic student handling. In the US, we send the vast majority of our students to high school; other countries reverse this entirely. Thus, the 12th-grade cohorts aren't even comparable between countries, even though they are presented as such by the media (among many others). While the 4th-grade cohorts may be similar, there is even some question about the comparing 8th-grade cohorts by some. For the two reasons above, I don't believe TIMSS is as valid an indicator of differences between national systems as its exhorters proclaim.

Finally, a word about why DvF keeps trying to get you to understand why comparing cohorts is important. Many states have been adjusting/rewriting their regulations (Pennsylvania), their state-mandated tests (Ohio), and their state-mandated curricula (Georgia) for the past decade or more. In mathematics, the National Council of Teachers of Mathematics (NCTM) issued its first set of standards on K-12 mathematics in 1989. This was the first step in the reform process, and several states began the process of reforming state curricula in the early 1990s. Others waited longer. However, the process is not an instantaneous one. As an example, Georgia instituted the Georgia Performance Standards (GPS) in 2003 or 2004. The standards still aren't fully implemented throughout the schools yet, and they won't be for two more years. So, yes, cohort matters, and we need to deal with the data that way. The only fair comparisons about gains and losses in the report's 12th-grade cohort would be to take the 2007 report's 12th-graders and compare that gap (assuming all the other confounding variables didn't exist) to the gap found in the 2003 report's 8th-graders and to the gap found in 1999 report's 4th-graders. This assumes that the tests across that EIGHT-YEAR SPREAD are equivalent.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 18, 2008, 04:49:12 PM
Are you sure that you've read that TIMSS study about our 12th grade scores?  The methodology for picking the cohorts was the same in both the 8th and 12th grade

They nevertheless are not the same cohort.  The reason is that the 8th graders were in 8th grade that year, and the 12th graders were in 12th grade that year.  In many cases, when the 12th graders were in middle school they had different curricula than the 8th graders did when they were in middle school.

This is not complicated stuff.  Really. - DvF

Now I understand your point.  Thank you very much for clarifying it.

Please point me to the evidence that there was a national, across the board, change in the curricula between 1991 and 1995 if you believe this to be a possible explanation.  Can the same be said for all of the other countries which took TIMSS?

If anything DID change (and this is not to even hint that anything changed) then would you not agree that our change was clearly for the worse and theirs was for the better?

Austria's scores were an exception in Europe, as they followed a similar pattern to the US, only more extreme.  While our boys' scores decreased 56 points, theirs decreased 85 points.  And while our girls' scores decreased 104 points, their decreased 137 points.  So while just the increase in the gender gap was 48 points in the US, it was 52 points in Austria.  This is not an insignificant decrease, since the standard deviation for US girls was 53, making this 0.91 S.D.  Since the standard deviation for Austrian girls was larger, at 71, the increase in their gender gap was smaller, at 0.73 S.D.

But there was already an 8 point gender gap in Austrian 8th graders, making their total gender gap by 12th grade 0.85 S.D.

I'm not clear on how changes in the curricula could have affected any of this.  I don't even know what can be changed to cause such huge race and sex gaps, or to make them bigger or smaller.  So it would be greatly appreciated if you'd provide an example.

Actually, I can think of one small example.  Not too long ago, Chinese educators were invited to visit the US to study our education system.  They asked many great questions, and my input was they should implement calculus in high school as Japan had.  They did that, and now 95% of Chinese students complete calculus before they graduate from high school.

Pretty smart, eh?  What have our educators done lately to top that?



I've tried to stay out of this one as DvF has done an admirable job of presenting the points I wanted to make. However, please allow me to add my two cents' worth. First, you are comparing different systems that do different things. You are comparisons are being made between countries where there are NATIONAL curricula, those where there are STATE curricula, and at least one where it is a hodgepodge of STATE and LOCAL curricula. So, we are comparing apples to oranges to pears

Also, we need to address the differences in systemic student handling. In the US, we send the vast majority of our students to high school; other countries reverse this entirely. Thus, the 12th-grade cohorts aren't even comparable between countries, even though they are presented as such by the media (among many others). While the 4th-grade cohorts may be similar, there is even some question about the comparing 8th-grade cohorts by some. For the two reasons above, I don't believe TIMSS is as valid an indicator of differences between national systems as its exhorters proclaim.

Finally, a word about why DvF keeps trying to get you to understand why comparing cohorts is important. Many states have been adjusting/rewriting their regulations (Pennsylvania), their state-mandated tests (Ohio), and their state-mandated curricula (Georgia) for the past decade or more. In mathematics, the National Council of Teachers of Mathematics (NCTM) issued its first set of standards on K-12 mathematics in 1989. This was the first step in the reform process, and several states began the process of reforming state curricula in the early 1990s. Others waited longer. However, the process is not an instantaneous one. As an example, Georgia instituted the Georgia Performance Standards (GPS) in 2003 or 2004. The standards still aren't fully implemented throughout the schools yet, and they won't be for two more years. So, yes, cohort matters, and we need to deal with the data that way. The only fair comparisons about gains and losses in the report's 12th-grade cohort would be to take the 2007 report's 12th-graders and compare that gap (assuming all the other confounding variables didn't exist) to the gap found in the 2003 report's 8th-graders and to the gap found in 1999 report's 4th-graders. This assumes that the tests across that EIGHT-YEAR SPREAD are equivalent.


The reason for comparing different state, national, and local curricula in an international study is that this is the reason for an international study.  When we simply make year to year or state to state or government education to private education comparisons, we have no guide post about our progress.  We can't just throw out international comparisons if we simply don't like the questions they ask, can we?

Also, TIMSS shows almost exactly the same rankings by country as PISA and IAEP, and all three of them put US education DEAD LAST on the list in quality and DEAD FIRST in cost.

There are opinions and there are facts.  If you dispute what TIMSS discovered about our low rate of 18 year olds graduating from high school compared to the very high rate of every single other TIMSS country, then you ought to provide the source which caused you to arrive at that opinion which disputes TIMSS, and which you can prove to be more credible than TIMSS.  I'm fairly certain you won't find it, because my research shows that TIMSS was actually pretty conservative in the way they arrived at these figures.  The fair way to do it is compare the total population of 18 year olds to the total number of high school graduates, which produces even lower figures than NCES's already low figures.

It's also a fact and not merely an opinion that every single standardized test available from the NCES and on the internet (including GRE, SAT, ACT, NAEP, IAEP, and of course TIMSS and PISA) shows statistically significant differences between races and sexes in every subject.  To ignore that is futile.  You cannot reject the facts and base your opinion on a narrow anecdote and expect to get much out of a discussion about US education.

The most interesting observation we might make about US education is one which NAEP can't make because they've used every excuse under the sun to not release state by state scores for 12th graders.  But SAT does, and it found that almost without exception the worst performing states are the states who spend as much as five times per student as the highest scoring states.  The differences in education quality is not insignificant--it's more than a standard deviation, or 170 SAT points.

How can you compare our success and failures in education to attempt to duplicate the successes in the failed states if you don't even have the data, or reject the data based on narrow anecdotes, or pretend there are no differences?


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 18, 2008, 08:38:07 PM
The reason for comparing different state, national, and local curricula in an international study is that this is the reason for an international study.  When we simply make year to year or state to state or government education to private education comparisons, we have no guide post about our progress.  We can't just throw out international comparisons if we simply don't like the questions they ask, can we?

Also, TIMSS shows almost exactly the same rankings by country as PISA and IAEP, and all three of them put US education DEAD LAST on the list in quality and DEAD FIRST in cost.

I'm not saying that I don't like the questions. The main problem with using TIMSS for international comparisons is one of STRUCTURE. MANY countries use very different structures than the US for educating their populations. The US sends a vast majority of its students to high schools while sending a very small number to technical/vocational schools; this is NOT the rule in MOST other countries. Some siphon off the "non-academic" students after 10th grade, some after 8th, and some earlier. Thus, comparing 12th-grade cohorts is worthless, and there has been some questions in educationist circles about comparing 8th-graders. Remember, the educationists are the ones who use TIMSS to ask for more money to fix perceived problems in education. If we want to fix perceived TIMSS problems, the first thing to do is refuse to allow the students who have very little academic potential to matriculate into high school. (NO, I DON'T BELIEVE WE SHOULD THIS.)

The other possibility for using TIMSS for international comparisons is to adjust the data based on the matriculation rate into high school for each country. However, TIMSS does not do this. Guess this won't work, after all.

There are opinions and there are facts.  If you dispute what TIMSS discovered about our low rate of 18 year olds graduating from high school compared to the very high rate of every single other TIMSS country, then you ought to provide the source which caused you to arrive at that opinion which disputes TIMSS, and which you can prove to be more credible than TIMSS.  I'm fairly certain you won't find it, because my research shows that TIMSS was actually pretty conservative in the way they arrived at these figures.  The fair way to do it is compare the total population of 18 year olds to the total number of high school graduates, which produces even lower figures than NCES's already low figures.

But this is not how TIMSS does it. Have you ever studied TIMSS' methodology? I have. They don't take total 18-year-old population as the baseline; they use students matriculating INTO secondary schools, which include high schools and vo-tech schools. I've long held that our dropout rate would be lower if we eliminated the idea that everyone needed to be prepared for COLLEGE and instead adopted a system closer to what the rest of the world used. However, this brings back the memories of "tracking", which is a very dirty word in education. Notice, however, that we are still discussing STRUCTURE.

It's also a fact and not merely an opinion that every single standardized test available from the NCES and on the internet (including GRE, SAT, ACT, NAEP, IAEP, and of course TIMSS and PISA) shows statistically significant differences between races and sexes in every subject.  To ignore that is futile.  You cannot reject the facts and base your opinion on a narrow anecdote and expect to get much out of a discussion about US education.

Almost everyone in education, even the most conservative ones among us, will tell you that standardized tests are a very poor way to measure anything. In fact, if you control first for QUALITY OF THE STUDENT'S SCHOOL (not necessarily measured in dollars), you find much lower differences between groups. Using standardized tests (written by the majority population) to draw conclusions about different groups is a very poor methodology. The problems arise from those confounding variables again.

The most interesting observation we might make about US education is one which NAEP can't make because they've used every excuse under the sun to not release state by state scores for 12th graders.  But SAT does, and it found that almost without exception the worst performing states are the states who spend as much as five times per student as the highest scoring states.  The differences in education quality is not insignificant--it's more than a standard deviation, or 170 SAT points.

Actually, it usually takes two SDs to be significant (p<0.05 for a two-tailed test). IIRC, I don't believe that 170 points makes that cut.

How can you compare our success and failures in education to attempt to duplicate the successes in the failed states if you don't even have the data, or reject the data based on narrow anecdotes, or pretend there are no differences?


I don't pretend there are no differences. I believe that we don't really know what the differences are due to CONFOUNDING VARIABLES for which there is no account in the vast majority of international studies, such as TIMSS. Until the methodology or analysis is changed to account for these confounding variables, we just don't know.

I'm not rejecting data based on narrow anecdotes; I'm rejecting it based on methodology. If I tested only the students in the top 5 high schools in my state and then tested students across the spectrum of high schools in your state, you would scream "UNFAIR!" at the top of your lungs, especially if it impacted the allocation of federal dollars in my state's favor. That is what we are talking about here. For a non-educational example of how confounding variables work, study the Truman-Dewey election of 1948.

We do have data, and it's not even international. NAEP, when taken in a gross way instead of a minute one, can point us toward the "better" states, and it has been used that way in states attempting educational reform. These are much better guides because they compare similarly structured systems. We have also used (see Georgia's GPS for an example)the curricula of countries that perform well on TIMSS for a guide on how we should be trying to restructure our own curricula. However, using the data for anything more (especially as it relates to drawing conclusions between groups) is dangerous at best.


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on December 18, 2008, 10:11:47 PM
How sad--or how wonderful--is it that I, a math phobic (in spite of doing well using statistical process control in a manufacturing environment) , have been following this discussion and even I understand DvF and cgfunmathguy's logic regarding methods, and understand it as valid?

For someone that likes to spout statistics, you (jacobisrael) would seem to be either being purposefully obtuse at understanding the importance of underlying methodology, or you would seem to have some different agenda that I would prefer not to explore.

*Thanks DvF and cgfunmathguy for providing clarity amidst the static*

*Disappears, with a better understanding of International educational comparison statistical studies than I had before I read*

(In fairness, some thanks to jacobisrael for providing the counterpoint that allowed the clarity to shine through, although it really didn't take me this far into the thread to see it.)

One cannot see light, unless there is darkness to provide a contrast.  (paraphrase, Bob Ross)

*poof*


Title: Re: assuming too much math knowledge?
Post by: circularity on December 18, 2008, 10:58:47 PM
The most interesting observation we might make about US education is one which NAEP can't make because they've used every excuse under the sun to not release state by state scores for 12th graders.  But SAT does, and it found that almost without exception the worst performing states are the states who spend as much as five times per student as the highest scoring states.  The differences in education quality is not insignificant--it's more than a standard deviation, or 170 SAT points.

Actually, it usually takes two SDs to be significant (p<0.05 for a two-tailed test). IIRC, I don't believe that 170 points makes that cut.

Er, you guys are mixing your meanings about SD's here. You can detect a difference - sometimes small - in the means of two normally distributed populations and prove that the difference is statistically significant at some p value with a test. It's certainly possible that, for example, the mean SAT score in state X is at least 1 SD (with respect to the SAT distribution) lower than in state Y, at a p value of <0.01 (which corresponds to something >3 SD's away in the distribution used to test this hypothesis).


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 18, 2008, 11:07:22 PM
The most interesting observation we might make about US education is one which NAEP can't make because they've used every excuse under the sun to not release state by state scores for 12th graders.  But SAT does, and it found that almost without exception the worst performing states are the states who spend as much as five times per student as the highest scoring states.  The differences in education quality is not insignificant--it's more than a standard deviation, or 170 SAT points.

Actually, it usually takes two SDs to be significant (p<0.05 for a two-tailed test). IIRC, I don't believe that 170 points makes that cut.

Er, you guys are mixing your meanings about SD's here. You can detect a difference - sometimes small - in the means of two normally distributed populations and prove that the difference is statistically significant at some p value with a test. It's certainly possible that, for example, the mean SAT score in state X is at least 1 SD (with respect to the SAT distribution) lower than in state Y, at a p value of <0.01 (which corresponds to something >3 SD's away in the distribution used to test this hypothesis).

True, it is possible; hence, my use of "usually". However, to declare it to be significant out of hand just because the number sounds big is disingenuous. The person whose conclusion I was doubting provided no evidence that ETS had found this to be statistically significant, an analysis the company does on a routine basis.


Title: Re: assuming too much math knowledge?
Post by: conjugate on December 18, 2008, 11:08:14 PM
The most interesting observation we might make about US education is one which NAEP can't make because they've used every excuse under the sun to not release state by state scores for 12th graders.  But SAT does, and it found that almost without exception the worst performing states are the states who spend as much as five times per student as the highest scoring states.  The differences in education quality is not insignificant--it's more than a standard deviation, or 170 SAT points.

Actually, it usually takes two SDs to be significant (p<0.05 for a two-tailed test). IIRC, I don't believe that 170 points makes that cut.

Er, you guys are mixing your meanings about SD's here. You can detect a difference - sometimes small - in the means of two normally distributed populations and prove that the difference is statistically significant at some p value with a test. It's certainly possible that, for example, the mean SAT score in state X is at least 1 SD (with respect to the SAT distribution) lower than in state Y, at a p value of <0.01 (which corresponds to something >3 SD's away in the distribution used to test this hypothesis).

Because the sampling deviation is the population deviation divided by the square root of the sample size.  Central Limit Theorem strikes again! 

Hah.  I just had to post this to show off that I remember some statistics.


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 18, 2008, 11:12:15 PM
How sad--or how wonderful--is it that I, a math phobic (in spite of doing well using statistical process control in a manufacturing environment) , have been following this discussion and even I understand DvF and cgfunmathguy's logic regarding methods, and understand it as valid?

For someone that likes to spout statistics, you (jacobisrael) would seem to be either being purposefully obtuse at understanding the importance of underlying methodology, or you would seem to have some different agenda that I would prefer not to explore.

*Thanks DvF and cgfunmathguy for providing clarity amidst the static*

*Disappears, with a better understanding of International educational comparison statistical studies than I had before I read*

(In fairness, some thanks to jacobisrael for providing the counterpoint that allowed the clarity to shine through, although it really didn't take me this far into the thread to see it.)

One cannot see light, unless there is darkness to provide a contrast.  (paraphrase, Bob Ross)

*poof*

You are most welcome, Mystic. If only our students understood these issues as well.


Title: Re: assuming too much math knowledge?
Post by: wanna_writemore on December 18, 2008, 11:14:35 PM
My survey history courses are full of engineering, business, and science majors.  When I ask them in class to tell me how many years passed between 2 major events, I get a roomful of blank stares.  I sometimes have to tell them that subtraction will get them there and prod them to figure it out.

It scares me that people this incapable are in my classes.  If they're not incapable, they're just lazy, and that's just as bad.


Explaining how to calculate their current course averages receives quite the result.  They all seem to think I'm a math whiz.  I'm not. I'm fairly competent in basic math to deal with bank accounts and personal finances, the minimal math needed in teaching and researching history, etc., but nothing complex.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 19, 2008, 02:39:14 AM
My survey history courses are full of engineering, business, and science majors.  When I ask them in class to tell me how many years passed between 2 major events, I get a roomful of blank stares.

That's because they didn't know they were supposed to bring their calculators to a humanities class. - DvF


Title: Re: assuming too much math knowledge?
Post by: conjugate on December 19, 2008, 02:46:11 AM
My survey history courses are full of engineering, business, and science majors.  When I ask them in class to tell me how many years passed between 2 major events, I get a roomful of blank stares.

That's because they didn't know they were supposed to bring their calculators to a humanities class. - DvF

It saddens me to see them use the calculator to figure out 84 ÷ 2.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 19, 2008, 03:10:26 AM
My survey history courses are full of engineering, business, and science majors.  When I ask them in class to tell me how many years passed between 2 major events, I get a roomful of blank stares.

That's because they didn't know they were supposed to bring their calculators to a humanities class. - DvF

It saddens me to see them use the calculator to figure out 84 ÷ 2.

Obviously, I agree, but (as you likely have already observed) students today are so wedded to calculators they can't even do noncomputational problems without having one nearby, as a kind of charm.

My son had his calculator confiscated once in middle school because he was using it to play a game. When his dean called me, I said they could keep the thing, we'd only bought it because it was a requirement and I would prefer my son to not use one.  The dean was surprised - she'd only ever talked about this kind of thing to people in Education departments, never to actual STEM practitioners, and didn't realize that many of us find calculators an impediment to learning.

I wanted to require slide rules for my classes, but nobody makes them anymore. - DvF


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on December 19, 2008, 03:51:30 AM
I still have 3 or 4 slide rules if you really need one.  It was a requirement in one (HS non-math class) to use slide rules (only in start of class quizzes, never in the actual class) that 'put the nail in the coffin', as the saying goes, for me, where math was concerned.  I can laboriously, if I have the directions handy, still manage to use one for the most basic calculations, but I've never been either fast or facile with it.

Last year my husband and I happened to mention them when talking with the teens at the zoo.  They'd never heard of them before.  I brought one in, along with the directions, and we had great fun watching as a few of the maths whizzes among them tried to decipher the basics.  They couldn't grasp it even after my husband, who was much better at math (and slide rules) than I, showed them how the calculations were done.

The most fun was watching the expressions on their faces when we pointed out that we first got to the moon--and, later, managed to do the calculations necessary to get Apollo 13 home safely (they'd all seen the movie)--using slide rules.

They still fascinate me, and I'm still more than a little po'd that my teacher used them in more of a punitive manner than in any way that would have actually fostered and encouraged any interest I might have had, given that their only place in the class was tangenital to everything else.  Altogether the single most frustrating experience I have ever exerienced in any class I have ever taken.  Truly a hate/love experience, given that I've kept them all these years.  (Then again, I have an abacus or two around here, too.)


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 19, 2008, 05:05:59 AM
I still have 3 or 4 slide rules if you really need one.

I have a few, but would like 30 or so cheapies that I could pass out to my students for use on quizzes and exams.  The problem with calculators is that some of them are too smart (a few can do Calculus) and promote cheating.  A slide rule can multiply, take roots, and compute basic transcendental functions all very easily, and that's really all I'd like my students to have access to in a computing aid. - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 19, 2008, 02:49:41 PM
How sad--or how wonderful--is it that I, a math phobic (in spite of doing well using statistical process control in a manufacturing environment) , have been following this discussion and even I understand DvF and cgfunmathguy's logic regarding methods, and understand it as valid?

For someone that likes to spout statistics, you (jacobisrael) would seem to be either being purposefully obtuse at understanding the importance of underlying methodology, or you would seem to have some different agenda that I would prefer not to explore.

*Thanks DvF and cgfunmathguy for providing clarity amidst the static*

*Disappears, with a better understanding of International educational comparison statistical studies than I had before I read*

(In fairness, some thanks to jacobisrael for providing the counterpoint that allowed the clarity to shine through, although it really didn't take me this far into the thread to see it.)

One cannot see light, unless there is darkness to provide a contrast.  (paraphrase, Bob Ross)

*poof*

You are most welcome, Mystic. If only our students understood these issues as well.

It doesn't seem like you understood the point?  Or maybe you don't want to understand the point?

It's a correct, accurate, and honest statement to say that the difference from state to state in SAT math scores is more than a standard deviation.  If you don't like the way the College Board calculates it, you need to talk directly to them and stop debating it here.

Since it appears to have hit a sore spot, let's be more specific with the figures.  Before SAT scores were "recentered" [a euphamism for "raising" scores artificially more than a standard deviation to conceal the 140 point drop in SAT scores], Iowa's SAT math score was 583, which was 119 points higher than Rhode Island's score of 464, and the standard deviation for Iowa was 99, meaning that Rhode Island scored 1.2 S.D. lower than Iowa.

That's a statement of fact.  That's not an opinion.  If the College Board is wrong, then you need to talk to TIMSS also, because they observed the same phenomena.

Pennsylvania scored 1.24 S.D. lower. Washington, DC, scored 1.4 S.D. lower.

You don't think that's worth examining?  When the highest scoring states spend one fourth or one fifth as much per student for education as the lowest scoring states, we need to know why.   And guess what?  According to NCES, and the "Glen Report", THEY CAN'T TELL YOU WHY.

When scores are different by THAT much, and when the difference is confirmed by TIMSS benchmarking studies, it would take an utter fool to not grasp the reason.

You can't recommend a solution if you don't even know the problem. 




Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 19, 2008, 03:01:46 PM
Are you sure that you've read that TIMSS study about our 12th grade scores?  The methodology for picking the cohorts was the same in both the 8th and 12th grade

They nevertheless are not the same cohort.  The reason is that the 8th graders were in 8th grade that year, and the 12th graders were in 12th grade that year.  In many cases, when the 12th graders were in middle school they had different curricula than the 8th graders did when they were in middle school.

This is not complicated stuff.  Really. - DvF

Now I understand your point.  Thank you very much for clarifying it.

Please point me to the evidence that there was a national, across the board, change in the curricula between 1991 and 1995 if you believe this to be a possible explanation.  Can the same be said for all of the other countries which took TIMSS?

If anything DID change (and this is not to even hint that anything changed) then would you not agree that our change was clearly for the worse and theirs was for the better?

Austria's scores were an exception in Europe, as they followed a similar pattern to the US, only more extreme.  While our boys' scores decreased 56 points, theirs decreased 85 points.  And while our girls' scores decreased 104 points, their decreased 137 points.  So while just the increase in the gender gap was 48 points in the US, it was 52 points in Austria.  This is not an insignificant decrease, since the standard deviation for US girls was 53, making this 0.91 S.D.  Since the standard deviation for Austrian girls was larger, at 71, the increase in their gender gap was smaller, at 0.73 S.D.

But there was already an 8 point gender gap in Austrian 8th graders, making their total gender gap by 12th grade 0.85 S.D.

I'm not clear on how changes in the curricula could have affected any of this.  I don't even know what can be changed to cause such huge race and sex gaps, or to make them bigger or smaller.  So it would be greatly appreciated if you'd provide an example.

Actually, I can think of one small example.  Not too long ago, Chinese educators were invited to visit the US to study our education system.  They asked many great questions, and my input was they should implement calculus in high school as Japan had.  They did that, and now 95% of Chinese students complete calculus before they graduate from high school.

Pretty smart, eh?  What have our educators done lately to top that?



I've tried to stay out of this one as DvF has done an admirable job of presenting the points I wanted to make. However, please allow me to add my two cents' worth. First, you are comparing different systems that do different things. You are comparisons are being made between countries where there are NATIONAL curricula, those where there are STATE curricula, and at least one where it is a hodgepodge of STATE and LOCAL curricula. So, we are comparing apples to oranges to pears

Also, we need to address the differences in systemic student handling. In the US, we send the vast majority of our students to high school; other countries reverse this entirely. Thus, the 12th-grade cohorts aren't even comparable between countries, even though they are presented as such by the media (among many others). While the 4th-grade cohorts may be similar, there is even some question about the comparing 8th-grade cohorts by some. For the two reasons above, I don't believe TIMSS is as valid an indicator of differences between national systems as its exhorters proclaim.

Finally, a word about why DvF keeps trying to get you to understand why comparing cohorts is important. Many states have been adjusting/rewriting their regulations (Pennsylvania), their state-mandated tests (Ohio), and their state-mandated curricula (Georgia) for the past decade or more. In mathematics, the National Council of Teachers of Mathematics (NCTM) issued its first set of standards on K-12 mathematics in 1989. This was the first step in the reform process, and several states began the process of reforming state curricula in the early 1990s. Others waited longer. However, the process is not an instantaneous one. As an example, Georgia instituted the Georgia Performance Standards (GPS) in 2003 or 2004. The standards still aren't fully implemented throughout the schools yet, and they won't be for two more years. So, yes, cohort matters, and we need to deal with the data that way. The only fair comparisons about gains and losses in the report's 12th-grade cohort would be to take the 2007 report's 12th-graders and compare that gap (assuming all the other confounding variables didn't exist) to the gap found in the 2003 report's 8th-graders and to the gap found in 1999 report's 4th-graders. This assumes that the tests across that EIGHT-YEAR SPREAD are equivalent.


This is about like (no, it's exactly like) saying that you know one girl who's taller than many of the boys, therefore girls are just as tall as boys.

In regard to height, the standard deviation for both sexes is the same, 2.8 inches.

But the GAP between the mean scores is, yet again, two standard deviations (1.893 to be exact).

There's no way to announce that a gender gap of 1.893 standard deviations is not significant. It has a HUGE impact on our world that simply cannot be ignored, not even in a theoretical sense.


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 19, 2008, 03:14:18 PM
It doesn't seem like you understood the point?  Or maybe you don't want to understand the point?

It's a correct, accurate, and honest statement to say that the difference from state to state in SAT math scores is more than a standard deviation.  If you don't like the way the College Board calculates it, you need to talk directly to them and stop debating it here.

Since it appears to have hit a sore spot, let's be more specific with the figures.  Before SAT scores were "recentered" [a euphamism for "raising" scores artificially more than a standard deviation to conceal the 140 point drop in SAT scores], Iowa's SAT math score was 583, which was 119 points higher than Rhode Island's score of 464, and the standard deviation for Iowa was 99, meaning that Rhode Island scored 1.2 S.D. lower than Iowa.

That's a statement of fact.  That's not an opinion.  If the College Board is wrong, then you need to talk to TIMSS also, because they observed the same phenomena.

Pennsylvania scored 1.24 S.D. lower. Washington, DC, scored 1.4 S.D. lower.

You don't think that's worth examining?  When the highest scoring states spend one fourth or one fifth as much per student for education as the lowest scoring states, we need to know why.   And guess what?  According to NCES, and the "Glen Report", THEY CAN'T TELL YOU WHY.

When scores are different by THAT much, and when the difference is confirmed by TIMSS benchmarking studies, it would take an utter fool to not grasp the reason.

You can't recommend a solution if you don't even know the problem. 

Actually, you have missed my point. I did NOT say that the numbers are wrong. I am NOT disputing their calculation. I am NOT even saying that it's not worth examining. My point was/is that stating that something is significant just because the number seems large is an invalid argument statistically. "Significant differences" is a term with a fairly precise meaning and is only stated along with a confidence level. This is something that anyone who has passed an introductory statistics course should know. Your emphasis on the size of the difference (whether normed or not) shows me that you really don't understand this very basic idea. Someone who did understand it would have already reported that the difference was ___, which is significant at the ___% level. You haven't done this.

For another view of it, let's look at your classroom. In a large lecture class, grades tend to be distributed "normally". This being the case, "curving" (with its true meaning) would assign Cs to the 68% of the students whose scores are within 1 SD of the mean. So, let's assume that the mean on Test 1 was 75 with a standard deviation of 8. So, any student with a score between 67 and 83, inclusive, should get a C. However, Susie with her 81 and Johnny with his 69 both got Cs! Is the difference significant? We don't know until we run tests on the scores. Even though the difference is 12 points (which is 1.5 SD), it is likely that this difference is NOT "statistically significant" at any appreciable level. To constantly quote raw numbers with no test results is worthless and misleading. Even those with an agenda don't do this because they know they will be accused of trying to bamboozle the people reading the report.

Take a stats class, and then come back into the discussion.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 19, 2008, 03:17:00 PM
When scores are different by THAT much, and when the difference is confirmed by TIMSS benchmarking studies, it would take an utter fool to not grasp the reason.

OK, here an exercise of the sort I assign in my senior-level undergraduate statistics courses:  Given 50 independent, identically-distributed normal random variables, what is the exact probability that all of them fall within 1 standard deviation?  Within 2 standard deviations?  What is the answer if we trim N extreme values from either end?  (Hint: "order statistics")

New rule: nobody, in a discussion like this, gets to call anyone else an "utter fool" if they cannot solve such a problem, and recognize its relevance to the discussion. - DvF


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 19, 2008, 03:20:14 PM
This is about like (no, it's exactly like) saying that you know one girl who's taller than many of the boys, therefore girls are just as tall as boys.

In regard to height, the standard deviation for both sexes is the same, 2.8 inches.

But the GAP between the mean scores is, yet again, two standard deviations (1.893 to be exact).

There's no way to announce that a gender gap of 1.893 standard deviations is not significant. It has a HUGE impact on our world that simply cannot be ignored, not even in a theoretical sense.

I don't understand how you claim dealing with height differences between the sexes is like the rest of the discussion. Now, you REALLY are comparing apples to oranges.

Provide the statistical analysis that supports calling differences significant along with the confidence level used for the test or STFU. I will ignore the remainder of your posts until this is done.

On preview: Thank you, DvF.


Title: Re: assuming too much math knowledge?
Post by: high_energy_photons on December 19, 2008, 03:47:09 PM
I wanted to require slide rules for my classes, but nobody makes them anymore. - DvF

You should talk to your local school districts.  They may have some in storage from back in the day.  I had a teacher who taught us how to use slide rules as part of an appreciation of technology lesson, and she got some really nice slide rules from the district.  I was not allowed to use calculators until middle school, and even then not until close to the end (and not graphing).  Before we started using calculators, we had a brief lesson on abacuses.  Then we had a few weeks of slide rule.  Finally, we got the calculators, and we understood their limitations by that point.

It makes me sad that so many of my students don't understand that their calculators are stupid machines.  Calculators are a drain on thinking, and I ban them as much as I can (banned them when I taught high school).


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on December 19, 2008, 05:48:50 PM
I wanted to require slide rules for my classes, but nobody makes them anymore. - DvF

You should talk to your local school districts.  They may have some in storage from back in the day.  I had a teacher who taught us how to use slide rules as part of an appreciation of technology lesson, and she got some really nice slide rules from the district.  I was not allowed to use calculators until middle school, and even then not until close to the end (and not graphing).  Before we started using calculators, we had a brief lesson on abacuses.  Then we had a few weeks of slide rule.  Finally, we got the calculators, and we understood their limitations by that point.

It makes me sad that so many of my students don't understand that their calculators are stupid machines.  Calculators are a drain on thinking, and I ban them as much as I can (banned them when I taught high school).

Google slide rule+buy and you'll get a lot of sites.  With a statement like this: "TEACHERS, do you need inexpensive rules for classes?
We have stock set aside for this purpose, and offer it at reduced prices. EMAIL SUSAN HERE [link removed] if you need help with this purchase, and have limited or no funding."  this site looks promising: http://www.sphere.bc.ca/test/cheap.html#catalog


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 19, 2008, 07:11:14 PM
This is about like (no, it's exactly like) saying that you know one girl who's taller than many of the boys, therefore girls are just as tall as boys.

In regard to height, the standard deviation for both sexes is the same, 2.8 inches.

But the GAP between the mean scores is, yet again, two standard deviations (1.893 to be exact).

There's no way to announce that a gender gap of 1.893 standard deviations is not significant. It has a HUGE impact on our world that simply cannot be ignored, not even in a theoretical sense.

I don't understand how you claim dealing with height differences between the sexes is like the rest of the discussion. Now, you REALLY are comparing apples to oranges.

Provide the statistical analysis that supports calling differences significant along with the confidence level used for the test or STFU. I will ignore the remainder of your posts until this is done.

On preview: Thank you, DvF.


Again, this was simply a quote, as I didn't do the actual calculation and don't know what the confidence level is. If the following will post on this forum, it will answer your question.

But--the reference was not to statistically significant.  It was to *significant*, which as you obviously know are not the same.

Agreed, comparing height and test scores are apples and oranges.  This is an allegory.  One person stated that they didn't trust the data because of their anecdotal experience with a TA.  The allegory is that it's like saying that since they know one female who's as tall as many of the males, that women are just as tall as men.  Wouldn't you agree it's an accurate allegory?

It was the authors of the Glen report who were referred to as idiots. I don't know a single person, not even a teacher (not even a female teacher) who doesn't think that was one of the most worthless thing to come out of Washington in a long time.  Entire organizations have been formed with millions of members for the express purpose of rejecting such nonsense.  If they're not technically idiots, what would you think would be a better term for the authors?

Is it your position that if the 1.9 S.D. gender gap in height is not statistically significant that it's not significant?




Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 19, 2008, 08:11:34 PM
Again, this was simply a quote, as I didn't do the actual calculation and don't know what the confidence level is. If the following will post on this forum, it will answer your question.

If it was a quote, then give us the link to the source. The source (preferably the report itself) would tell you the confidence level (and the result of the calculation).

But--the reference was not to statistically significant.  It was to *significant*, which as you obviously know are not the same.

Any "report" that refers to "significance" is either (a) dealing with statistical significance or (b) using misleading language to further an agenda. What you have done is (a) post without understanding statistics in general and/or (b) pertuated the agenda by repeating the misleading language. Yes, when presenting statistics, "significant" = "statistically significant".

Agreed, comparing height and test scores are apples and oranges.  This is an allegory.  One person stated that they didn't trust the data because of their anecdotal experience with a TA.  The allegory is that it's like saying that since they know one female who's as tall as many of the males, that women are just as tall as men.  Wouldn't you agree it's an accurate allegory?

Yes, I agree that your analogy (NOT allegory) is comparable to the TIMSS report, but that is not because of any statistical differences between the groups. It is because the groups are not comparable. Comparing Norwegian HS 12th-graders to American HS 12th-graders is as much apples-to-oranges as comparing heights of men to heights of women. If the groups aren't comparable, the comparisons CANNOT BE MADE RELIABLY.

Is it your position that if the 1.9 S.D. gender gap in height is not statistically significant that it's not significant?

Is it your position that comparing non-comparable groups results in significance? I will say it again: TAKE A STATISTICS COURSE OR STFU.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 19, 2008, 08:35:20 PM
Google slide rule+buy and you'll get a lot of sites.  With a statement like this: "TEACHERS, do you need inexpensive rules for classes?

I've already been through this exercise; "inexpensive" usually means $20-40.  I'm not ready to fork out $600-1200 for a set of slide rules for my class!  - DvF


Title: Re: assuming too much math knowledge?
Post by: galactic_hedgehog on December 20, 2008, 01:25:08 AM
Google slide rule+buy and you'll get a lot of sites.  With a statement like this: "TEACHERS, do you need inexpensive rules for classes?

I've already been through this exercise; "inexpensive" usually means $20-40.  I'm not ready to fork out $600-1200 for a set of slide rules for my class!  - DvF

How 'bout having the students build their own (http://www.sphere.bc.ca/test/build.html)?


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 20, 2008, 02:56:26 AM
Again, this was simply a quote, as I didn't do the actual calculation and don't know what the confidence level is. If the following will post on this forum, it will answer your question.

If it was a quote, then give us the link to the source. The source (preferably the report itself) would tell you the confidence level (and the result of the calculation).

But--the reference was not to statistically significant.  It was to *significant*, which as you obviously know are not the same.

Any "report" that refers to "significance" is either (a) dealing with statistical significance or (b) using misleading language to further an agenda. What you have done is (a) post without understanding statistics in general and/or (b) pertuated the agenda by repeating the misleading language. Yes, when presenting statistics, "significant" = "statistically significant".

Agreed, comparing height and test scores are apples and oranges.  This is an allegory.  One person stated that they didn't trust the data because of their anecdotal experience with a TA.  The allegory is that it's like saying that since they know one female who's as tall as many of the males, that women are just as tall as men.  Wouldn't you agree it's an accurate allegory?

Yes, I agree that your analogy (NOT allegory) is comparable to the TIMSS report, but that is not because of any statistical differences between the groups. It is because the groups are not comparable. Comparing Norwegian HS 12th-graders to American HS 12th-graders is as much apples-to-oranges as comparing heights of men to heights of women. If the groups aren't comparable, the comparisons CANNOT BE MADE RELIABLY.

Is it your position that if the 1.9 S.D. gender gap in height is not statistically significant that it's not significant?

Is it your position that comparing non-comparable groups results in significance? I will say it again: TAKE A STATISTICS COURSE OR STFU.

TIMSS was a massive undertaking, done in a credible manner, accepted by countries all around the world.  Not even Riley claimed that our low scores were an aberration.  The scores, the test questions, standard deviations, standard errors, are available by a number of variables, all the way from sex to public/private education, to parent's education, etc.  Would you say that this helps greatly to analyze where our problems and shortfalls are?

One of the low points on our scores was in numbers and equations, with only Austria scoring significantly lower than us.  In geometry, nobody scored significantly lower.  You can cross reference the score we received to the average percent correct to figure out exactly how poorly our students did in these subjects. 

Were you aware that they actually scored lower on a third of the questions than if they'd just guessed?  Do we need to make a comparison to Norway to recognize that something is wrong about the way our students are taught these subjects?  The only reason for mentioning Norway is that this appeared to be an easy test for them.  Countries like Japan, Korea, and Taiwan who scored more than 100 points higher than us in the 8th grade tests weren't even in the 12th grade tests, though, so this comparison to Norway is almost misleading by comparison.



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 20, 2008, 03:55:34 AM
Numbers are like guns: powerful in the hands of people who know how to use them, but those untrained in their use inevitably shoot themselves in the foot. - DvF


Title: Re: assuming too much math knowledge?
Post by: cs_prof on December 20, 2008, 11:34:39 AM
First of all, I think that it is bad idea for the instructor offering to solve equations like this:
(z= X - mean of X  /   standard deviation)

This one would be much better:
z= (X - mean of X ) / standard deviation


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 20, 2008, 11:41:24 AM
Numbers are like guns: powerful in the hands of people who know how to use them, but those untrained in their use inevitably shoot themselves in the foot. - DvF

Precisely my point.

How else can it be explained that American students would score lower on one third of the numbers and equations questions than if they'd just guessed?

To be specific, item K-2 is the following question:

"in how many ways can one arrange on a bookshelf 5 thick books, 4 medium sized books, and 3 thin books so that books of the same size remain together".

Since this is a 5 part multiple choice question, is it true that if this many students just guessed on this question, but had no idea of what the answer is, that 20% of them would get it right?  

How then can it be explained that only 15% of our students got it right?

If this was an aberration, you could argue that there was some other reason other than that they were taught the WRONG thing about this topic.  

Did you know this phenomena is repeated throughout TIMSS?

Would your educated guess be that it's not that they had no information about this question--but that they had the WRONG information?

Where do you think the wrong information come from?



Title: Re: assuming too much math knowledge?
Post by: kedves on December 20, 2008, 11:44:54 AM
I have recently come to the conclusion that yes, we are assuming too much math knowledge.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 20, 2008, 01:07:03 PM

Is it your position that if the 1.9 S.D. gender gap in height is not statistically significant that it's not significant?

Is it your position that comparing non-comparable groups results in significance? I will say it again: TAKE A STATISTICS COURSE OR STFU.

It's interesting that the standard deviation and confidence level for the NHANES III study from which this height information came doesn't seem to be available anywhere on the net.  I agree with you that it's important and would like to see it as much as you would.  This is the url for that reference:

http://investing.calsci.com/statistics.html

The point about comparing the heights of sexes was only to illustrate that you can't say that since one female was as tall as many of the males, that females are just as tall as males.  The "gender gap" as it's now called [it's a demeaning term] in DHHS information on height shows that 3% of males are taller than 75", which is 6" taller than the tallest 3% of females at 69".  It also shows that 3% of males are shorter than 64.2" (the average for females), which is 5.2" taller than the shortest 3% of females at 59".

Even if it's not statistically significant, do you consider it at all interesting that only 3% of females are taller than 69", compared to 54% of males who are?


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 20, 2008, 01:17:54 PM
I have recently come to the conclusion that yes, we are assuming too much math knowledge.

Exactly.

If the answer to the following TIMSS question Item L.10 is indicative of the combined math knowledge in this country, then you might presume negative knowledge rather than no knowledge:

"A warning system installation consists of two independent alarms having probabilities of operating in an emergency of 0.95 and 0.90 respectively.  Find the probability that at least one alarm operates in an emergency".

The absolute worst performance of our students in TIMSS was in probability and statistics, and this is just one example of how badly they performed.

Being a five part multiple choice question, how many students do you believe would have gotten it correct had they just guessed if they knew nothing about the answer?

Good.

Did you know that less than that percent of our students got it correct?

Any idea why?


Title: Re: assuming too much math knowledge?
Post by: homelessscientist on December 20, 2008, 02:18:23 PM

"in how many ways can one arrange on a bookshelf 5 thick books, 4 medium sized books, and 3 thin books so that books of the same size remain together".

Since this is a 5 part multiple choice question, is it true that if this many students just guessed on this question, but had no idea of what the answer is, that 20% of them would get it right?  

How then can it be explained that only 15% of our students got it right?

[...]

Would your educated guess be that it's not that they had no information about this question--but that they had the WRONG information?

Where do you think the wrong information come from?


I would guess that it's due to the presence of attractive distractors among the answer choices.  If a student has no idea what to do with a question on a standardized test, a strategy that is often successful (*too* often successful) is to find a way to manipulate the numbers in the problem to give a number that matches an answer choice.

I think the correct answer to this problem is 3! = 6 if books of the same size are considered indistinguishable, or 3! 5! 4! 3! = 103680 if all books are distinguishable.  Neither of those answers can be obtained by adding or multiplying the numbers in the problem.  I would be willing to bet that 5*4*3 = 60 was offered as a distractor.


Title: Re: assuming too much math knowledge?
Post by: darkmatter on December 20, 2008, 02:30:06 PM
Are we allowed to rotate the books?


Title: Re: assuming too much math knowledge?
Post by: homelessscientist on December 20, 2008, 02:32:00 PM
Are we allowed to rotate the books?

I like the way you think. :-)


Title: Re: assuming too much math knowledge?
Post by: kedves on December 20, 2008, 03:10:51 PM
I have recently come to the conclusion that yes, we are assuming too much math knowledge.

Exactly.

I'm sorry.  I was being obscure.  If you agreed with me, then you would take CGFunMathGuy's advice.  Any discussion about statistics is meaningless if one or more parties to the discussion does not know the meaning of statistical significance.

I used to think the type of word problem on this page was the thing most likely to make me want to hit my head on my desk, but recently I have come to the conclusion that there are other things that give me the same impulse.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 20, 2008, 03:21:06 PM
How else can it be explained that American students would score lower on one third of the numbers and equations questions than if they'd just guessed?

Actually, this is more a symptom of a bad test then of bad students.

How's that foot doing? - DVF



Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 20, 2008, 06:56:45 PM
How else can it be explained that American students would score lower on one third of the numbers and equations questions than if they'd just guessed?

Actually, this is more a symptom of a bad test then of bad students.

How's that foot doing? - DVF



Explain.

The point is that no other country complained about the quality of this question, or any of the other questions.  Could it be that they didn't complain because 40-57% of their students managed to answer it correctly, while our educators do complain only because our score was essentially a negative?

Our published analysis of TIMSS never once mentioned that the questions should have been worded differently, or that they were unfair questions, or that they were biased, or irrelevant, or politically incorrect, or not germaine to American education.

I've heard people's arguments for why this is not a valid question, or that not enough information was available, etc.

It would be interesting to hear your argument.  Or why you think 57% of Australian boys DID think it was a valid question, DID know that there was enough information available to answer it, and DID answer it correctly, while essentially none of ours did (or to be mathematically precise, 4% fewer of our students answered it correctly than if they'd just guessed)?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 20, 2008, 09:24:34 PM
Explain.

It has already been explained to you up above.  To be completely blunt, you do not seem to be very good at understanding points even when they are laid out for you in "cartoon guide" form.

However, before I answer any more of your questions, I would like you to solve the elementary statistics exercise I set above.  Otherwise, I am wasting my time arguing with you: so far your arguments have the tenor and depth commensurate with a 109th grade debater with a chip on his shoulder.  - DvF


Title: Re: assuming too much math knowledge?
Post by: cc_alan on December 21, 2008, 11:24:11 AM
First of all, I think that it is bad idea for the instructor offering to solve equations like this:
(z= X - mean of X  /   standard deviation)

This one would be much better:
z= (X - mean of X ) / standard deviation

*groan*

Why do a few of my chemistry students still have difficulties at the end of the term with order of operations? Perhaps I had similar problems as a freshpeep and I've simply forgotten them. I don't recall having problems with order of operations, however.

Alan


Title: Re: assuming too much math knowledge?
Post by: scienceprof on December 21, 2008, 11:36:07 AM
I am not sure that some of them even know that the concept of order of operations exists.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 21, 2008, 02:00:07 PM
Explain.

It has already been explained to you up above.  To be completely blunt, you do not seem to be very good at understanding points even when they are laid out for you in "cartoon guide" form.

However, before I answer any more of your questions, I would like you to solve the elementary statistics exercise I set above.  Otherwise, I am wasting my time arguing with you: so far your arguments have the tenor and depth commensurate with a 109th grade debater with a chip on his shoulder.  - DvF

OK, I'll answer my own question.

TIMSS illustrates that our *average* student had ZERO knowledge and understanding of probability and statistics.  That was the *average* student, not educators.

It also shows that educators in the many countries whose students scored MUCH higher than us come from the highest intellectual strata of the country.

Conversely, GRE shows that even social science majors score higher in "analytical" skills than our educators (557 vs. 497).  It also shows, that annually, only 2% or 555 of our education majors who take GRE score higher than 603, the *average* for tens of thousands of engineering and physical science majors--about the minimum required to actually know what is *significant* and what is not.

You don't appear to be one of those 555 education majors.  So it's possible that your misrepresentation of statistical significance is based on misunderstanding it, just as almost ALL of the American students who took TIMSS proved beyond the shadow of all doubt that they misunderstood it.

This is not intended as a personal slur.  This is simply social commentary.  When you read something in a book that tells you one thing, and you believe it for decades, it's hard to accept that the book was wrong.  I know how that works, because it happened to me, and it took DECADES to come to terms with it.  Since I made the same mistake, I'm not faulting you for it.

That's the entire point about TIMSS which our education experts obviously missed by a mile.  They're so hung up on the theory of statistical significance that the reality of our very poor test scores on ALL the international tests appears to have completely escaped them.  The reason they don't appear to be to concerned about our incredibly low test scores is because they don't think they're valid, or they're not "statistically significant".

TIMSS goes into great depth on this topic.  If anyone on this forum is aware of a single US educator or publication which has successfully refuted their analysis, they ought to refer us to it here.

Why did you not explain precisely what you meant by "Actually, this is more a symptom of a bad test then of bad students", though?

It would be greatly appreciated if you would take the time to lay it out.  I should add that in a previous forum about this topic, almost all of the American students who examined it claimed there wasn't enough information to answer the question.

How do you explain, then, that 57% of Australian students DID answer it, correctly, while our students had a NEGATIVE score?

Why have you not explained how it is that on such a credible probability and statistics test, our students managed to score lower on one third of of the questions than if they'd just guessed?

Is it possible that this one question proves that our students cannot be properly educated in the existing education infrastructure?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 21, 2008, 07:01:20 PM
You don't appear to be one of those 555 education majors.  So it's possible that your misrepresentation of statistical significance is based on misunderstanding it

This is very funny. 

How are you coming on that exercise I gave you?  - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 22, 2008, 12:03:50 AM
You don't appear to be one of those 555 education majors.  So it's possible that your misrepresentation of statistical significance is based on misunderstanding it

This is very funny. 

How are you coming on that exercise I gave you?  - DvF


Of course you won't explain why you think that question was "more a symptom of a bad test then of bad students", because deep down inside you know that it was a fair and reasonable test question that a majority of our students SHOULD have answered correctly had they been educated properly.

To expand on this point, let's address a different question, Question K8 on the TIMSS Math portion given to 12th graders around the world, revealing an additional astounding difference in math skills between the countries who participated.  Since this was also a multiple choice question with four answers, can you tell us how much the scores need to be adjusted for correct guesses?

24% of American students got it right.  Can you tell us what percent of them demonstrated knowledge of the subject? The question is:  "Which of the following conics is represented by the equation (x - 3y)(x + 3y) = 36", with the choices being circle, ellipse, parabola, and hyperbola.

Is this too "more a symptom of a bad test then of bad students" in your opinion?




Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 22, 2008, 03:40:59 AM
An I quote:

Because TI MSS is fundamentally a study of mathematics and science
achievement among fourth and eighth grade students, the precision of
survey estimates of student achievement and characteristics was of primary
importance. However, TI MSS also reports extensively on school, teacher,
and classroom characteristics, so it is necessary to have sufficiently large
samples of schools and classes. The TI MSS standards for sampling precision
require that all student samples have an effective sample size of at least 400
students for the main criterion variable, which is mathematics and science
achievement. In other words, all student samples should yield sampling
errors that are no greater than would be obtained from a simple random
sample of 400 students.
Given that sampling error, when using simple random sampling, can be
expressed as SESRS S / n where S gives the population standard deviation
and n the sample size, a simple random sample of 400 students would yield
a 95 percent confidence interval for an estimate of a student-level mean of
±10 percent of its standard deviation ( 1.96 g S / 400 ). Because the TI MSS
achievement scale has a standard deviation of 100 points, this translates into
a ±10 points confidence limit (or a standard error estimate of approximately
5 points). Similarly, sample estimates of student-level percentages would have
a confidence interval of approximately ±5 percentage points.
Notwithstanding these precision requirements, TI MSS required that
all student sample sizes should not be less than 4,000 students. This was
necessary to ensure adequate sample sizes for analyses where the student
population was broken down into many subgroups. For countries involved in
the previous TI MSS cycle in 2003, this minimum student sample size was set
to 5,150 students in order to compensate for participaton in the TI MSS 2007
Bridging Study. Furthermore, since TI MSS planned to conduct analyses at the
school and classroom level in addition to the student level, all school sample
sizes were required to be not less than 150 schools, unless a complete census
failed to reach this minimum. Under simple random sampling assumptions,
a sample of 150 schools yields a 95 percent confidence interval for an estimate
of a school-level mean that is ±16 percent of a standard deviation.
Although the TI MSS sampling precision requirements are such that
they would be satisfied by a simple random sample of 400 students, sample
designs such as the TI MSS 2007 school-and-class design, typically require
much larger student samples to achieve the same level of precision. Because
students in the same school and even more so in the same class, tend
to be more like each other than like other students in the population,
sampling a single class of 30 students will yield less information per student
than a random sample of students drawn from across all students in the
population. TI MSS uses the intraclass correlation, a statistic indicating
how much students in a group are similar on an outcome measure, and a
related measure known as the design effect to adjust for this “clustering”
effect in planning sample sizes.
For countries taking part in TI MSS for the first time in 2007, the
following mathematical formulas were used to estimate how many schools
should be sampled to achieve an acceptable level of sampling precision:

<end quote>

The rest of the discussion about the confidence interval of TIMSS can be seen at:

http://timss.bc.edu/TIMSS2007/PDF/T07_TR_Chapter5.pdf


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 22, 2008, 04:04:22 AM
It doesn't seem like you understood the point?  Or maybe you don't want to understand the point?

It's a correct, accurate, and honest statement to say that the difference from state to state in SAT math scores is more than a standard deviation.  If you don't like the way the College Board calculates it, you need to talk directly to them and stop debating it here.

Since it appears to have hit a sore spot, let's be more specific with the figures.  Before SAT scores were "recentered" [a euphamism for "raising" scores artificially more than a standard deviation to conceal the 140 point drop in SAT scores], Iowa's SAT math score was 583, which was 119 points higher than Rhode Island's score of 464, and the standard deviation for Iowa was 99, meaning that Rhode Island scored 1.2 S.D. lower than Iowa.

That's a statement of fact.  That's not an opinion.  If the College Board is wrong, then you need to talk to TIMSS also, because they observed the same phenomena.

Pennsylvania scored 1.24 S.D. lower. Washington, DC, scored 1.4 S.D. lower.

You don't think that's worth examining?  When the highest scoring states spend one fourth or one fifth as much per student for education as the lowest scoring states, we need to know why.   And guess what?  According to NCES, and the "Glen Report", THEY CAN'T TELL YOU WHY.

When scores are different by THAT much, and when the difference is confirmed by TIMSS benchmarking studies, it would take an utter fool to not grasp the reason.

You can't recommend a solution if you don't even know the problem. 

Actually, you have missed my point. I did NOT say that the numbers are wrong. I am NOT disputing their calculation. I am NOT even saying that it's not worth examining. My point was/is that stating that something is significant just because the number seems large is an invalid argument statistically. "Significant differences" is a term with a fairly precise meaning and is only stated along with a confidence level. This is something that anyone who has passed an introductory statistics course should know. Your emphasis on the size of the difference (whether normed or not) shows me that you really don't understand this very basic idea. Someone who did understand it would have already reported that the difference was ___, which is significant at the ___% level. You haven't done this.

For another view of it, let's look at your classroom. In a large lecture class, grades tend to be distributed "normally". This being the case, "curving" (with its true meaning) would assign Cs to the 68% of the students whose scores are within 1 SD of the mean. So, let's assume that the mean on Test 1 was 75 with a standard deviation of 8. So, any student with a score between 67 and 83, inclusive, should get a C. However, Susie with her 81 and Johnny with his 69 both got Cs! Is the difference significant? We don't know until we run tests on the scores. Even though the difference is 12 points (which is 1.5 SD), it is likely that this difference is NOT "statistically significant" at any appreciable level. To constantly quote raw numbers with no test results is worthless and misleading. Even those with an agenda don't do this because they know they will be accused of trying to bamboozle the people reading the report.

Take a stats class, and then come back into the discussion.

You might be interested in the following study by Howard Wainer about how grades are given to boys and girls in an unfair way.

Wainer, Howard;  Steinberg, Linda S., Sex Differences in Performance on the Mathematics Section of the Scholastic Aptitude Test: A Bidirectional Validity Study. Harvard Educational
Review;  v62 n3 p323-36 Fall 1992

His study shows that girls who were given As had SAT math scores equivalent to boys who were given Cs, and that girls who were given Cs had SAT math scores 30 points lower than boys who were given Fs.

Any idea how that might happen?  It seems to be a nationwide problem.  It might explain why math education has been given such a low priority in the US, and why our TIMSS scores are consistently last in the industrialized world.



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 22, 2008, 04:16:25 AM
Or, it could be an indicator that college board scores are imperfec predictors of ability or future performance.   This is what the authors of this study suggest in that article, which you apparently haven't read (but I know well, as I was on a university admissions task force where it was discussed). - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 22, 2008, 01:58:51 PM
Or, it could be an indicator that college board scores are imperfec predictors of ability or future performance.   This is what the authors of this study suggest in that article, which you apparently haven't read (but I know well, as I was on a university admissions task force where it was discussed). - DvF

No question that our educators are ignoring college board scores.  Otherwise how can it be explained that two thirds of the most qualified high school graduates are now denied admission to college, while two thirds of those admitted were patently unqualified and were admitted only because of affirmative action (which is why we voters in California changed the state constitution for the express purpose of OUTLAWING such invidious systemic discrimination).

As an employer who must weed through thousands of resumes, college board scores are the first thing that weeds out a potential employee.  High scores don't automatically guarantee employment, but low scores guarantee no interview (that is, until affirmative action FORCED me to hire IDIOTS, which I will NEVER do, ever again, no matter what the ..... law says).

I now know Indian veterinarians and doctors [from India that is, where the average IQ is 81] who were denied admission to med or veterinarian school in India because of their poor academic performance, but got into an American university through affirmative action with no problem at all.

Are you happy?  Does that warm the cockles of your heart to hear that?
 


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 22, 2008, 06:33:06 PM
How else can it be explained that American students would score lower on one third of the numbers and equations questions than if they'd just guessed?

Actually, this is more a symptom of a bad test then of bad students.

How's that foot doing? - DVF




Another question which you might believe is a bad test rather than bad students (which of course means bad teachers) is H-7:

"A fixed mass sof gas is heated at constant volume.  Which of the following diagrams best shows the correct shape of the graph of pressure (p) against temperature (theta) for the gas?  Temperature is measured in degrees Celsius". Following that are four graphs, making this a four part multiple choice question.

It wouldn't be so bad if we just got ZERO (which of course is bad enough).   But only 10% of our students got it right, which is 15% fewer than would have gotten it right had they known nothing about the answer and just wildly guessed.

How do you explain that?  This isn't an aberration.  ONE THIRD of our answers were like that.  This is statistical PROOF that they were taught the WRONG thing.

What do you believe is the source of that MIS-information?  HOW are our students being MIS-informed about such key concepts?

And before you cry statistically insignificant, don't forget that the boys' international average on that question was 46%, way beyond pure guesses and standard errors.  MOST did demonstrate knowledge and understanding of the facts and concepts, while ours demonstrated negative knowledge and intelligence.  This is not new either.  It dates all the way back to IAEP in 1972.  And in all this time, all that happened is that our education infrastructure got WORSE, not better.


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on December 23, 2008, 11:12:17 AM
Time to give up, DvF. Jacobisrael refuses to discuss statistical studies in an intelligent manner, leading me to believe that s/he does not understand statistics. S/he refuses to respond to points made in a coherent manner, especially when it is obvious that s/he might actually be required to acknowledge that someone else is correct about the topic at hand.

I will no longer reply to Jacobisrael because s/he refuses to answer reasonable questions and to discuss statistics responsibly (which is something I require of all of my frosh quantitative reasoning students).


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 23, 2008, 01:51:00 PM
Time to give up, DvF. Jacobisrael refuses to discuss statistical studies in an intelligent manner, leading me to believe that s/he does not understand statistics. S/he refuses to respond to points made in a coherent manner, especially when it is obvious that s/he might actually be required to acknowledge that someone else is correct about the topic at hand.

I will no longer reply to Jacobisrael because s/he refuses to answer reasonable questions and to discuss statistics responsibly (which is something I require of all of my frosh quantitative reasoning students).

How much more patient can someone be with someone who keeps saying STFU, who appears to have an educator's rather than a scientist's view of statistics, and many of whose students probably understand probability and statistics better than him?  It's simply not correct that a statistical comparison of American students to Norwegian students is impossible, as this is exactly what TIMSS accomplished, time and time again.  Not even the Glen report, which is politically correct and ridiculous to the extreme, made such a claim.  Statistically, you're an outlier whose only hope is to be discarded.

Since DvF won't explain why he thinks the probability and statistics question which was posted is the sign of a bad test and not bad students, it would be greatly appreciated if you would come to bat for him and explain why almost two thirds of the boys in Switzerland and Australia disagreed, and answered it correctly.

This not an attempt to avoid your question.  It's a good question.  It makes a good point.  But it tends to make people who are statistics impaired believe that because it might be statistically insignificant that it's not literally significant.  And of course you do know the difference even if they don't and never will.

The most revealing question in TIMSS was Item K15 which wasn't even a multiple guess question.  Yet our 12th graders managed to score no higher than the standard error, yet again.  The international average was 18%, Russia was 34%, and even France did well here at 57%.

So it's a real important question.  Our so-called "enemies" teach their students probability and statistics while we obviously don't (having lived in both Russia and France, I don't buy the cold war propaganda about them being "enemies", but they ARE global economic competitors and such knowledge is a drop dead issue in economics).

Graphics can't be posted here, so let's use "zeee" to represent the conjugate of z, which on the test was a z with a line over it:

"Determine all the complex numbers z that satisfy the equation z + 2zeee = 3 + i where zeee denotes the conjugate of z".

Why oh why did so many American 18 year olds show up at the 12th grade without even knowing this?  How could they possibly have taken so many years of math and never learned it?  According to TIMSS, American students spend MORE time in the classroom, have far more teachers per student, spend MORE time on homework, than students in countries like France--but never learned this?  How?

Furthermore, while the belief on this forum appears to be that we have a high rate of educating our youth, your own NCES claims that only 74% of our 18 year olds are in secondary school, compared to 93% or more in the most competitive industrialized nations:

http://nces.ed.gov/pubs2001/2001034.pdf Table 390

But little ole' TIMSS comes along and puts a lie to those stats by discovering to our apparent amazement that the figure is actually closer to two thirds rather than 74%.  A simple comparison of our population statistics for 18 year olds to high school graduates confirms TIMSS and rejects NCES, yet again.  Over three decades, the population of 18 year olds varied from 3.4 to 4.4 million, while the number of high school graduates paralleled that rise and fall, with one million 18 year olds missing each year.  That alone is 30 million American 18 year olds who weren't even included in our breathtakingly low TIMSS scores.



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 23, 2008, 06:28:46 PM
How much more patient can someone be with someone who keeps saying STFU, who appears to have an educator's rather than a scientist's view of statistics, and many of whose students probably understand probability and statistics better than him?

Just to be absolutely clear, I am a university educator and also a researcher in a STEM field with 30 years of publications in fields including Mathematics, Statistics, Biostatistics, and Computer Science.  I believe cgmathfunguy is similarly credentialed, but if not he is right nevertheless.

Aside from your misunderstandings of statistics - which are legion - and your inability to accept that below-random results on a multiple choice exam is a strong indicator of too-attractive alternate answers (the whole idea of testing mathematics with multiple choice exams is wrongheaded, of course) , nobody has any idea of your point.  What specific action are you proposing?  For example, should girls not be admitted into college - despite the fact that they perform better there than boys on average - because their SATs are lower?  - DvF


Title: Re: assuming too much math knowledge?
Post by: ratiosrule on December 23, 2008, 08:36:08 PM
My syllabus for Statistics now contains the following phrases:

"Will I pass this class?

That depends on your arithmetic skills. In particular, you need to know how to change 0.575 to a percent and how to change 47.2% to a decimal. You also need to be able to tell me which is larger, 0.006 or 0.052. If you cannot do these things, I am telling you on day one of the class that I do not expect you to pass the class unless you spend a  substantial amount of time in the learning center beginning today."

You would be amazed how many of my students think 0.006 is larger than 0.052. This makes p-values difficult to discuss.

I love this, Wittgenstein! I must adopt a similar statement -- in my math classes!


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 23, 2008, 08:39:37 PM
How much more patient can someone be with someone who keeps saying STFU, who appears to have an educator's rather than a scientist's view of statistics, and many of whose students probably understand probability and statistics better than him?

Just to be absolutely clear, I am a university educator and also a researcher in a STEM field with 30 years of publications in fields including Mathematics, Statistics, Biostatistics, and Computer Science.  I believe cgmathfunguy is similarly credentialed, but if not he is right nevertheless.

Aside from your misunderstandings of statistics - which are legion - and your inability to accept that below-random results on a multiple choice exam is a strong indicator of too-attractive alternate answers (the whole idea of testing mathematics with multiple choice exams is wrongheaded, of course) , nobody has any idea of your point.  What specific action are you proposing?  For example, should girls not be admitted into college - despite the fact that they perform better there than boys on average - because their SATs are lower?  - DvF

Explain.

Exactly how can girls "perform better there than boys on average - because their SATs are lower"??

If their "SATs are lower", then they certainly cannot "perform better there than boys on average", can they?

Did you read that Howard Wainer study?  Do you know the phenomenon I'm referring to?

As an employer, I know how wildly and arbitrarily grades are awarded.  The only real objective measurements, at least to an employer, are scores like SAT (and GRE, TIMSS, NAEP, IAEP, PISA, etc.).

You have heard of affirmative action, right?  I know that 78% of college professors in California can't even define it properly, but your presence on this forum suggests you might have a little better understanding of how affirmative action works than them?

Even AFTER we OUTLAWED affirmative action in California, the UC system got caught DISOBEYING the law, as they had been for several years before they got caught.

<<<At UC Berkeley, where it's called "comprehensive review," the system is under attack. A study last month commissioned by UC Board of Regents Chairman John Moores and reported by the Los Angeles Times found that in 2002 Berkeley admitted 375 students with SAT scores between 600 and 1000, and rejected about 3,200 students with SAT scores above 1400.>>>

<<<Data subsequently released by the University of California show that UC Berkeley and UCLA in the past two years collectively have rejected more than 10,000 applicants who scored above 1400 (out of a possible 1600) on the SAT. That's nearly half the applicants in that category who applied to Berkeley, and nearly a third of those who applied to UCLA.>>>

Do you like that?  Is that something that you believe a just nation should engage in?  Does none of this matter when you have just one TA who defies all the odds?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 23, 2008, 09:52:48 PM
Exactly how can girls "perform better there than boys on average - because their SATs are lower"??

In college.  Girls perform better in college, have done for years.  Please read my posts before frothing off at the mouth.  Oh, and don't forget the two exercises I've set you: first, the elementary statistics problem; and second, an articulation of your point. - DvF


Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 23, 2008, 10:11:01 PM
[I know I will regret this, but I'm going to jump in here anyway]

Jacobisrael, 

In addition to the excellent points made by DvF, Cfunmathguy, and others, have you even considered the fact that all of those test scores don't matter if the tests are testing the wrong things or are effectively comparing apples, cheese, and screwdrivers?

I am touched by your firm belief that any one particular test given at one particular moment in time tells us everything we need to know about people's ability to function as competent adults later in life.  Yes, no one ever does poorly on random standardized tests that cover material that hasn't yet been taught to the testtakers or is irrelevant to the real-world tasks that one wants people to be able to do.  Success only means doing well on timed, closed-book tests.  The ability to think logically, use references appropriately, and pick the right tool for the job means nothing in terms of success in school or life.

Every so often your true agenda peeks out with the rants against affirmative action.  Apparently, women, people with certain levels of melanin, and people who have specific accents are all just lost causes and should be dismissed out of hand.  Therefore, the few outliers can be safely ignored as irrelevant.  I hope that you aren't teaching anywhere with that attitude and certainly not statistics, logic, rhetoric, or composition based on your posts here.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 24, 2008, 12:10:25 AM
[I know I will regret this, but I'm going to jump in here anyway]The ability to think logically, use references appropriately, and pick the right tool for the job means nothing in terms of success in school or life.

This is a breathtaking admission.

And of course you'll claim I'm singling you out simply because you're a "minority" [even though 52% of our population are women and only 48% men].

What you discard as irrelevant happens to be EXACTLY, *precisely*,  where the rubber meets the road.  Yet, you probably will never know that, and your cohorts will be groveling all over the floor to prove you right.

In a competitive "global economy", when you throw all that out, and our competitors don't, we're history, plain and simple.  That's not even economics 101.

However--that's not the original point, nor the original theory.  What you suggest for the reason for the gender gap between American girls and Norwegian boys being 3.6 S.D. is in my view only a partial explanation, if it's applicable at all.

But as an educator, you might have some insights here that might be valuable to our understanding our problem.  Do you believe this is the only explanation?  Do you believe that the only reason Norwegian boys scored so high is their "ability to think logically, use references appropriately, and pick the right tool for the job", whereas American girls don't?  Or can't?  Or don't want to?

Since you raise this theory, could you elaborate on it? Why do you believe this would be the case?  Do you believe this is the result of poor education policy on our part, or an innate ability in Norwegians?  Do you believe we can change our education policy to improve the situation, or do you believe we're doomed to oblivion?







Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 24, 2008, 12:43:15 AM

Not every step along the way is necessarily cumulative, but it's also
not impossible that the total number of standard deviations of
separation between American black females in DC and boys in Norway is
a total of 14 to 18.5 standard deviations.

It is if we're assuming anything even remotely like a normal distribution.  Getting outside of three standard deviations is very unlikely (three-tenths of a percent); getting outside of 10 or 12 is a miracle of Biblical proportions.

So you don't believe Obama when he says his IQ is 132?

Great point.

In 2003, 3 African nations, Ghana, s. Africa, and Botswana participated in TIMSS physics.  The average score for the 5,150 students in Botswana who took the test was 443, seven of whom scored over 505, and none of whom scored over 549.  The average score for the 8,952 students in South Africa who took the test was 244, thirteen of whom scored over 447, and none of whom scored over 514.  So also in Ghana, where the average score for their 5,100 students was 239, seven of whom scored over 427, and none of whom scored over 514.

Conversely, the average score for the 6,018 students in Singapore was 579, eight of whom scored lower than 462, and none of whom scored lower than 423.  At best we can say that eight students in Singapore MAY have scored lower than SEVERAL of the thirteen highest scoring students in South Africa and SEVERAL of the seven highest scoring students in Ghana.  No student in Singapore scored 4 standard deviations higher than their mean, or 735, much less 5 standard deviations higher, at 774.

So needless to say, no student in Botswana, South Africa, nor Ghana ever scored four standard deviations higher, or 549, 514, or 489, respectively, either, much less five standard deviations higher, or 593, 581, or 551 respectively.  Such scores are in the range of the average for Taipei and Korea, whose IQs are in the range of 105 IQ points.  It simply boggles the imagination for us to be expected to believe that Obama was the ONE Kenyan in the entire world who scored not just one but TWO standard deviations higher than a place where NO Ghanan, Botswanan, or South African has ever ventured.  To claim that his IQ is 132 IQ points, yet another three standard deviations higher than the impossible, is the height of absurdity.  Yet that’s exactly the claim that his presidential campaign made and you should be embarrassed to the hilt to see so many of your fellow countrymen fall for this circus act.

The average IQ of Kenya is 71 IQ points, the same as for Ghana, and 1 point lower than both Botswana and South Africa, at 72 IQ points.  Out of 38 million Kenyans, do you know how many score more than 5 standard deviations higher than that?  Only 11 do, at an IQ of only 96 IQ points, four standard deviations higher than their mean, and NONE have an IQ higher than 101 IQ points, five standard deviations higher than the mean.  [Edited because of offensive language. -moderator]

California voters consider affirmative action to be CHEATING, which is why we outlawed it with Proposition 209 which actually amended the state constitution for the express purpose of KILLING it.  Obama is clearly left over from those days.

Why not simply require him to take the normal IQ test which any dog catcher in the country has to take in order to qualify for his job?

You can bet that this would settle the matter once and for all.

Correction, Tues. Dec. 23, 2008: 7% of the population of Botswana are Whites who score similar to their brethren back in England at 545, meaning that the 93% who’re blacks scored 358.  Only seven black students from Botswana scored over 456 and none of them scored over 514.  Therefore, none of the lowest scoring eight students in Singapore who scored lower than 462 are likely to have scored lower than the seven top scoring black students from Botswana, meaning there was no overlap of test scores between Singapore and Botswana.

 



Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 24, 2008, 01:30:49 AM
[I know I will regret this, but I'm going to jump in here anyway]The ability to think logically, use references appropriately, and pick the right tool for the job means nothing in terms of success in school or life.

This is a breathtaking admission.

Sorry, I forgot that your sarcasm meter was probably broken.  No, of course I don't believe that, but your posts about minutiae on this one stupid test lead me to think that you believe that.

And of course you'll claim I'm singling you out simply because you're a "minority" [even though 52% of our population are women and only 48% men].
*chuckle*
Oh, I don't even know where to begin on this one.  I have a Ph.D. in engineering.  Professionally, I am surrounded by men, many of them foreign nationals from the countries you cite, every single day.  I can play with the big boys who are, according to you, better educated than I am and not get crushed.  Bring it on.


What you discard as irrelevant happens to be EXACTLY, *precisely*,  where the rubber meets the road.  Yet, you probably will never know that, and your cohorts will be groveling all over the floor to prove you right.
Yes.  Please continue to make my point for me.

In a competitive "global economy", when you throw all that out, and our competitors don't, we're history, plain and simple.  That's not even economics 101.

And there is my point.  The American educational system, unlike those in many of the countries that score higher than the US on this particular test does not educate primarily for rote memorization on one test.  We do not educate for specialization in high school, unlike nearly every European country.  Yet somehow, we do somehow manage to graduate people who are creative thinkers able to do great things if allowed to acquire the necessary tools for the job.


However--that's not the original point, nor the original theory.  What you suggest for the reason for the gender gap between American girls and Norwegian boys being 3.6 S.D. is in my view only a partial explanation, if it's applicable at all.

Must I really hammer again on the "don't compare apples to screwdrivers" argument?  (1) Standard deviation doesn't mean what you appear to think it means.  (2) Since I didn't suggest a reason for the gender gap between American girls and Norwegian boys, I'm completely clueless about how it would be a partial explanation.

But as an educator, you might have some insights here that might be valuable to our understanding our problem.  Do you believe this is the only explanation?  Do you believe that the only reason Norwegian boys scored so high is their "ability to think logically, use references appropriately, and pick the right tool for the job", whereas American girls don't?  Or can't?  Or don't want to?

Sorry, I'll try to type slower and use fewer big words this time.  I don't believe that the TIMSS test indicates anything other than the fact that some groups of people have the skills to do better on this one test this particular sitting of it than other groups.  However, scores on the test mean nothing about how well any of those groups of people would actually do in a real world setting--which apparently you agree is the true test of education. 

Since you raise this theory, could you elaborate on it? Why do you believe this would be the case?  Do you believe this is the result of poor education policy on our part, or an innate ability in Norwegians?  Do you believe we can change our education policy to improve the situation, or do you believe we're doomed to oblivion?

I grew up in an area where the dominant heritage was Norwegian so I assure you that it's not some innate genetic ability.  The Norwegian educational system is vastly different from the American system.  I'm not really sure what your purpose is in continuing to claim that the comparison between the Norwegian students who are specialized in math and science at the middle-school and high-school level and the general American population that hasn't specialized yet is valid.  It's not.  It doesn't matter.  Our best graduates can compete with the best graduates anywhere.  The fact that our future English and history majors are not as good as the future engineers and scientists of other countries at science and math doesn't bother me.

I think a very telling piece of evidence is the flow patterns between countries for higher education.  Which way does that flow go?  If the American system were really extremely poor, why would so many of the top students from other countries come here for their postsecondary education?  That's another case of where the rubber meets the road.


Title: Re: assuming too much math knowledge?
Post by: bryanalwright on December 24, 2008, 06:54:34 AM
I think you better give your student an extra task to motivate her study algebra. Like writing a paper about it. I don't think she's dumb. She just missed the opportunity to learn about it.


Title: Re: assuming too much math knowledge?
Post by: egilson on December 24, 2008, 08:42:12 AM
Folks, why in the world are you feeding this troll?


Title: Re: assuming too much math knowledge?
Post by: prytania3 on December 24, 2008, 10:11:37 AM
I am not sure that some of them even know that the concept of order of operations exists.

Order of Operations

Please
Excuse
My Dear
Aunt Sally

1st solve what is in Parentheses
2nd do the Exponents
3rd Multiply and Divide
4th Add and Subtract


Title: Re: assuming too much math knowledge?
Post by: prytania3 on December 24, 2008, 10:19:58 AM


Wow.

I'm sorry, but this has turned into the land of dead kittens.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on December 24, 2008, 10:50:53 AM


Shh... I've discovered that they deep-fry really well.

<grabs a basket of popcorn kittens and a very large Pepsi>

<with an innocent look on his face>

Please go on. This is fascinating!

Alan


Title: Re: assuming too much math knowledge?
Post by: jonesey on December 24, 2008, 11:29:47 AM
When did the PR flack for Stormfront start posting in the CHE? 

I go away for a bit to fiddle with SPSS and when I come back someone's trying to start a Race War.

Be honest, you don't interview anyone for a job, let alone give the IQ tests.  It doesn't take a high IQ to spray paint a swastika or shoot rifles while listening to Skrewdriver in your wife-beater tank top.

Go back to your Coeur d'Alene compound. 


Title: Re: assuming too much math knowledge?
Post by: kiana on December 24, 2008, 04:38:51 PM


Someone's never heard of hybrid vigor either.

Edited: I'm being rather sarcastic in response to his allusions to livestock breeding, which he clearly knows nothing about. I hope noone would think I was serious, but felt I had to add.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 24, 2008, 05:00:23 PM
Pry:  I hadn't seen that mnemonic before; it is delightful.

Quote
I think a very telling piece of evidence is the flow patterns between countries for higher education.  Which way does that flow go?  If the American system were really extremely poor, why would so many of the top students from other countries come here for their postsecondary education?

We could also count Nobel Prizes in Physics.  (How many have gone to Norwegians?  And where did he do his higher education?)  Of course, this is only somewhat better as a test of the US educational system than standardized multiple-choice tests.

Sorry all for feeding the troll, especially as I was probably the first to call for his starvation back after his first post.  For a while I thought he was serious, and not just another mindless angry troglodyte. - DvF


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 25, 2008, 09:46:44 AM
Pry:  I hadn't seen that mnemonic before; it is delightful.

Quote
I think a very telling piece of evidence is the flow patterns between countries for higher education.  Which way does that flow go?  If the American system were really extremely poor, why would so many of the top students from other countries come here for their postsecondary education?

We could also count Nobel Prizes in Physics.  (How many have gone to Norwegians?  And where did he do his higher education?)  Of course, this is only somewhat better as a test of the US educational system than standardized multiple-choice tests.

Sorry all for feeding the troll, especially as I was probably the first to call for his starvation back after his first post.  For a while I thought he was serious, and not just another mindless angry troglodyte. - DvF

And the answer is?

Affirmative action.

The average IQ of India is 81 IQ points, perfectly in line with their average income of $79 per month.

So what happens to Indian students who're too stupid to get into med or veterinarian schools in India?

They come here where they are all readily admitted through affirmative action.

Does that make them smarter.  Absolutely not.  Do they then qualify as  "many of the top students from other countries [who] come here for their postsecondary education"?

Did you know that 85% of the top patent holders of AMERICAN patents are JAPANESE, not Indians?  Nor Americans.  Do THEY "come here for their postsecondary education"?  No.  Their "top students" already scored two standard deviations higher than their AVERAGE students at the 8th grade, their AVERAGE student already scored a standard deviation higher than us by the 8th grade, the REAL competition in education there begins after that, and we don't even know how well they do by the 12th grade because no Asian country even participated in TIMSS at that level.  There's NOTHING a "top student" from Japan could learn here.  In the semiconductor industry, Japan is already two generations ahead of us, and Korea is another generation ahead of Japan.  95% of their high school students FINISH calculus, while less than 5% of ours TAKE calculus "OR pre-calculus".

Funny that you should mention Nobel Prizes.  Per million people, Norway has won 2.4 of them, more than twice as many as us.  As well as ten times as many Olympic Gold Medals as us, and 403 times as many as Kenya.



Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 10:07:36 AM
When did the PR flack for Stormfront start posting in the CHE? 

I go away for a bit to fiddle with SPSS and when I come back someone's trying to start a Race War.

Be honest, you don't interview anyone for a job, let alone give the IQ tests.  It doesn't take a high IQ to spray paint a swastika or shoot rifles while listening to Skrewdriver in your wife-beater tank top.

Go back to your Coeur d'Alene compound. 

Please, I've lived near Coeur d'Alene.  Even those people have standards for engagement that aren't met by our newest ... forumite.

Now on the order of operations argument, apparently that's becoming a lost art.  I was using Excel one day (stop snickering) and kept getting strange plots.  Well, eventually I tracked down the problem to the fact that while parentheses are evaluated first, all the other operations went in order from left to right, which did very bad things because my exponential operations happened to be last and the base was raised to an additive power.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 25, 2008, 10:13:39 AM
[I know I will regret this, but I'm going to jump in here anyway]The ability to think logically, use references appropriately, and pick the right tool for the job means nothing in terms of success in school or life.

This is a breathtaking admission.

Sorry, I forgot that your sarcasm meter was probably broken.  No, of course I don't believe that, but your posts about minutiae on this one stupid test lead me to think that you believe that.


Sarcasm?

That is NOT a good idea on an internet forum.

Before replying to the rest of your erroneous assumptions, why don't you quit playing games and explain EXACTLY what you meant by the remark?

No, never mind.  Let's address this one first:

<<<And there is my point.  The American educational system, unlike those in many of the countries that score higher than the US on this particular test does not educate primarily for rote memorization on one test.  We do not educate for specialization in high school, unlike nearly every European country.  Yet somehow, we do somehow manage to graduate people who are creative thinkers able to do great things if allowed to acquire the necessary tools for the job>>>


Have you seen the test questions which were posted?  Can you point out which is NOT the result of reasoning rather than "rote memorization"?

I'm in the semiconductor industry.  Do you have any idea how many people in my industry can't answer these BASIC questions?  Or how long they would last if they can't?

Do you know WHERE all our semiconductors are made now?  The same place ALL our cars, and EVEN SHOES, are made now?  And it's NOT HERE?

Because of our poor education system?  Of course.

The following table of top AMERICAN patent holders didn't post properly--the first figure is the number of patents, the second is the percent of the total, and the third is the percent which are held by Japanese?  Can you read that table?  Can you tell us why so FEW Americans are top patent holders?

Even though Motorola is listed as having no Japanese patent holders, I can tell you that in my industry, 99% of the top scientists in AMERICAN companies are ASIAN engineers:

International Business Machines Corp.
 1,867
 17.1%
  17.1%
 
Canon Kabushiki Kaisha
 1,541
 14.1%
 14.1%
 
Motorola Inc.
 1,064
 9.8%
  9.8%
 
NEC
 1,043
 9.6%
 9.6%
 
Hitachi, LTD
 963
 8.8%
 8.8%
 
Mitsubishi Denki Kabushiki Kaisha
 934
 8.6%
 8.6%
 
Toshiba Corporation
 914
 8.4%
 8.4%
 
Fujitsu Limited
 869
 8.0%
 8.0%
 
Sony Corporation
 855
 7.9%
 7.9%
 
Matsus***a Electric Industrial Co., Ltd.
 841
 7.7%
 7.7%
 
Percent of Patents
 10,891
 100.0%
 73.1%
 
 


Title: Re: assuming too much math knowledge?
Post by: galactic_hedgehog on December 25, 2008, 10:58:41 AM
[I know I will regret this, but I'm going to jump in here anyway]The ability to think logically, use references appropriately, and pick the right tool for the job means nothing in terms of success in school or life.

This is a breathtaking admission.

Sorry, I forgot that your sarcasm meter was probably broken.  No, of course I don't believe that, but your posts about minutiae on this one stupid test lead me to think that you believe that.


Sarcasm?

That is NOT a good idea on an internet forum.

Works for me.

(I would have been more sarcastic, but I wanted to be inclusive.)


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 25, 2008, 11:05:39 AM
Actually, Japan has really fallen off the turnip truck since that chart was first made.  Today, "only" 46% of the top 25 holders of AMERICAN patents are Japanese, Koreans are 9%, Germans 5%, and Dutch 2.5%.

This leaves 38% for "American" patent holders of AMERICAN patents, with the caveat that NONE of the top scientists and engineers I deal with in "American" companies are actually Americans--they are almost all ASIANS, with a few Iranians sprinkled in (giving you an idea of just how perverse affirmative action really is).  It would be extremely conservative to say that 4% of that 38% are Americans and the rest or 34% Asians [mostly not even American "citizens" either].

In this technological age, if you don't know calculus, you don't get patents.  And if you don't learn it by high school, your chances of learning it approach zero fast:

1 INTERNATIONAL BUSINESS MACHINES CORP -- 3651
2 SAMSUNG ELECTRONICS CO LTD KR -- 2453
3 CANON K K JP -- 2378
4 MATSUs***A ELECTRIC INDUSTRIAL CO LTD JP -- 2273
5 HEWLETT-PACKARD DEVELOPMENT CO L P -- 2113
6 INTEL CORP -- 1962
7 SONY CORP JP -- 1810
8 HITACHI LTD JP -- 1749
9 TOSHIBA CORP JP -- 1717
10 MICRON TECHNOLOGY INC -- 1612
11 FUJITSU LTD JP -- 1513
12 MICROSOFT CORP -- 1463
13 SEIKO EPSON CORP JP -- 1205
14 GENERAL ELECTRIC CO -- 1051
15 FUJI PHOTO FILM CO LT D JP -- 918
16 INFINEON TECHNOLOGIES AG DE -- 904
17 KONINKLIJKE PHILIPS ELECTRONICS NV NL -- 901
18 TEXAS INSTRUMENTS INC -- 884
19 SIEMENS AG DE -- 857
20 HONDA MOTOR CO LTD JP -- 836
21 SUN MICROSYSTEMS INC -- 776
22 DENSO CORP JP -- 770
23 NEC CORP JP -- 744
24 RICOH CO LTD JP -- 695
25 LG ELECTRONICS INC KR -- 695





Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 11:10:06 AM
WARNING!  WARNING!  WARNING!  This is the final warning to put your kittens in a safe place and break out your balloon animals or <whisper so Grasshopper can't hear> snacks of choice.  This thread is about to go BOOOM!

Sarcasm?

That is NOT a good idea on an internet forum.

Hmmm.  I hadn't considered that.  Why do you think that is?  Are Americans incapable of using sarcasm effectively in a global setting?  Are we sarcasm deficient and just watching our feeble attempts makes people from other countries feel embarrassed for us?  I would like your thoughts on this matter.

Before replying to the rest of your erroneous assumptions, why don't you quit playing games and explain EXACTLY what you meant by the remark?

<aside to the viewers at home>  He don't know me very well, do he?  Imagine just asking me to do something like that.

You want me to explain EXACTLY what I meant by that remark?  What remark?  Whose remark?  I don't know.  THIRD BASE!



Have you seen the test questions which were posted?  Can you point out which is NOT the result of reasoning rather than "rote memorization"?

Pointing is not polite.  Did you just ask me to be impolite?  I must refuse on the basis that my mama didn't raise me to be lead astray by the first troll man who came along.

I'm in the semiconductor industry.  Do you have any idea how many people in my industry can't answer these BASIC questions?  Or how long they would last if they can't?

518.5.  The 0.5 comes from Edgar who can but only when his coin is in good working order.   George, Frieda, and Emile can when they haven't been drinking.  Jorge, Hassan, Ramona, and Iris can, but they don't feel that tests adequately reflect their abilities, so they won't. 

3.76 months on average with a standard deviation of two years.  It's a skewed distribution, but, hey, waddaya gonna do?


Do you know WHERE all our semiconductors are made now?  The same place ALL our cars, and EVEN SHOES, are made now?  And it's NOT HERE?

And by HERE, you mean, my office?  Well, of course not.  The rolltop desk and the three filing cabinets hardly fit.  How would I add a whole car assembly line?  Your basic reasoning skills are failing you.  Silly man, thinking he could fit an assembly line into an 8x8x10 ft office.

Because of our poor education system?  Of course.
Yep, because manufacturing requires huge levels of education while design is so easy even a child can do it.  Let me just break out my legos and spirograph to get Blocky on the road to success.

The following table of top AMERICAN patent holders didn't post properly--the first figure is the number of patents, the second is the percent of the total, and the third is the percent which are held by Japanese?  Can you read that table?  Can you tell us why so FEW Americans are top patent holders?

Yep, yep, and yep.  Can you explain why you have two questions, but three question marks?  Yes, even with my poor American education, I can identify a table.  Do I get extra points for that?

You have selected one particular industry to give statistics from INTERNATIONAL companies who filed AMERICAN patents to protect their interests in the American market.  My basic reasoning skills tell me not to be shocked about one carefully selected data point that supports one's argument.  Many patents filed with the American patent office are to protect the interests of INTERNATIONAL companies in one of the biggest markets in the world.  So what?

Hey, let's continue to play games with basic reasoning skills.  The game is seven card stud, high low, reverse hold card is wild, last card comes up or down on a Communist option.  Ready?



Title: Re: assuming too much math knowledge?
Post by: yellowtractor on December 25, 2008, 11:17:47 AM
I resent the implied criticism of Ramona.  I know Ramona.  She's a valued coworker, a kind heart, and a team player.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 11:20:18 AM
I resent the implied criticism of Ramona.  I know Ramona.  She's a valued coworker, a kind heart, and a team player.
But she refuses to take the test or ante.

King of Clubs has first bet.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 12:56:23 PM
I see your white chip and raise two blue ones.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 25, 2008, 01:09:17 PM

Sarcasm?

That is NOT a good idea on an internet forum.

Hmmm.  I hadn't considered that.  Why do you think that is?  Are Americans incapable of using sarcasm effectively in a global setting?  Are we sarcasm deficient and just watching our feeble attempts makes people from other countries feel embarrassed for us?  I would like your thoughts on this matter.

Before replying to the rest of your erroneous assumptions, why don't you quit playing games and explain EXACTLY what you meant by the remark?

<aside to the viewers at home>  He don't know me very well, do he?  Imagine just asking me to do something like that.

You want me to explain EXACTLY what I meant by that remark?  What remark?  Whose remark?  I don't know.  THIRD BASE!



Have you seen the test questions which were posted?  Can you point out which is NOT the result of reasoning rather than "rote memorization"?

Pointing is not polite.  Did you just ask me to be impolite?  I must refuse on the basis that my mama didn't raise me to be lead astray by the first troll man who came along.




You ought to know that none of the problems which were posted were memorization questions, and that they were reasoning questions.

There were many memorization questions though, and American girls actually did fairly well there, demonstrating that they were even BETTER at "rote memorization" than Norwegian boys.  They haven't been posted though.

The point about the Asian dominance in OUR patents is that employees in Asian companies are not educated in OUR education system which you think is doing so well.  The fact that the percent of AMERICAN companies who hold AMERICAN patents dropped  from 65% to less than 40% SHOULD give you a clue that "education" here is not working as you claim it is, or at least think it is.  

No Asian company would agree with you that they are an "international" company.  Just because they sell stuff here doesn't mean you'll ever see their intellectual property no matter how many patents they file.

You may have missed the link to the Digest of Education Statistics which shows that, contrary to the claims on this forum that we have a high rate of educating students, more than ONE MILLION 18 year olds annually don't even graduate from high school, compared to 93% in Norway, Belgium and Finland who DO, 97% in Sweden who DO, and 94% in Japan who DO.  Wherever that sheer misleading rumor started, it ought to END here:

http://nces.ed.gov/pubs2001/2001034.pdf

Additional proof that nobody's knocking the doors down to be educated here as you believe, the above url shows that the percent of 22 to 25 year olds enrolled in postsecondary institutions in the US is no higher than most other industrialized nations, and in fact is significantly lower than Finland, Denmark, Norway, and even Spain.

iow, even Spain has more students knocking down their doors than we do.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 01:17:41 PM
So the board is right?  Great. 

<deals another card to everyone>

Suited king and jack of clubs still bets.


Title: Re: assuming too much math knowledge?
Post by: toda2 on December 25, 2008, 01:18:58 PM
Math knowledge is not highly valued in many classrooms around the country, and students as well as some teachers "delegate" the skill to TI calculators. By so doing, they are essentially throwing out the substantial part of logical training. You can find very basic mistakes e.g., 1/p+1/q=2/(p+q) even in a graduate student's exam.

Toda


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 25, 2008, 01:24:57 PM
Funny that you should mention Nobel Prizes.  Per million people, Norway has won 2.4 of them, more than twice as many as us. 

Not in the sciences.  It is certainly true that Norwegian writers have won the Literature Nobel way out of proportion to their population.

Our higher education system is the envy of the world.  I did recently visit a colleague in Oslo, and will admit that their office chairs are far more comfortable than ours.

Jonesey, I think you've got it about right. - DvF


Title: Re: assuming too much math knowledge?
Post by: toda2 on December 25, 2008, 01:34:18 PM
I think average quality of math/science education in public schools is not directly related to high achievements such as Nobel prizes. The fact that US has resources to attract the best and brightest minds from around the world, is the most significant factor, not the excellence in education.

Toda


Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 01:43:46 PM
Toda2 has upped the ante.  Do I see another blue chip from the suited king-jack showing?


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 25, 2008, 05:44:04 PM
[quote author=jacobisrael

For another view of it, let's look at your classroom. In a large lecture class, grades tend to be distributed "normally". This being the case, "curving" (with its true meaning) would assign Cs to the 68% of the students whose scores are within 1 SD of the mean. So, let's assume that the mean on Test 1 was 75 with a standard deviation of 8. So, any student with a score between 67 and 83, inclusive, should get a C. However, Susie with her 81 and Johnny with his 69 both got Cs! Is the difference significant? We don't know until we run tests on the scores. Even though the difference is 12 points (which is 1.5 SD), it is likely that this difference is NOT "statistically significant" at any appreciable level. To constantly quote raw numbers with no test results is worthless and misleading. Even those with an agenda don't do this because they know they will be accused of trying to bamboozle the people reading the report.

Take a stats class, and then come back into the discussion.

You complain about referring to different cohorts, then launch into a comparison between a large lecture room and an international study of hundreds of thousands of students.  You're comparing apples to trucks.

You CANNOT compare these and make any sense out of it. You literally can’t adjust for guesses on multiple choice questions in the “large” lecture hall, but you CAN when there are hundreds of thousands of students taking the SAME test in their own languages.  Do you know what TIMSS is?  Before you invite anyone to “take a statistics class” again, you ought to invite yourself to examine their methodology.  You are as wrong about this as you are about “In the US, we send the vast majority of our students to high school” in the following statement:

"Also, we need to address the differences in systemic student handling. In the US, we send the vast majority of our students to high school; other countries reverse this entirely. Thus, the 12th-grade cohorts aren't even comparable between countries, even though they are presented as such by the media (among many others). While the 4th-grade cohorts may be similar, there is even some question about the comparing 8th-grade cohorts by some. For the two reasons above, I don't believe TIMSS is as valid an indicator of differences between national systems as its exhorters proclaim."

This is patently false.  Fortunately, it’s PROVABLY false.  Our OWN data from NCES claims that 74% of American 18 year olds graduate from high school, compared to more than 90% in most industrialized nations:

http://nces.ed.gov/pubs2001/2001034.pdf

The reason nobody has ever posted a cite which disputes that is that there is no cite, AND TIMSS disputes it in a different direction, claiming that they found that only 63% of American students are in their “TCI”, compared to 82% in Switzerland, 84% in Norway, 75% in Germany, 88% in Slovenia, etc.

http://timss.bc.edu/timss1995i/TIMSSPDF/SRAppA.pdf 

They found that 1,245,594 American children of high school graduation age, 67% of that population, weren’t even IN high school, and thus were never included in our already LOW TIMSS scores.  If the worst students were the ones who weren’t in high school, can you even IMAGINE how low our scores would have been had they been INCLUDED?  If this is the reason you don’t “believe TIMSS is as valid an indicator of differences between national systems as its exhorters proclaim”, you need to use your new-found knowledge to go back and rethink your position.

"I've tried to stay out of this one as DvF has done an admirable job of presenting the points I wanted to make. However, please allow me to add my two cents' worth. First, you are comparing different systems that do different things. You are comparisons are being made between countries where there are NATIONAL curricula, those where there are STATE curricula, and at least one where it is a hodgepodge of STATE and LOCAL curricula. So, we are comparing apples to oranges to pears."

The entire PURPOSE of an international study IS to compare different education systems to each other, which is exactly what TIMSS does.  Just like the entire PURPOSE of a national study like NAEP is to make state to state comparisons to see what works and what fails. It’s not BAD to make international and national comparisons, it’s GOOD.

"Finally, a word about why DvF keeps trying to get you to understand why comparing cohorts is important. Many states have been adjusting/rewriting their regulations (Pennsylvania), their state-mandated tests (Ohio), and their state-mandated curricula (Georgia) for the past decade or more. In mathematics, the National Council of Teachers of Mathematics (NCTM) issued its first set of standards on K-12 mathematics in 1989. This was the first step in the reform process, and several states began the process of reforming state curricula in the early 1990s. Others waited longer. However, the process is not an instantaneous one. As an example, Georgia instituted the Georgia Performance Standards (GPS) in 2003 or 2004. The standards still aren't fully implemented throughout the schools yet, and they won't be for two more years. So, yes, cohort matters, and we need to deal with the data that way. The only fair comparisons about gains and losses in the report's 12th-grade cohort would be to take the 2007 report's 12th-graders and compare that gap (assuming all the other confounding variables didn't exist) to the gap found in the 2003 report's 8th-graders and to the gap found in 1999 report's 4th-graders. This assumes that the tests across that EIGHT-YEAR SPREAD are equivalent."
   
None of which is relevant.  The entire POINT of TIMSS is to make international comparisons, not state to state comparisons.  Your idea that something in our education system was the “first step in the reform process” is the same thing educators have been mimicking for decades, and none of it ever worked.  Furthermore, all American parents I know believe that every single one of these so-called “reforms” only brought us back quicker to the stone age and improved nothing.

TIMSS also proves how SAT scores have been politicized, feminized, manipulated, and watered down to the point they’re no longer credible.  That's why TIMSS will most likely take over as the standard.



Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 06:09:35 PM
So all bets have been placed this round?  Good.  Another up card for the table.

Oooh, king, jack, ten all in clubs has the first bet.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 25, 2008, 09:06:06 PM
TIMSS also proves how SAT scores have been politicized, feminized, manipulated, and watered down to the point they’re no longer credible. 

A few posts ago you were claiming that boys did better on SATs than girls, and that is why we should trust them, instead of college performance, as indicators.  Now you are saying that SATs are "feminized" (whatever that means).  Make up your mind, please.

Here (http://www.huffingtonpost.com/gerald-bracey/is-timss-meaningful_b_147772.html) is a nice interpretation of the TIMSS results by Gerald Bracey:
Quote
It might be good to keep a few things in mind when considering the data:

1. The Institute for Management Development rates the U. S. #1 in global competitiveness.

2. The World Economic Forum ranks the U. S. #1 in global competitiveness.

3. The U. S. has the most productive workforce in the world.

4. "The fact is that test-score comparisons tell us little about the quality of education in any country." (Iris Rotberg, Education Week June 11, 2008).

5. "That the U. S., the world's top economic performing country, was found to have schooling attainments that are only middling casts fundamental doubts on the value, and approach, of these surveys." British economist, S. J. Prais, PISA According to PISA, p. 154 (a terrible title since the chapters, all by European researchers, severely criticize PISA).
- DvF




Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 25, 2008, 09:11:25 PM
Wow.  Remember the limit was three raises for a maximum of a twenty dollars per betting round.  DvF has pushed us near that limit.  Next bet, please.


Title: Re: assuming too much math knowledge?
Post by: kiana on December 26, 2008, 03:00:00 PM
Obama’s not even a Kenyan.  He’s a mixed breed and most mixed breeds of most species are of lower quality and intelligence than the pure breeds (otherwise why don’t mules race in horse races)?

This is the statement I was referencing.

In the first place, a mule is an inter-species crossbreed, not merely a mixed breed. This is why most of them are sterile. I do hope you're not arguing that black people and white people are different species.

In the second place, your statement about mixed breeds of most species being of lower quality and intelligence than the pure breeds is flatly not true. A cross between two pure breeds of livestock will often be significantly stronger and hardier and higher quality than either parent, assuming that the parents were chosen to pass on the desirable qualities to their offspring.  Mules are not racing animals because donkeys are not racing animals, and one of the parents of a mule is a donkey. They are quite a bit more intelligent than either horses or donkeys.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 27, 2008, 12:58:40 PM
TIMSS also proves how SAT scores have been politicized, feminized, manipulated, and watered down to the point they’re no longer credible. 

A few posts ago you were claiming that boys did better on SATs than girls, and that is why we should trust them, instead of college performance, as indicators.  Now you are saying that SATs are "feminized" (whatever that means).  Make up your mind, please.

Here (http://www.huffingtonpost.com/gerald-bracey/is-timss-meaningful_b_147772.html) is a nice interpretation of the TIMSS results by Gerald Bracey:
Quote
It might be good to keep a few things in mind when considering the data:

1. The Institute for Management Development rates the U. S. #1 in global competitiveness.

2. The World Economic Forum ranks the U. S. #1 in global competitiveness.

3. The U. S. has the most productive workforce in the world.

4. "The fact is that test-score comparisons tell us little about the quality of education in any country." (Iris Rotberg, Education Week June 11, 2008).

5. "That the U. S., the world's top economic performing country, was found to have schooling attainments that are only middling casts fundamental doubts on the value, and approach, of these surveys." British economist, S. J. Prais, PISA According to PISA, p. 154 (a terrible title since the chapters, all by European researchers, severely criticize PISA).
- DvF




The so-called "gender gap" in SAT scores is only .7 S.D.

But TIMSS shows it to be as high as 2 S.D.

And NAEP claims that the 7 point "gender gap" in their math scores is "statistically insignificant".

Since us idiot sheeple "don't understand statistics", why don't you oh so "intelligent educators" explain to us exactly how that can be?

In order to try to "narrow the gender gap", SAT added an entire new part to the test which nobody pays attention to, because they cannot be graded objectively.  Can you explain why they would do that?



Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 27, 2008, 01:14:58 PM
[I know I will regret this, but I'm going to jump in here anyway]The ability to think logically, use references appropriately, and pick the right tool for the job means nothing in terms of success in school or life.

This is a breathtaking admission.

Sorry, I forgot that your sarcasm meter was probably broken.  No, of course I don't believe that, but your posts about minutiae on this one stupid test lead me to think that you believe that.

And of course you'll claim I'm singling you out simply because you're a "minority" [even though 52% of our population are women and only 48% men].
*chuckle*
Oh, I don't even know where to begin on this one.  I have a Ph.D. in engineering.  Professionally, I am surrounded by men, many of them foreign nationals from the countries you cite, every single day.  I can play with the big boys who are, according to you, better educated than I am and not get crushed.  Bring it on.


What you discard as irrelevant happens to be EXACTLY, *precisely*,  where the rubber meets the road.  Yet, you probably will never know that, and your cohorts will be groveling all over the floor to prove you right.
Yes.  Please continue to make my point for me.

In a competitive "global economy", when you throw all that out, and our competitors don't, we're history, plain and simple.  That's not even economics 101.

And there is my point.  The American educational system, unlike those in many of the countries that score higher than the US on this particular test does not educate primarily for rote memorization on one test.  We do not educate for specialization in high school, unlike nearly every European country.  Yet somehow, we do somehow manage to graduate people who are creative thinkers able to do great things if allowed to acquire the necessary tools for the job.


However--that's not the original point, nor the original theory.  What you suggest for the reason for the gender gap between American girls and Norwegian boys being 3.6 S.D. is in my view only a partial explanation, if it's applicable at all.

Must I really hammer again on the "don't compare apples to screwdrivers" argument?  (1) Standard deviation doesn't mean what you appear to think it means.  (2) Since I didn't suggest a reason for the gender gap between American girls and Norwegian boys, I'm completely clueless about how it would be a partial explanation.

But as an educator, you might have some insights here that might be valuable to our understanding our problem.  Do you believe this is the only explanation?  Do you believe that the only reason Norwegian boys scored so high is their "ability to think logically, use references appropriately, and pick the right tool for the job", whereas American girls don't?  Or can't?  Or don't want to?

Sorry, I'll try to type slower and use fewer big words this time.  I don't believe that the TIMSS test indicates anything other than the fact that some groups of people have the skills to do better on this one test this particular sitting of it than other groups.  However, scores on the test mean nothing about how well any of those groups of people would actually do in a real world setting--which apparently you agree is the true test of education. 

Since you raise this theory, could you elaborate on it? Why do you believe this would be the case?  Do you believe this is the result of poor education policy on our part, or an innate ability in Norwegians?  Do you believe we can change our education policy to improve the situation, or do you believe we're doomed to oblivion?

I grew up in an area where the dominant heritage was Norwegian so I assure you that it's not some innate genetic ability.  The Norwegian educational system is vastly different from the American system.  I'm not really sure what your purpose is in continuing to claim that the comparison between the Norwegian students who are specialized in math and science at the middle-school and high-school level and the general American population that hasn't specialized yet is valid.  It's not.  It doesn't matter.  Our best graduates can compete with the best graduates anywhere.  The fact that our future English and history majors are not as good as the future engineers and scientists of other countries at science and math doesn't bother me.

I think a very telling piece of evidence is the flow patterns between countries for higher education.  Which way does that flow go?  If the American system were really extremely poor, why would so many of the top students from other countries come here for their postsecondary education?  That's another case of where the rubber meets the road.

You can't hold a conversation in a bucket.

In person, your shuck and jive might be cute, even sexy, even entertaining, but on an internet forum it comes across about as flat as your "irony"--it appears sad, even pathetic.  If you're trying to prove that you "can play with the big boys", you're doing a miserable job of it by avoiding all of the key questions, particularly the ones asking you to explain exactly what you mean by your vague, confusing remarks.

I know lots of "big boys".  If I ask them a simple question like this, they can answer it in seconds without a single arm waving, without jumping up and down even once, without a single irrelevant slur, without trying to distract attention from the original point even once, and without claiming that questions that test reasoning ability simply test "rote memorization".

Are you going to qualify what you meant by that?  Can you at least tell us which question you think tests "rote memorization", why you think so, and post a question which you think would be a better test of reasoning ability than that?

I would think that you would at least realize that the more you obfuscate about this point, the more you prove the original point?


Title: Re: assuming too much math knowledge?
Post by: cc_alan on December 27, 2008, 02:18:10 PM
There are 72 different breeds or species of dogs.  Most of them can be interbred, and in fact entire businesses have been created doing just that.  Can you name just one cross breed which is more viable, desirable, or of better quality or intelligence than the original pure breeds from which they were bred?

My limited understanding of dog breeds is that many pure breeds have physical problems (hip displasia, etc.) that can be minimized with interbreeding.

However, I'm not a dog expert and I've also not stayed at a Holiday Inn Express.

Alan


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on December 27, 2008, 05:23:24 PM
In order to try to "narrow the gender gap", SAT added an entire new part to the test which nobody pays attention to, because they cannot be graded objectively.  Can you explain why they would do that?

The writing part of the SAT is there to determine the level of competency students have in composition.  I do not know of any way to judge a student's writing skills using multiple choice exams, but they can certainly be graded objectively.  In particularly, the people doing the marking use very detailed rubriks, and do not know whether the paper they are marking was written by a male, female, person of color, or anyone else. - DvF


Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 27, 2008, 08:38:15 PM
Are you going to qualify what you meant by that?  Can you at least tell us which question you think tests "rote memorization", why you think so, and post a question which you think would be a better test of reasoning ability than that?

Well, we could return to your complex number question or even the combination question about the books.  Both of them are immediately obvious if one has been taught those concepts and are hugely time consuming to think through if one has to go with pure reasoning.  Indeed, most of the math questions fall into this category; straightforward if one has encountered the concepts and can identify a standard method of approach, but will chew up a lot of time (thereby resulting in a lower score because fewer questions can be completed) if one must start from scratch.  Huh, imagine that.  One gets a very poor score by attempting to reason out many questions and must guess on some because of lack of time, but one obtains a good score if one has encountered many questions of the similar type and can immediately apply the proper method for solution.

Irrelevant anecdote: I competed on the math team in middle and high school in a very rural, poor area because I was one of the best students.  The only reason that I encountered many of these "basic" mathematical ideas before college is because the team had a lot of "reason this out and then I'll show you the fast way" practice sessions with the math teacher.

The science questions are often more amenable to reason, but again, one cannot reason some basic nomenclature or have the time to think deeply about every single question.  If one is familiar with the material, taking the next step is easy.  If one has to start from square one with observations from daily life, well, that person will not be able to complete very many questions.

Many of the questions presented on the TIMSS are perfectly fine for testing reasoning ability among comparably educated populations.  They would also be perfectly fine questions if the students had unlimited time and/or access to reference materials.  However, saying "Explain why people who only have algebra preparation score lower in math than people who have had training in calculus" itself demonstrates a lack of reasoning.

I would think that you would at least realize that the more you obfuscate about this point, the more you prove the original point?

Yes?  No?  Maybe?  Am I unable to answer that because I'm only a poorly educated American woman of mixed heritage or because I have no idea what to do about a statement that ends in a question mark?

So, do you want that last card up or down?  Remember, it's a communist option so you don't have to pay extra either way.


Title: Re: assuming too much math knowledge?
Post by: jacobisrael on December 27, 2008, 09:29:56 PM
Are you going to qualify what you meant by that?  Can you at least tell us which question you think tests "rote memorization", why you think so, and post a question which you think would be a better test of reasoning ability than that?

Well, we could return to your complex number question or even the combination question about the books.  Both of them are immediately obvious if one has been taught those concepts and are hugely time consuming to think through if one has to go with pure reasoning.  Indeed, most of the math questions fall into this category; straightforward if one has encountered the concepts and can identify a standard method of approach, but will chew up a lot of time (thereby resulting in a lower score because fewer questions can be completed) if one must start from scratch.  Huh, imagine that.  One gets a very poor score by attempting to reason out many questions and must guess on some because of lack of time, but one obtains a good score if one has encountered many questions of the similar type and can immediately apply the proper method for solution.

Irrelevant anecdote: I competed on the math team in middle and high school in a very rural, poor area because I was one of the best students.  The only reason that I encountered many of these "basic" mathematical ideas before college is because the team had a lot of "reason this out and then I'll show you the fast way" practice sessions with the math teacher.

The science questions are often more amenable to reason, but again, one cannot reason some basic nomenclature or have the time to think deeply about every single question.  If one is familiar with the material, taking the next step is easy.  If one has to start from square one with observations from daily life, well, that person will not be able to complete very many questions.

Many of the questions presented on the TIMSS are perfectly fine for testing reasoning ability among comparably educated populations.  They would also be perfectly fine questions if the students had unlimited time and/or access to reference materials.  However, saying "Explain why people who only have algebra preparation score lower in math than people who have had training in calculus" itself demonstrates a lack of reasoning.

I would think that you would at least realize that the more you obfuscate about this point, the more you prove the original point?

Yes?  No?  Maybe?  Am I unable to answer that because I'm only a poorly educated American woman of mixed heritage or because I have no idea what to do about a statement that ends in a question mark?

So, do you want that last card up or down?  Remember, it's a communist option so you don't have to pay extra either way.

The whole point of posting that question about the order of the books is that it demonstrated a few things:

A) When only 16% of your students answer such a five part multiple guess question correctly, you prove not that they know nothing about the subject, but that they DO know something--and that something was wrong.

B) Only Austria and Italy had this problem--the rest of the countries at least scored higher than if they'd just guessed.

c) In each and every country, two to three times as many boys as girls answered correctly.

D)  As the "gender gap" increased, the percent of boys AND girls who answered correctly increased--46% of Israeli boys answered correctly, but only 33% of Israeli girls did.

E) As noted before, American girls did very well on the "rote memorization" questions, of which there were plenty, but on the reasoning questions like this (one third of the test) they scored lower than if they'd just guessed.

F) It disputes the assertions that:

1) We can't compare different education systems around the world.

2)  TIMSS was "biased" or "invalid".

3) You need to quote the confidence level to understand the significance.

4) Just like the rest of TIMSS, this question is statistically insignificant.

5) Statistically insignificance implies insignificance.

What does it mean to you that r-squared for correlation of "gender gap" to boys' scores is 0.82?

What other factors do you believe there are, and how much do you believe they influenced the correlation?

Does it tell you anything about how we scored so durn low on 12th grade TIMSS?

Do you believe the assertions on this forum that our children just don't want to learn math are true?  Or do you believe that the purpose of education is to *educate* children, not to blame the failure by grown up adults to educate them *on the children* themselves?



Title: Re: assuming too much math knowledge?
Post by: polly_mer on December 27, 2008, 10:05:28 PM
E) As noted before, American girls did very well on the "rote memorization" questions, of which there were plenty, but on the reasoning questions like this (one third of the test) they scored lower than if they'd just guessed.

I know that DvF answered this question already, but I will give it another go.  Having many people choose an answer at a rate lower than pure chance indicates that they are using a logical method to choose that answer and we should ask what they are doing to choose that answer.

F) It disputes the assertions that:

1) We can't compare different education systems around the world.

2)  TIMSS was "biased" or "invalid".

3) You need to quote the confidence level to understand the significance.

4) Just like the rest of TIMSS, this question is statistically insignificant.

5) Statistically insignificance implies insignificance.


Well, all of those things add up to me to indicate that your reading comprehension isn't good and that you still need a remedial course in statistics.  If the words "Statistically insignificant" doesn't imply "insignificant" to you, I cannot help you.

What does it mean to you that r-squared for correlation of "gender gap" to boys' scores is 0.82?
What other factors do you believe there are, and how much do you believe they influenced the correlation?

We've been over this.  Apparently, I'm not the only one who cannot carry a conversation in a bucket.


Does it tell you anything about how we scored so durn low on 12th grade TIMSS?

Is your current conclusion is that I personally lowered the scores by sheer force of will or is it that we have too many girls taking the test and if we only had Israeli boys, we would do better?  What happened to the Norwegians?  Weren't they the gold standard a couple of posts ago?  I'm sticking by the fact that we scored low in part because the majority of Americans do not take calculus in high school while the majority of students in other countries who graduate from high school do.


Do you believe the assertions on this forum that our children just don't want to learn math are true? 

No.  Have you read any of my other hundred posts on this topic on other threads?  I am a vocal proponent of math and science education for everyone.

Or do you believe that the purpose of education is to *educate* children, not to blame the failure by grown up adults to educate them *on the children* themselves?
Why does the question "Have you stopped beating your wife?" come to mind?

What is your point?  Some children are failed by their school systems and, through no fault of their own, receive a substandard education.  Many of us (including the posters on this thread with whom you keep arguing) are working to fix those systems so that every child will have the opportunity to get a quality education.  Yelling at us for having our heads in the sand about education in the US just makes you look foolish when (A) we are working on fixing the actual problem and (B) you use faulty logic to make specious arguments about a substantially less important issue.

That being said, your arguments, particularly the racist/sexist/nationalist comments irritate the tar out of those of us who are working on bettering education for the masses.  Even if your premises were true (which for the record, a substantial body of evidence indicates they are not), what would that prove?  Would you be happy if we all just threw up our hands and said, "Nope, can't teach any except the select few genetically gifted"?  Does no one teach Twain's Puddin' Head Wilson any more?

I didn't see an answer to my question: do you want that last card up or down or are you folding?


Title: Re: assuming too much math knowledge?
Post by: scheherazade on December 28, 2008, 07:17:35 PM

It's the cross breeds, not the pure breeds, which have these problems, and many others.


This is incorrect. Pure breeds have inherited health problems, the occurrence of which are minimized in mixed breeds. Please see any number of articles on the subject in Dog Fancy, Dog World, Dog's Life, or just talk to your vet.

Or take a high school biology class.


Title: 12th Grade Timss Math Scores
Post by: johnknight on July 26, 2010, 04:01:22 PM
These are the latest TIMSS Math Scores of American 12th grade students.

Comments?

12th Grade,8th Grade,,,,
586,520,Boys,Sweden,,
585,545,Boys,Netherlands,,
585,545,Boys,Bulgaria,,
579,539,Boys,Israel,,
576,545,Boys,Slovenia,,
575,535,Boys,Ireland,,
570,530,Boys,Belgium,,
563,535,Boys,Russia,,
561,472,Boys,Cyprus,,
552,512,Boys,NewZealand,,
548,508,Boys,England,,
547,537,Boys,Hungary,,
547,517,Boys,Thailand,,
546,506,Boys,Scotland,,
540,511,Boys,Denmark,,
525,490,Boys,Greece,,
524,527,Boys,Australia,,
519,548,Boys,Switzerland,,
515,512,Boys,Germany,,
514,569,Boys,CzechRepublic,,
509,496,Boys,Latvia,,
499,526,Boys,Canada,,
492,492,Boys,Spain,,
488,488,Boys,Iceland,,
483,483,Boys,Romania,,
477,477,Boys,Lithuania,,
470,542,Boys,France,,
460,460,Boys,Portugal,,
459,544,Boys,Austria,,
446,502,Boys,UnitedStates,,
434,434,Boys,"Iran,Islamic",,
416,386,Boys,Colombia,,
400,360,Boys,SouthAfrica,,
394,394,Boys,Kuwait,,
632,645,Girls,Singapore,,
587,600,Girls,Japan,,
585,598,Girls,Korea,,
564,577,Girls,HongKong,,
554,567,Girls,Belgium,,
532,545,Girls,SlovakRepublic,,
524,537,Girls,Hungary,,
523,536,Girls,Netherlands,,
523,501,Girls,Norway,,
522,535,Girls,Bulgaria,,
517,518,Girls,Sweden,,
513,526,Girls,Thailand,,
511,524,Girls,Belgium,,
507,536,Girls,RussianFederation,,
507,520,Girls,Ireland,,
496,509,Girls,Israel,,
496,475,Girls,Cyprus,,
490,503,Girls,NewZealand,,
489,504,Girls,England,,
489,478,Girls,Greece,,
487,537,Girls,Slovenia,,
483,494,Girls,Denmark,,
477,490,Girls,Scotland,,
474,532,Girls,Australia,,
473,486,Girls,Iceland,,
470,483,Girls,Spain,,
468,491,Girls,Latvia,,
467,480,Girls,Romania,,
465,478,Girls,Lithuania,,
453,509,Girls,Germany,,
449,449,Girls,Portugal,,
444,543,Girls,Switzerland,,
440,558,Girls,CzechRepublic,,
440,530,Girls,Canada,,
437,536,Girls,France,,
423,527,Girls,US Catholic,,
421,421,Girls,"Iran,Islamic",,
400,390,Girls,Kuwait,,
399,536,Girls,Austria,,
394,384,Girls,Colombia,,
394,349,Girls,SouthAfrica,,
393,497,Girls,UnitedStates,,


Title: Re: assuming too much math knowledge?
Post by: nebo113 on July 26, 2010, 04:37:08 PM
I took and passed two years of algebra and geometry in highschool.  Math is a definite weakness, so I figured out how to avoid it in college.  Then I got to grad school and had to take a quantitative methods course.  The prof kew that many of us were weak in the basics, so she gave us a basic math test, telling us that if we didn't do well on that test, then we probably wouldn't do well in the class.  She was absolutely right!!!  I'm not surprised that liberall arts/social science students are underprepared for OP's class.  I would definitelyrecommend a basic math test at the beginning of thesemester.

Reading this was deja vue all over again!  I could have written every word.  DEFINITELY:  basic math test.



Title: Re: assuming too much math knowledge?
Post by: johnknight on July 26, 2010, 06:16:34 PM
Well, if the following study is accurate, even students who participate in NSF physics programs have exactly the same problem:

http://eaja.net/Documents/TIMSS_NSFphysicsStudy99.pdf

What Table 3 of this report shows is that The less than 140 girls in the NSF Physics program who participated in 12th grade TIMSS performed very poorly in TIMSS physics: 41 points lower than the *average*12th grade girl in Cyprus, 34 points lower than the *average* girl in Greece, 13 points lower than Latvian girls, 68 points lower than Norwegian girls, 52 points lower than Russian girls, 62 points lower than Swedish girls, 19 points lower than Australian girls, 28 points lower than Danish girls, and 32 points lower than Slovenian girls.  And of course compared to boys from all countries (*except* the US whose boys scored 9 points lower than NSF girls) they scored significantly lower than all others:  40 points lower than boys in the NSF physics program, 44 points lower than Canadian boys, 96 points lower than Cypriot boys, 59 points lower than Czech boys,  15 points lower than French boys,60 points lower than German boys, 70 points lower than Greek boys, 54 points lower than Latvian boys, 132 points lower than Norwegian boys, 109 points lower than Russian boys, 131 points lower than Swedish boys, 64 points lower than Swiss boys, 69 points lower than Australian boys, and 69 points lower than the international average.


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on July 26, 2010, 10:46:50 PM
Johnknight, you are posting (in multiple places) US students' (pre higher ed) scores on math tests.  But you are adding no commentary.  So what?  Yes, these may be the students inherited, but what of it?  They are.  Um, thank you.(?)

Let me guess: you are really good at math, but not so much at other social discourse?  The scores bother you, but you don't feel comfortable enough to actually start a discussion other than to post numbers? Sorry, that's not good enough, IMO.  A table presented without commentary is not a discussion starter.


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 27, 2010, 12:04:37 AM
Johnknight, you are posting (in multiple places) US students' (pre higher ed) scores on math tests.  But you are adding no commentary.  So what?  Yes, these may be the students inherited, but what of it?  They are.  Um, thank you.(?)

Let me guess: you are really good at math, but not so much at other social discourse?  The scores bother you, but you don't feel comfortable enough to actually start a discussion other than to post numbers? Sorry, that's not good enough, IMO.  A table presented without commentary is not a discussion starter.

Well, let's put it this way.

The Mean Achievement of the Top 5% of American Physics Students is lower than Girls in Cyprus.  The score of 485 for our top 5% of physics students is only 9 points higher than the TIMSS Physics Base Score of 476 and almost 200 points lower than Sweden's top 5%.

As you might guess, our performance in math and science for the *average* student was even worse.

If that's not a topic starter, what is?


Title: Re: assuming too much math knowledge?
Post by: pigou on July 27, 2010, 12:15:04 PM
That ignores a ton of information, though. For one, you're better off looking at individual US states, rather than the country as a whole. When comparing Louisiana to California, you might as well compare two different countries. I'd wager that the "progressive" states can keep pace with the good European performers.

If we want to evaluate the education system, let's not ignore demographics. Compare, for example, Sweden with Switzerland. Two small, wealthy countries - yet with widely differing results. Do the Swiss have a terrible education system? That doesn't sound likely. However, consider that more than a quarter of Switzerland's population is non-Swiss. In my experience, this is even more of an issue in schools (recent immigrants have more children). Once you consider that the local language already poses a challenge to some students, it's not surprising that they have difficulties learning content. It's also worth noting that students in Switzerland are required to learn 2 foreign language to fluency, so that would necessarily reduce the time available for other subjects that are tested for international comparison. I have no idea if it's a worthy trade-off, but we're clearly not comparing like with like here.

The United States, of course, deals with inner-city issues that can't be addressed by the public school system, yet clearly impact performance. I'd again bet that Sweden has less of an issue with gangs than, say, Chicago.

It's really difficult to compare data between countries, and I more often than not see it done incorrectly. e.g. I saw a chart comparing stimulus spending with GDP growth for the financial crisis. The problem? What's considered "stimulus spending" is hardly universal. Germany, for example, includes funding for existing unemployment benefits, whereas Switzerland's unemployment benefits were already funded. The US included funding for existing medicare obligations, which was neither new spending nor stimulus spending by any stretch of the definition. Or, to put it all more humorously: people in Singapore may be more likely to survive a heart attack than people in the US, but that's because they live closer to the hospital. :)


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 27, 2010, 12:17:03 PM
Johnknight, you are posting (in multiple places) US students' (pre higher ed) scores on math tests.  But you are adding no commentary.  So what?  Yes, these may be the students inherited, but what of it?  They are.  Um, thank you.(?)

Let me guess: you are really good at math, but not so much at other social discourse?  The scores bother you, but you don't feel comfortable enough to actually start a discussion other than to post numbers? Sorry, that's not good enough, IMO.  A table presented without commentary is not a discussion starter.

Since you're so interested in engaging in other social discourse, and since you have such a high interest in my ability or lack there of to communicate, certainly you've studied the following NSF report and can comment knowledgeably on Table 12?

To be specific, in raising and educating several children, my wife and I noticed that calculators, TVs, IPODs, cell phones, and computers actually interfered with their ability to think on their own.  Don't get me wrong, I could not live without a computer and have been very impressed with their abilities ever since using a "mainframe" to calculate 100,000 second order partial differential equations, something that took a guy named Polhausen about ten years to manually do just ten of.

So it was not much of a surprise when I asked her, before showing her Table 12, if she thought that computers improved education, and she relied , "no".  As you obviously know by now, Table 12 proves just that, in spades?

But just for the edification of those who haven't studied this NSF report as closely as you have, what it shows is the remarkable fact that even in the US, those who use computers in "Every Lesson" score only 4 points higher than those who use them only in "Some Lessons".

But that's just the beginning of an interesting revelation.  NSF physics students who use computers in "Every

Lesson" score 14 points lower than NSF physics students who use them "Never or Almost Never", students in Cyprus 28

points lower, and Slovenian students 32 points lower.  And compared to students who use computers in "Most

Lessons", students who "Never or Almost Never" use computers in their physics lessons score 16 points higher in

Canada, 30 points higher in Cyprus, 6 points higher in Denmark, 2 points higher in France, 31 points higher in

Greece, 16 points higher in Latvia, 9 points higher in Russia, and 16 points higher in Slovenia.

So the urban legend that computers dumb down students is no longer a legend.

Furthermore, compared to students who use computers in "Some Lessons", students who "Never or Almost Never" use

computers score 13 points higher in Canada, 54 points higher in Cyprus, 3 points higher in France, 17 points higher

in Greece, and 8 points higher in Slovenia.

Of course you understand that the main point of all this is that the highest scoring American student, the one who

uses computers in "Every Lesson", scores only 435, which is a whopping 100 points lower than a Swedish student who

uses computers just as frequently, and 150 points lower than a Norwegian student who never uses computers at all.

    
This observation is consistent with PISA which shows the same phenomena for 13 year olds, or 8th graders, even in Third World Countries.


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 27, 2010, 12:43:08 PM
That ignores a ton of information, though. For one, you're better off looking at individual US states, rather than the country as a whole. When comparing Louisiana to California, you might as well compare two different countries. I'd wager that the "progressive" states can keep pace with the good European performers.

It would appear from your post that you view California as a "progressive" state and that Lousiana is not, but having lived in both places, and having seen the test scores, I would argue that it's the other way around.  Consistently California has scored at the BOTTOM of the stack on SAT scores (both math and verbal) while Lousiana has often ranked in the top ten.

And the trend shows California is getting much worse very fast.  In 1975, the gap between California and Lousiana in SAT math was only 18 points (491 vs. 473) but by 1995 the gap had grown to 50 points (535 vs. 485).  My bet is that the gap is even bigger today.

You make a good point, though.  It's more useful to examine the extremes, like North Dakota and Rhode Island who are on opposite ends of the SAT spectrum.  In the most recent SAT tests, Rhode Island scored 495 in verbal and 498 in math, vs. 594 and 604 for North Dakota, a gap of  205 SAT points.



Title: Re: assuming too much math knowledge?
Post by: menotti on July 27, 2010, 12:56:25 PM
That ignores a ton of information, though. For one, you're better off looking at individual US states, rather than the country as a whole. When comparing Louisiana to California, you might as well compare two different countries. I'd wager that the "progressive" states can keep pace with the good European performers.

It would appear from your post that you view California as a "progressive" state and that Lousiana is not, but having lived in both places, and having seen the test scores, I would argue that it's the other way around.  Consistently California has scored at the BOTTOM of the stack on SAT scores (both math and verbal) while Lousiana has often ranked in the top ten.

And the trend shows California is getting much worse very fast.  In 1975, the gap between California and Lousiana in SAT math was only 18 points (491 vs. 473) but by 1995 the gap had grown to 50 points (535 vs. 485).  My bet is that the gap is even bigger today.

You make a good point, though.  It's more useful to examine the extremes, like North Dakota and Rhode Island who are on opposite ends of the SAT spectrum.  In the most recent SAT tests, Rhode Island scored 495 in verbal and 498 in math, vs. 594 and 604 for North Dakota, a gap of  205 SAT points.



Students in the midwest take the ACT, not the SAT, to attend local and state schools.  The only people who take the SAT are those headed out-of-state, so they are the most motivated, highest achieving students. 



Title: Re: assuming too much math knowledge?
Post by: johnknight on July 27, 2010, 01:41:20 PM


Students in the midwest take the ACT, not the SAT, to attend local and state schools.  The only people who take the SAT are those headed out-of-state, so they are the most motivated, highest achieving students. 



Of about 2 1/2 million high school graduates, about a million of them, or 40%, take the SAT.  So you're saying that 40% of high school graduates is a select group of the "most motivated, highest achieving students" who aren't representative of the other 60%?

How do we know that the other 60% might not have scored even higher?  Hasn't the goal of affirmative action been to deny the most qualified students admission to college?  Isn't that why the Bush administration joined the affirmative action lawsuit against the University of Michigan?


Title: Re: assuming too much math knowledge?
Post by: midtownlabgeek on July 27, 2010, 01:54:16 PM
But that's just the beginning of an interesting revelation.  NSF physics students who use computers in "Every
Lesson" score 14 points lower than NSF physics students who use them "Never or Almost Never", students in Cyprus 28 points lower, and Slovenian students 32 points lower.  And compared to students who use computers in "Most Lessons", students who "Never or Almost Never" use computers in their physics lessons score 16 points higher in Canada, 30 points higher in Cyprus, 6 points higher in Denmark, 2 points higher in France, 31 points higher in
...

I'm going to go out on a limb here and speculate that the test in question is not computer-based, or doesn't allow computers to be the same way as they are in classes where students use computers "Most Lessons".

In other words, some students were tested under conditions similar to those in which they've been trained, and other students were tested under very different conditions.  My scientific training did benefit from computers, but even I can see that that experiment design has some flaws.

As far as comparing students from different countries - reread the report again, and notice where it says that each country got to test whichever students it wanted.  Some tested a very small fraction (Russia, 1.5%); the USA tested a larger fraction (15%).  There's no mention of whatever they could've done to ensure that every country tested similar samples.

Quote
So the urban legend that computers dumb down students is no longer a legend.

They certainly make it possible to assemble statistics faster, and to cherry-pick data that prove your hypothesis, but that doesn't help much when the experiment was poorly conducted.  It might as well have concluded that "oranges from the USA scored lower than apples from Germany in two separate measures of redness".

On preview:  Affirmative action has nothing to do with this.  Why start a fire if you don't need the smoke?


Title: Re: assuming too much math knowledge?
Post by: pigou on July 27, 2010, 02:28:41 PM
It would appear from your post that you view California as a "progressive" state and that Lousiana is not, but having lived in both places, and having seen the test scores, I would argue that it's the other way around.  Consistently California has scored at the BOTTOM of the stack on SAT scores (both math and verbal) while Lousiana has often ranked in the top ten.
California was, indeed, a bad example. I completely ignored their issue with immigration - of course that should drag down averages. I stick with Louisiana, however: http://nces.ed.gov/nationsreportcard/states/statecomparisontable.aspx?sbj=MAT&gr=8&yr=2009&sample=R3&jur=LA&st=MN

This seems like a better assessment than SAT or ACT scores (as mentioned, they can be fairly selective in who gets tested), and Louisiana ranks #46 in math, for example.


Title: Re: assuming too much math knowledge?
Post by: pgher on July 27, 2010, 04:14:10 PM


Students in the midwest take the ACT, not the SAT, to attend local and state schools.  The only people who take the SAT are those headed out-of-state, so they are the most motivated, highest achieving students. 



Of about 2 1/2 million high school graduates, about a million of them, or 40%, take the SAT.  So you're saying that 40% of high school graduates is a select group of the "most motivated, highest achieving students" who aren't representative of the other 60%?

How do we know that the other 60% might not have scored even higher?  Hasn't the goal of affirmative action been to deny the most qualified students admission to college?  Isn't that why the Bush administration joined the affirmative action lawsuit against the University of Michigan?

What was said by menotti, and what I have seen in the various places I have lived, is that students IN THE MIDWEST who take the SAT are among the "most motivated, highest achieving students."  Everyone else who wants to go to college takes the ACT instead.  So to make a valid comparison between, say, Illinois (a predominantly ACT state) and Pennsylvania (an SAT state), you would need to somehow combine the ACT and SAT results.


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 27, 2010, 05:17:56 PM


What was said by menotti, and what I have seen in the various places I have lived, is that students IN THE MIDWEST who take the SAT are among the "most motivated, highest achieving students."  Everyone else who wants to go to college takes the ACT instead.  So to make a valid comparison between, say, Illinois (a predominantly ACT state) and Pennsylvania (an SAT state), you would need to somehow combine the ACT and SAT results.

What would settle this question is if NAEP would release their math scores by state for the 12th grade test.  Instead, the only thing NAEP scores can tell us about state to state performance are the 8th grade math scores.  And on that test, North Dakota scores at the top at 286, and Rhode Island scores at the bottom at 275.

While this gap of 11 points might seem small , it's actually proportionate to the 100 point gap in SAT math scores, particularly when you consider how much this gap widens between 8th and 12th grade (re: TIMSS math scores).


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 27, 2010, 05:58:50 PM
It would appear from your post that you view California as a "progressive" state and that Lousiana is not, but having lived in both places, and having seen the test scores, I would argue that it's the other way around.  Consistently California has scored at the BOTTOM of the stack on SAT scores (both math and verbal) while Lousiana has often ranked in the top ten.
California was, indeed, a bad example. I completely ignored their issue with immigration - of course that should drag down averages. I stick with Louisiana, however: http://nces.ed.gov/nationsreportcard/states/statecomparisontable.aspx?sbj=MAT&gr=8&yr=2009&sample=R3&jur=LA&st=MN

This seems like a better assessment than SAT or ACT scores (as mentioned, they can be fairly selective in who gets tested), and Louisiana ranks #46 in math, for example.

Thanks for that link which puts Louisiana's public schools NAEP math score 2 points ahead of California (272 vs. 270).

As you aptly point out, there are other considerations which need to be taken into account, like how many minorities are in these school systems, and how many students attend private schools like those in Louisiana which score as much as 30 points higher than the public schools on this table.  One factor which drives California's score down relative to Lousiana is that California's private schools score only about 20 points higher than their public schools.

Ironically, the highest scoring public school students in the nation are Whites  in DC, at 303 (which also has the nation's lowest scoring blacks, at 231), and they score 16 points higher than Whites in Montana, 20 points higher than Whites in Massachusetts, 28 points higher than Whites in Rhode Island, and 37 points higher than Whites in Louisiana.







Title: Re: assuming too much math knowledge?
Post by: johnknight on July 28, 2010, 04:41:21 PM
But that's just the beginning of an interesting revelation.  NSF physics students who use computers in "Every
Lesson" score 14 points lower than NSF physics students who use them "Never or Almost Never", students in Cyprus 28 points lower, and Slovenian students 32 points lower.  And compared to students who use computers in "Most Lessons", students who "Never or Almost Never" use computers in their physics lessons score 16 points higher in Canada, 30 points higher in Cyprus, 6 points higher in Denmark, 2 points higher in France, 31 points higher in
...


As far as comparing students from different countries - reread the report again, and notice where it says that each country got to test whichever students it wanted.  Some tested a very small fraction (Russia, 1.5%); the USA tested a larger fraction (15%).  There's no mention of whatever they could've done to ensure that every country tested similar samples.





You need to study up on how TIMSS determines the schools to be sampled.  They have one of the most disciplined sampling procedures of all these standardized tests.  More than two dozen countries did meet the 12th grade sampling requirements, and all agreed with the results, and the sampling procedures.  Only a few, like the US, didn't meet the sampling requirements and not even our experts disputed their procedures. 

For the record, on this 12th grade study, most European nations had sampling coverage of more than 80%, with the US at anly 27% (and the Asian countries had more than 90% in the 8th grade study)

It could be argued that only the best schools participate in TIMSS, and thus our scores would have been even lower than 393 for 12th grade American girls and 446 for American 12th grade boys if we had met the sampling requirement of 85%.

However, it's hard to imagine how any schools could have scored even lower than that.  This already represents a drop between 8th and 12th grade of 104 points for our girls and 56 points for our boys.  And on these very same tests, Swedish boys' scores increased 66 points and Greek girls' scores increased 11 points.

What is it that schools all the way from Greece to Sweden are doing for their students (both boys AND girls) that we aren't?  Is it even possible that American high schools reduce academic performance by this much, while most foreign schools IMPROVE it by this much?

Or is there another explanation?


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 28, 2010, 07:02:46 PM
Following is some more interesting news about our top NSF physics students from :Table 5 of the following report

http://eaja.net/Documents/TIMSS_NSFphysicsStudy99.pdf

As low as it is, a score of 587 in "mathematics and science literacy" and 595 in "science literacy" is proof that the NSF physics students HAVE been taught the subjects, DO understand the terms, and SHOULD have been able to apply the principles to solving physics problems like those on "electricity and magnetism" where NSF physics students scored only 446, lower than any other country whose students took a physics course.   It's significant that in this age of the semiconductor, sudents in Sweden score 124 points higher, in Norway 119 points higher, and in war-torn Slovenia 63 points higher (while our top NSF female physics student scores another 20 points lower).

Our very best NSF physics student, and in particular our very best female NSF physics student, can’t even begin to compete with the WORST physics students from more than a dozen Western European nations, and can barely keep up with a war-torn Slovenian who hardly has time to worry about physics instruction.  It’s not like we have not been trying—our average physics student already takes between 3 to 5 hours of physics instruction per week, while students in the Czech Republic (with an equivalent score), Germany (43 points higher), Latvia, Sweden (116 points higher), and Switzerland (70 points higher),  take less than 3 hours per week. Notably, the 43% of the NSF physics students who report that they take more than 5 hours of physics instruction score 26 points LOWER than the 6% of the NSF physics student who takes 3-4 hours per week AND than the 45% who take 4-5 hours per week.  Clearly the NSF has selected not the best students, but possibly the worst, and attempted to make up for it by cramming physics down their throats, and failed worse than miserably. 

The NSF could raise its average physics score by 26 points simply by eliminating almost half (42%) of the students from the program who evidently study endlessly but never are able to learn.  If these half were replaced by Swedish students (two thirds of whom take less than 3 hours per week of physics instruction but score 579), not only would they raise their average score by 55 points (plus 26 points), but they would eliminate many frustrated teachers.

In relation to the amount of physics homework assigned to students, the lowest scoring NSF student is one who is assigned homework once or twice a week and scores 455, a score 8 points lower than a Canadian student and equivalent to a Swiss student who is not even taking physics. 


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on July 28, 2010, 08:16:40 PM
My experience, as someone who has taught STEM graduate students from many of the countries who do much better on these tables than US students, is that the students from these countries do not in general do better than the US-educated students, where "better" includes such factors as performance, diligence, creativity, and later success as an academic researcher.  It is not obvious whether what these tests measure is any more meaningful from a long-term POV as, say, measuring the height of 5th-graders is a useful measure of a nation's basketball prowess.

That said, it is interesting to see how the students from various countries stack up on these tests.

There can be many reasons for such relative performance, and it is easy and superficial to jump to conclusions about our educational system.  In fact, I suspect that the US would do very poorly on a test designed to measure how carefully people examine such issues before leaping to conclusions. 

(Moreover, it would be wrong to draw too many conclusions from such a leaping-to-conclusions test.)

It is also interesting that Calculus and Physics can be taught to most high-school-age students, just as can Shakespeare and Civil War History and Auto Mechanics be taught, but this is not surprising to those of us who teach such subjects. - DvF


Title: Re: assuming too much math knowledge?
Post by: polly_mer on July 29, 2010, 07:14:17 AM
It is also interesting that Calculus and Physics can be taught to most high-school-age students, just as can Shakespeare and Civil War History and Auto Mechanics be taught, but this is not surprising to those of us who teach such subjects. - DvF

It's also not surprising to those of us who teach students who come from countries mentioned as doing better on these tests to use information about the differences in the ways that schools are arranged to interpret the data.  Someone who is majoring in chemistry in a German secondary school is probably going to do a lot better on a science test than someone who is taking chemistry in high school because everyone going to college has to take two years of science and much better than someone who is in chemistry class because science is required, but the student's interest is in art.


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 29, 2010, 01:07:33 PM
My experience, as someone who has taught STEM graduate students from many of the countries who do much better on these tables than US students, is that the students from these countries do not in general do better than the US-educated students, where "better" includes such factors as performance, diligence, creativity, and later success as an academic researcher.  It is not obvious whether what these tests measure is any more meaningful from a long-term POV as, say, measuring the height of 5th-graders is a useful measure of a nation's basketball prowess.

That said, it is interesting to see how the students from various countries stack up on these tests.

There can be many reasons for such relative performance, and it is easy and superficial to jump to conclusions about our educational system.  In fact, I suspect that the US would do very poorly on a test designed to measure how carefully people examine such issues before leaping to conclusions. 

(Moreover, it would be wrong to draw too many conclusions from such a leaping-to-conclusions test.)

It is also interesting that Calculus and Physics can be taught to most high-school-age students, just as can Shakespeare and Civil War History and Auto Mechanics be taught, but this is not surprising to those of us who teach such subjects.)DvF

The last year that the US competed in the semiconductor industry was in 1983, when the Japanese (95% of whose high school students graduate with calculus behind them) took over.  Even then, the vast majority of the design engineers of AMERICAN semiconductors were foreign born, mainly Taiwan and China. I actually met NONE who had graduated from American high schools (and now with incomes up so high in Taiwan and taxes relatively low, most of those Taiwanese who went to American universities have returned to Taiwan where they very effectively compete with us, working for companies like TSMC).

For the last three decades, up to 75% of the top holders of AMERICAN patents (all patents, not just semiconductor patents) were Japanese, while Americans hold about zero Japanese patents.

In the semiconductor industry, Korea is now a generation ahead of Japan (who is 2 generations ahead of us), and our chips are now made in just about every other country BUT the US, all the way from Malayasia, to Portugal, to Ireland (where Intel built a plant with almost 5,000 employees), even to Israel.

You can't build chips if you don't know calculus. And only 5% of our high school students even take calculus, and most of those take "pre-calculus" which ain't calculus.  You also can't understand how important it is to have a personal savings rate (Japan's is 33%, Korea's is 38%, Singapore's is 51%, and ours is NEGATIVE) unless you know math.

TIMSS not only proved that our students DON'T know math, but that somehow they managed to leave high school in worse shape than when they left 8th grade.

But then you need to know math to know that.


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 29, 2010, 01:45:43 PM
My experience, as someone who has taught STEM graduate students from many of the countries who do much better on these tables than US students, is that the students from these countries do not in general do better than the US-educated students, where "better" includes such factors as performance, diligence, creativity, and later success as an academic researcher.  It is not obvious whether what these tests measure is any more meaningful from a long-term POV as, say, measuring the height of 5th-graders is a useful measure of a nation's basketball prowess.



With all due respect, with what we've seen from academic researchers, it's a complete and total waste of time for either academia or government to get involved in research.  The US government's grand plan to restore the US semiconductor industry by establishing Sematech to help us compete with the Japanese ended exactly as I predicted it would:  with the Japanese controlling Sematech.  And for the US government to spend $6 billion annually on the NSF to now produce physics students who score lower than Greek girls is the penultimate waste of electrons.  Nothing against Greek girls, it's just that I was at the Parthenon one day when a bunch of male Greek workers (who scored even higher than female Greeks) showed up with a concrete block to attempt to repair the beautiful marble face of the Parthenon, only to end up making it look worse.  Modern Greeks can't even REPAIR, much less duplicate, these magnificent structures built by the ancient Greeks, a bit prescient of our current course.

What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).

[Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points].


Title: Re: assuming too much math knowledge?
Post by: kraken on July 29, 2010, 02:03:08 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.


Title: Re: assuming too much math knowledge?
Post by: conjugate on July 29, 2010, 02:15:02 PM
More to the point, John Knight, what are we supposed to do about it?

I mean, let's suppose for the sake of argument you've convinced me.  I decide that Armageddon for America is imminent, and I head straight to my office, with the fire of determination burning in me.  I get to my cubicle, and I stand there, hands on hips, jutting my jaw determinedly, and...

See, it's the next bit I have trouble with.  I could re-write my syllabi, perhaps.  Recycle more of the papers on my desk?  Ooh!  I know, I'll rearrange my filing cabinet!  That'll teach those Asians who's boss!

It seems to me you've come here, rattling the saber of inadequate high school education, and gotten little response because none of us (well, few of us) are in the position of improving high school education.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on July 29, 2010, 03:24:33 PM
The last year that the US competed in the semiconductor industry was in 1983

This is absolutely false, unless you are talking about simply manufacturing the chips, which requires no special skills other than willingness to work for low wages.

Quote
Even then, the vast majority of the design engineers of AMERICAN semiconductors were foreign born, mainly Taiwan and China.

Also false.  (For the record, I was in Silicon Valley just 3 days ago having dinner with an Intel manager, born in New England.)

Quote
For the last three decades, up to 75% of the top holders of AMERICAN patents (all patents, not just semiconductor patents) were Japanese, while Americans hold about zero Japanese patents.

Absolutely false.  USPTO figures show well over 50% of US patents filed by domestic companies over each of the last 10 years.  This stuff is as easy to look up (as I just did, here (http://www.uspto.gov/web/offices/ac/ido/oeip/taf/cst_utl.htm)) as to make up (as you seem to be doing).

Quote
You can't build chips if you don't know calculus.

Of course you can.  Do you know anything about VLSI design?

Quote
And only 5% of our high school students even take calculus

According to the NAEP it was over 16% in 2005, when the last study was done.  Where are your numbers from, or are you just making stuff up again?

Quote
and most of those take "pre-calculus" which ain't calculus.

Nope.  The number is for actual Calculus.

I thought what you were posting before was somewhat interesting, but you obviously have no clue about any of what you are saying, and I no longer believe any of your numbers, I think you're just making stuff up.  Bye bye. - DvF


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 29, 2010, 06:32:56 PM
The last year that the US competed in the semiconductor industry was in 1983

This is absolutely false, unless you are talking about simply manufacturing the chips, which requires no special skills other than willingness to work for low wages.

Quote
Even then, the vast majority of the design engineers of AMERICAN semiconductors were foreign born, mainly Taiwan and China.

Also false.  (For the record, I was in Silicon Valley just 3 days ago having dinner with an Intel manager, born in New England.)

Quote
For the last three decades, up to 75% of the top holders of AMERICAN patents (all patents, not just semiconductor patents) were Japanese, while Americans hold about zero Japanese patents.

Absolutely false.  USPTO figures show well over 50% of US patents filed by domestic companies over each of the last 10 years.  This stuff is as easy to look up (as I just did, here (http://www.uspto.gov/web/offices/ac/ido/oeip/taf/cst_utl.htm)) as to make up (as you seem to be doing).

Quote
You can't build chips if you don't know calculus.

Of course you can.  Do you know anything about VLSI design?

Quote
And only 5% of our high school students even take calculus

According to the NAEP it was over 16% in 2005, when the last study was done.  Where are your numbers from, or are you just making stuff up again?

Quote
and most of those take "pre-calculus" which ain't calculus.

Nope.  The number is for actual Calculus.

I thought what you were posting before was somewhat interesting, but you obviously have no clue about any of what you are saying, and I no longer believe any of your numbers, I think you're just making stuff up.  Bye bye. - DvF

In 1983, you could buy chips made in Taiwan, after they paid their taxes, shipped them accross the Pacific, paid our import duties (which are very high), at one third the COST of making them in remote, relatively regulation-free like Pocatello, Idaho, and at two or three times the performace.  The price/performance advantage of manufacturing chips off-shore has increased to at least 12x since then, and no semiconductor manufacturer makes them here any more.  Intel is the one company who CLAIMS to be manufacturing them here, but I also can point you to numerous Intel managers who can confirm that none of their local facilities are making money, while all of the off-shore facilities are.  Micronix also claims to be an American manufacturer, but all they do is package chips which are actually manufactured by Samsung in Korea, with their plant in Idaho being a mere prototyping lab.  Japanese don't make chips at one fourth the cost and three times the performance because making chips "requires no special skills other than willingness to work for low wages", because a Japanese engineer will cost you three times what an American engineer will cost you (except they CAN get results and we CANNOT).

The problem with our teaching of calculus won't be understood much less solved by focusing on which scource is correct about what percentage of American students take calculus.  The simple undisputed fact is that our score on calculus for students who HAVE taken advanced math is so low that they MUST have been taught the WRONG thing.  To wit, American 12th grade girls scored 439, which is 101 points lower than Greek men and 97 points lower than Greek women.


They would have scored higher, much higher, if they had just GUESSED.



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on July 29, 2010, 07:27:52 PM
The problem with our teaching of calculus won't be understood much less solved by focusing on which scource[sic] is correct about what percentage of American students take calculus.

"Which source is correct?" I had a source.  You made shit up didn't.  Please use the word "which" correctly on this academic forum.

Nothing to see here folks.  Please move along. - DvF


Title: Re: assuming too much math knowledge?
Post by: polly_mer on July 30, 2010, 08:46:42 AM
The problem with our teaching of calculus won't be understood much less solved by focusing on which scource[sic] is correct about what percentage of American students take calculus.

"Which source is correct?" I had a source.  You made shit up didn't.  Please use the word "which" correctly on this academic forum.

Nothing to see here folks.  Please move along. - DvF

Now, now, Daniel_von_Flanagan, let's not be hasty.

I have some fun anecdotes (not as good as real data, but great fun with fake data).

I am one of those losers who didn't take calculus in high school and thus could not have passed a calculus test administered in high school.

I did, however, have several lovely math medals from competing on math teams in middle school and high school.

I did take calculus starting as a college freshmen and a good portion of my undergraduate and graduate training was in how to design and manufacture semiconductor devices because of my materials and chemical engineering background and having companies like Intel funding researchers in those departments.

So, JohnKnight, yep, I would have been a lower scorer on those tests at the time of administration than some people in other countries.  However, after high school and before entering the professional workforce, I received more training in useful fields, just the way the system is designed to work, and I now have a doctorate in engineering and help educate other people to do the things you are holding up as examples of necessary education.

I spend a lot of time and energy trying to improve science and math literacy in the general public and in the schools, but, as Conjugate and DvF pointed out, your whatever-it-is-you-think-you're-doing-here is just plain useless both in terms of being a convincing argument and in terms of helping get the system in a better track for the things that we (other people on these fora and those in the science/math literacy community) agree need doing.


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 30, 2010, 11:25:23 AM
The problem with our teaching of calculus won't be understood much less solved by focusing on which scource[sic] is correct about what percentage of American students take calculus.

"Which source is correct?" I had a source.  You made shit up didn't.  Please use the word "which" correctly on this academic forum.

Nothing to see here folks.  Please move along. - DvF

"TIMSS data do encourage us to focus on rigorous content, focused curriculum, and good teaching as critical to improved national performance. For example, while most countries introduce algebra before high school, in the U.S. only 25 percent of students take algebra before high school. Similarly, fully 90 percent of all U.S. high school students stop taking mathematics before getting to calculus. And 55 percent of physical science teachers in this country (i.e., teachers of chemistry, physics, earth science or physical science) lack either a major or minor in their teaching sub-field." Pascal D. Forgione, Jr., Ph.D., U.S. Commissioner of Education Statistics, National Center for Education Statistics, Office of Educational Research and Improvement, U.S. Department of Education, 555 New Jersey Avenue, N.W., Room 400, Washington, DC 20208, 202-219-1828 (Telephone)

Here are some interesting statistics and insight from the Mathematics Association of America:

"The same pressures that are pushing Calculus I into the high school curriculum are doing the same for Calculus II. Traditionally, it was a very elite group of students who took BC Calculus, covering the entire two-semester college syllabus. That group of students also grew by 6–8% per year until the mid-1990s. Over the period 1995–98, the rate of growth of BC calculus accelerated to 10–11% per year, a rate that has held up since then. In 2004, the number of students taking the BC Calculus exam exceeded 50,000. It will likely exceed 60,000 by 2005–06, the year of the next CBMS survey.

"In 2002, 23% of the students who took BC Calculus did so before their senior year [7]. These high school students are not necessarily well served by taking classes in linear algebra, several variable calculus, or differential equations at a local college. Picking up additional college credits is far less useful for them than deepening and broadening the mathematics they already think they know. These students need to be challenged, but they also need to be prepared for and enticed into a deep study of further mathematics in the company of their peers."


Considering the VERY low calculus score of 449 for American students who DID take advanced math, it's not even clear that "BC calculus" is teaching the proper thing.

What percent of American 18 year olds does this represent, though?  According to the US Census Bureau, there were more than 4 million in 2006, so these 60,000 who took the BC Calculus exam represented only 1.5% of our 18 year olds.

If it's these elite 60,000 or our top 1.5% who participated in TIMSS, then how can it be explained that they scored 20 points lower on a calculus exam than if they'd just GUESSED?  How can it be explained that the AVERAGE student in ITALY and GREECE scored 60 points higher, the AVERAGE student in Russia and Cyprus scored 100 and 99 points higher, the AVERAGE student in FRANCE scored 109 points higher, and NO country which participated (which excluded the highest scoring countries at the 8th grade level, like Korea, Japan, Singapore, and Taiwan) scored lower than 24 points higher than our top 1.5%?

Is France still such a power-house in math and physics instruction that their students, who now include many Arabs, outperform our top 1.5% by more than a standard deviation?  If so, then why don't we simply adopt French calculus books and teachers and be done with it?


Or better yet, Korean books and teachers.





Title: Re: assuming too much math knowledge?
Post by: johnknight on July 30, 2010, 11:41:47 AM
According to the following NSF site, between 1973 and 1996, only two fifths of the top American patent holders were Japanese corporations.

But by 1996, three quarters were Japanese:

http://www.nsf.gov/sbe/srs/seind98/c6/tt06-04.htm
   
Text table 6-4.
     
Top patenting corporations
     
     
Company
 Number of patents
   
     
In 1996
 Number
 Percent
 Percent Japan
 Percent US
 
International Business Machines Corp.
 1,867
 17.1%
  17.1%
 
Canon Kabushiki Kaisha
 1,541
 14.1%
 14.1%
 
Motorola Inc.
 1,064
 9.8%
  9.8%
 
NEC
 1,043
 9.6%
 9.6%
 
Hitachi, LTD
 963
 8.8%
 8.8%
 
Mitsubishi Denki Kabushiki Kaisha
 934
 8.6%
 8.6%
 
Toshiba Corporation
 914
 8.4%
 8.4%
 
Fujitsu Limited
 869
 8.0%
 8.0%
 
Sony Corporation
 855
 7.9%
 7.9%
 
Matsus***a Electric Industrial Co., Ltd.
 841
 7.7%
 7.7%
 
Percent of Patents
 10,891
 100.0%
 73.1%
 26.9%
 
     
From 1977-96
  %
 Japan
 US
 
General Electric Corp.
 16,206
 13.3%
  13.3%
 
International Business Machines Corp.
 15,205
 12.5%
  12.5%
 
Hitachi, LTD
 14,500
 11.9%
 11.9%
 
Canon Kabushiki Kaisha
 13,797
 11.4%
 11.4%
 
Toshiba Corporation
 13,413
 11.0%
 11.0%
 
Mitsubishi Denki Kabushiki Kaisha
 10,192
 8.4%
 8.4%
 
U.S. Philips Corporation
 9,943
 8.2%
  8.2%
 
Eastman Kodak Company
 9,729
 8.0%
  8.0%
 
AT&T Corporation
 9,380
 7.7%
  7.7%
 
Motorola Inc.
 9,143
 7.5%
  7.5%
 
 121,508
 100.0%
 42.7%
 57.3%
 




In 2006, the Patent Office reported that the percent of the top 25 patent holders of AMERICAN patents who were Japanese was down to 46%, 9% were Koreans, 5% were Germans, 2 1/2% were Dutch, and only 46% were Americans. 

The problem, though, is that the vast majority of the top scientists and engineers in American companies are Asians, most of whom aren't even American citizens, and many who weren't even educated here.  Many of those who were educated here at our expense now go back to their homelands where, after personal taxes are considered, their take-home pay is higher than here.

1 INTERNATIONAL BUSINESS MACHINES CORP -- 3651
2 SAMSUNG ELECTRONICS CO LTD KR -- 2453
3 CANON K K JP -- 2378
4 MATSUs***A ELECTRIC INDUSTRIAL CO LTD JP -- 2273
5 HEWLETT-PACKARD DEVELOPMENT CO L P -- 2113
6 INTEL CORP -- 1962
7 SONY CORP JP -- 1810
8 HITACHI LTD JP -- 1749
9 TOSHIBA CORP JP -- 1717
10 MICRON TECHNOLOGY INC -- 1612
11 FUJITSU LTD JP -- 1513
12 MICROSOFT CORP -- 1463
13 SEIKO EPSON CORP JP -- 1205
14 GENERAL ELECTRIC CO -- 1051
15 FUJI PHOTO FILM CO LT D JP -- 918
16 INFINEON TECHNOLOGIES AG DE -- 904
17 KONINKLIJKE PHILIPS ELECTRONICS NV NL -- 901
18 TEXAS INSTRUMENTS INC -- 884
19 SIEMENS AG DE -- 857
20 HONDA MOTOR CO LTD JP -- 836
21 SUN MICROSYSTEMS INC -- 776
22 DENSO CORP JP -- 770
23 NEC CORP JP -- 744
24 RICOH CO LTD JP -- 695
25 LG ELECTRONICS INC KR -- 695


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 30, 2010, 12:10:07 PM
It would appear from your post that you view California as a "progressive" state and that Lousiana is not, but having lived in both places, and having seen the test scores, I would argue that it's the other way around.  Consistently California has scored at the BOTTOM of the stack on SAT scores (both math and verbal) while Lousiana has often ranked in the top ten.
California was, indeed, a bad example. I completely ignored their issue with immigration - of course that should drag down averages. I stick with Louisiana, however: http://nces.ed.gov/nationsreportcard/states/statecomparisontable.aspx?sbj=MAT&gr=8&yr=2009&sample=R3&jur=LA&st=MN

This seems like a better assessment than SAT or ACT scores (as mentioned, they can be fairly selective in who gets tested), and Louisiana ranks #46 in math, for example.


To clarify the original point about NAEP math scores in Lousiana, about one in five students in Lousiana attend private schools.  Private schools across the nation score about 20 to 31 points higher than public schools.  Whites in public schools in Lousiana score around 266, so it's possible that Whites in Lousiana's private schools score somewhere between 286 to 297.  If they score 286, then private schools in Lousiana outperform all the states' public schools in NAEP math, and may score almost as high as Whites in DC who score 303.

If so, would it be reasonable to expect that SAT math scores of Lousiana would consistently be 50 points higher than California, 58 points higher than Massachusetts, and 72 points higher than Rhode Island?


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 30, 2010, 12:28:48 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.

An interesting way to answer that question is PISA:

http://pisa2000.acer.edu.au/interactive_results.php

If you query it for Korea, and use a school variable of "public/private" you will find that 52% of Korean 8th graders attend private schools and score about 4 points higher than the 48% who attend their public schools.

In most countries, the gap is much bigger: German private schools score 84 points higher in reading, 62 points higher in math, and 59 points higher in science.  American private schools score 41 points higher in reading, 40 points higher in math, and 42 points higher in science.

What we need to worry about is that even at the 8th grade level, before competition in Korea really gets fierce, Korean private school 8th graders already score 60 points higher than our public school 8th graders in math.

What do you think they do right that we do wrong?

Why not ask them?








Title: Re: assuming too much math knowledge?
Post by: johnknight on July 30, 2010, 12:42:04 PM


Students in the midwest take the ACT, not the SAT, to attend local and state schools.  The only people who take the SAT are those headed out-of-state, so they are the most motivated, highest achieving students. 



Of about 2 1/2 million high school graduates, about a million of them, or 40%, take the SAT.  So you're saying that 40% of high school graduates is a select group of the "most motivated, highest achieving students" who aren't representative of the other 60%?

How do we know that the other 60% might not have scored even higher?  Hasn't the goal of affirmative action been to deny the most qualified students admission to college?  Isn't that why the Bush administration joined the affirmative action lawsuit against the University of Michigan?

My personal observation, which is consistent with a cursory review of the data, is that the majority of those now attending our universities and our graduate schools are not the highest performing students.  I would not bet my life that the highest performing or most motivated students are the ones taking SAT and GRE.  One small example is that two thirds of college admissions now are girls, yet they are only one third of those who score higher than around 580 on any of these tests.

Furthermore, "Moores's first report contained data showing that 3,218 students with SAT I scores of 1,400 or higher were denied entry into UC Berkeley in 2002. The SAT I, a basic aptitude test, has a top score of 1,600. It's true that many straight-A students with high test scores don't get into UC Berkeley — there just aren't enough spaces. However, Moores discovered that Berkeley admitted 374 students with SAT I scores of only 600 to 1,000. The average score for admission into Berkeley is 1,337".

This is not an isolated case.  And this was YEARS after we the people passed Proposition 209 to end such inviduous discrimination.


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 30, 2010, 01:26:51 PM
If we want to evaluate the education system, let's not ignore demographics. Compare, for example, Sweden with Switzerland. Two small, wealthy countries - yet with widely differing results. Do the Swiss have a terrible education system? That doesn't sound likely. However, consider that more than a quarter of Switzerland's population is non-Swiss. In my experience, this is even more of an issue in schools (recent immigrants have more children). Once you consider that the local language already poses a challenge to some students, it's not surprising that they have difficulties learning content. It's also worth noting that students in Switzerland are required to learn 2 foreign language to fluency, so that would necessarily reduce the time available for other subjects that are tested for international comparison. I have no idea if it's a worthy trade-off, but we're clearly not comparing like with like here.

Thanks for those observations about the Swiss, which is something I hadn't thought about before.  I've been to both countries and would have suspected that it would be the Swiss who scored higher than the Swedes.  But as you point out, Switzerland's score of 488 is much lower than Sweden's score of 573, and not that much higher than our score of 423.  And it's certain that it's recent changes in Swiss immigration policy which are behind it.

What's interesting, though, is that in math *literacy* (Table A3) and in science *literacy* (Table A4), the Swiss do surprisingly well, scoring only 12 points lower in math and 36 points lower in science, than Sweden.

This is the exact same pattern followed by NSF physics students--they do very well in the literacy tests, but are an utter flop in physics achievement tests.  So the Swiss and the NSF education programs DO succeed in teaching the basics of science and math, but for whatever reason, their students seem to have a universal problem in applying those basics to problem solving.


Title: Re: assuming too much math knowledge?
Post by: post_functional on July 30, 2010, 04:22:03 PM
...but apologies for the sextuple post. 


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on July 30, 2010, 05:02:33 PM
According to the following NSF site, between 1973 and 1996, only two fifths of the top American patent holders were Japanese corporations.

Your original assertion was on the nuber of patents granted, not the number of corporations getting patents.  If you don't see that these are very different things, then the problem is not innumeracy, but illiteracy.

Quote
The problem, though, is that the vast majority of the top scientists and engineers in American companies are Asians, most of whom aren't even American citizens, and many who weren't even educated here.
[some numbers deleted]

Assuming this is even a problem - I'm not sure why, it sounds a bit like the complaints in the 1940s that a disproportionate number of students in US universities were Jewish - I assume that the ones who were educated here were educated here?  So nothing wrong with our system then?  As this is a forum for higher education, please remind me of which national university systems you think are better than the US system?

Quote
I am one of those losers who didn't take calculus in high school and thus could not have passed a calculus test administered in high school.

Actually, there is pretty good evidence that students who take math throughout high school, but defer Calculus to college, learn Calculus better.  (David Bressoud has some white papers on this at the American Math. Society website.)  This is not really surprising, in that by college they have a better idea of why they are learning the subject, and their teachers have a better understanding of it as well.

This is one reason why all the stuff we're being hammered with here is not really important.

Quote
Is France still such a power-house in math and physics instruction that their students, who now include many Arabs, outperform our top 1.5% by more than a standard deviation?  If so, then why don't we simply adopt French calculus books and teachers and be done with it?

France would kill to have our economy (or - for that matter - our scientific infrastructure).  Your arguments just get stranger and stranger. - DvF


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 30, 2010, 06:38:16 PM
According to the following NSF site, between 1973 and 1996, only two fifths of the top American patent holders were Japanese corporations.


Quote
Is France still such a power-house in math and physics instruction that their students, who now include many Arabs, outperform our top 1.5% by more than a standard deviation?  If so, then why don't we simply adopt French calculus books and teachers and be done with it?

France would kill to have our economy (or - for that matter - our scientific infrastructure).  Your arguments just get stranger and stranger. - DvF

There's nothing about the US that the French envy us for, nor should envy us for.  They do very well on their own, thank you.  They have a higher per capita income than we do, plus have a 21% personal savings rate, which is infinitely higher than our negative personal savings rate.  According to the Bureau of Economic Analysis, our rate has been a negative 2-3% for years now.  Their crime, divorce, incarceration, murder, and rape rates are as much as an order of magnitude lower than ours. 

Wouldn't you agree that all of this is consistent with their higher math, science, physics, and calculus scores, which reflects a somewhat better, though not at all the best, education system?

It doesn't take calculus to figure out that having a negative personal savings rate cannot continue forever, or that France is able to maintain its own economy while we have to borrow from the Saudi's and the Japanese and now the Chinese, does it?

The last time we had such a high rate was prior to WWII, so it's WE who "ought to kill" to have such an economy.


Title: Re: assuming too much math knowledge?
Post by: post_functional on July 30, 2010, 10:17:10 PM
Oh, right, it's this guy again.  There was a one-issue trollish poster awhile ago who just kept harping and harping on U.S. citizens taking on too much personal debt (as opposed to the citizens of other countries).  Don't remember the name, though.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on July 31, 2010, 12:31:51 AM
French GNP in PPP dollars: $2.14 trillion  Population 62277432  GNP/Pop=$34,362
US GNP in PPP dollars: $14.7 trillion Population 304060000  GNP/Pop=$48,346
PPP=adjusted to purchasing power
Data from 2008 World Bank via Google

Quote
than we do, plus have a 21% personal savings rate, which is infinitely higher than our negative personal savings rate

According to this (https://econ365.files.wordpress.com/2008/10/gross-savings-rate.pdf), ours is very similar to your model countries, Japan and Korea.  Stop cherry-picking your examples.

Quote
According to the Bureau of Economic Analysis, our rate has been a negative 2-3% for years now.

Time to fact check.  The BEA website data is here (http://www.bea.gov/briefrm/saving.htm), and once again shows that you're just making stuff up.


Quote
Their crime, divorce, incarceration, murder, and rape rates are as much as an order of magnitude lower than ours.

Wouldn't you agree that all of this is consistent with their higher math, science, physics, and calculus scores

Also consistent with lower scores.

You're seriously arguing that studying math and science leads to less crime? - DvF



Title: Re: assuming too much math knowledge?
Post by: intheno on July 31, 2010, 02:03:16 AM
It does depend on the state, but colleges are offering prealgebra and algebra I courses, which means that students have not all had those courses. However, at some universities, the lowest math course is usually Precalculus. However, with a course like yours, I am surprised that Intermediate or College Algebra are not prerequisites. For a first stats course in my state, Intermediate Algebra (Algebra II) is required with at least a grade of C. I'm not sure who said linear algebra and single variable calculus. I guess I would have to see what your course entailed. Are you usuing calculus or linear algebra concepts?



Title: Re: assuming too much math knowledge?
Post by: intheno on July 31, 2010, 02:04:46 AM
Another thing that struck me as odd is that AFTER the first test, the student said she'd never had Algebra. Now, what happened before the test? I mean, during the unit, didn't you do problems that involved Algebra? Why didn't she and/or others say something or withdraw if they saw there was that material being taught in the course. This really doesn't make sense.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on July 31, 2010, 08:19:28 AM
Quote
Their crime, divorce, incarceration, murder, and rape rates are as much as an order of magnitude lower than ours.

Wouldn't you agree that all of this is consistent with their higher math, science, physics, and calculus scores

Also consistent with lower scores.

You're seriously arguing that studying math and science leads to less crime? - DvF

I like the idea that divorce rates are not only somehow correlated with math and science scores, but also in the same category as crime, incarceration, murder, and rape rates.  I am also amused by the idea that physics and calculus are somehow separate categories from math and science.

Psst, JK, you do know that the social inhibitions against divorce in some of these places you are citing are so high that people live apart from their spouses for years, but simply never get legally divorced because not living together is normal for various reasons, but abandoning family is beyond the pale, right?  How about those European countries where the norm is not to get married so that of course the divorce rate is lower because only people who really, really, really want to be married bother to get married?

You do know that a possible reason for lower incarceration rates is that penalties for various crimes are higher to the point of death or exile, right? 

You do know that some of these countries are notorious for not collecting statistics in the same way as other countries so that their reported rates are meaningless, right?

I may not have taken calculus in high school, but there's nothing wrong with my reasoning ability and critical thinking, which is something not tested in many of the exams you cite  and that arguably is more important that the kind of knowledge often tested on the tests you cite.


Title: Re: assuming too much math knowledge?
Post by: bellefromhell on July 31, 2010, 09:44:45 AM

My kids are the kind that just get math, discuss it at the dinner table, make jokes about math, just really like it. 
yet, my daugher has been bored, and not liking it so much, stuck with slower classmates, even in a private school that starts 9th graders on geometry.

So, my children are taking on-line courses to advance in math.

My entering 8th grade daughter is fast at math.  Give her the formula and why, and she will zip on.  Plot on a graph?  Solve an equation?  No problem.  Add in word problems?  Ok, but she is annoyed at the time they take.  Give it to her 6 different ways to make sure each child understands?  She is ready to toss away the laptop!  She hates repetitive busy work!

And she never had an opportunity to hear, "math is hard!"  She has always been chasing after her big brother.  Anything he can do, she can do faster!

I about had a laughing fit when I saw that she had drawn on her white board, a large circle with an x inside, with the words, "Bang head here."

Her frustration?  She had been working on word problems about exercise pamphlets- manufacturing and distribution costs at a community event.  She had done all the math.  Got an A.  (rental fees, amounts to make to profit, how many could be disttrbuted by how many volunteers, etc...)

Now she was being asked to write an essay about how she felt about the importance of exercise. 
This was for her first semester final.  Since we were not taking it for a grade, I told her to write on and have fun. 
She basically went off on the test, explained that she was 12 years old and a competitive gymnast so she understood exercise, and that she preferred to have math in math class, thank-you very much!

The robo-grading simply gave her another A for filling in the space, no comments.

Yes, we have checked her work, and have her older brother's book to give her the right information that she needs for their private school testing to advance. 

btw--my kids have never had calcualtors in any math classes.  Not even for tests. (yes, not even for graphing!)  They work on graph paper to keep it neat.

But if that first semester final is what public school kids are getting nowadays, I completely understand how you could pass a math class and have nothing to show for it!









Title: Re: assuming too much math knowledge?
Post by: johnknight on July 31, 2010, 12:38:28 PM


Students in the midwest take the ACT, not the SAT, to attend local and state schools.  The only people who take the SAT are those headed out-of-state, so they are the most motivated, highest achieving students. 



Of about 2 1/2 million high school graduates, about a million of them, or 40%, take the SAT.  So you're saying that 40% of high school graduates is a select group of the "most motivated, highest achieving students" who aren't representative of the other 60%?

How do we know that the other 60% might not have scored even higher?  Hasn't the goal of affirmative action been to deny the most qualified students admission to college?  Isn't that why the Bush administration joined the affirmative action lawsuit against the University of Michigan?

What was said by menotti, and what I have seen in the various places I have lived, is that students IN THE MIDWEST who take the SAT are among the "most motivated, highest achieving students."  Everyone else who wants to go to college takes the ACT instead.  So to make a valid comparison between, say, Illinois (a predominantly ACT state) and Pennsylvania (an SAT state), you would need to somehow combine the ACT and SAT results.

Could you please clarify this?

I think your argument is that having a larger percentage of the students taking SAT drives down SAT math scores?  There's some truth to that argument, but there are notable exceptions.  For example, eight states, Texas, Connecticut, Massachusetts, New Jersey, Maryland, Hawaii, Nevada, and West Virginia, all score within 10 points of each other (between 474 and 484), yet the percent who took the SAT test varied from 17% in West Virginia to 80% or more in Connecticut and Massachusetts.  And the spread in SAT scores of the 6 states where  less than 6% take the test, was from 523 to 592, or 69 points, almost a full standard deviation.

So you see  there are significant differences between the academic skills of states which cannot be explained by different levels of test taking, or different percentages of students who take SAT?

Why do you believe Whites in Rhode Island, 70% of whose students take SAT, would score only 519 in SAT math while WHITES in Connecticut, 81% of whose students take SAT, score 14 points higher, or 533.  And why would they score 13 points lower in SAT verbal (516 vs. 529)?  What else can explain it other than the difference in the way these two different states teach their students—OR a difference in the quality of the students in the first place?

Looking at the state to state differences between states within ONE race, the White Race, doesn't it seem that the 11 point NAEP math gap between Rhode Island and North Dakota is equivalent to the 103 point gap in their SAT math scores (with the possible exception of your point that the scores might be influenced by different percentages of test takers)?


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 31, 2010, 01:25:28 PM
French GNP in PPP dollars: $2.14 trillion  Population 62277432  GNP/Pop=$34,362
US GNP in PPP dollars: $14.7 trillion Population 304060000  GNP/Pop=$48,346


Quote
According to the Bureau of Economic Analysis, our rate has been a negative 2-3% for years now.

Time to fact check.  The BEA website data is here (http://www.bea.gov/briefrm/saving.htm), and once again shows that you're just making stuff up.




You're seriously arguing that studying math and science leads to less crime? - DvF







http://www.bea.gov/national/nipaweb/Nipa-Frb.asp?Freq=Qtr

Comparison of Personal Saving in the National Income and Product Accounts (NIPAs) with Personal Saving in the Flow of Funds Accounts (FFAs)

What this shows is that no matter which way you measure it, our most creative accountants could not conceal that the US has a NEGATIVE personal savings rate, and has had since 1998 when the FFA's showed a negative 0.8% personal savings rate in the fourth quarter. It was negative all of 2000, reaching a low of -2.7% in the fourth quarter.  It reached a low of -3.2% in the second quarter of 2002, it reached a low of -1.7% in the first quarter of 2005, a low of -1.9% in the fourth quarter of 2006, an all time low of -6.5% in the second quarter of 2007.  The recent claim that our personal savings rate in 2008 was 8.8% was disputed by the NIPA savings rate of 4.4%.  2009 is still being massaged and when they're all done, we all know what will happen--they will suddenly "discover" that they over-estimated it and reduce it back to its traditional, decade-long negative savings rate.

We are the ONLY industrialized nation with a NEGATIVE savings rate.  Japan's is more than 33% and Korea's is more than 38%.

This is not an argument that crime tracks IQ.  It's merely an observation that the French envy us for nothing, not our high crime rate, and especially not our NEGATIVE personal savings rate.


Title: Re: assuming too much math knowledge?
Post by: duchess_of_malfi on July 31, 2010, 02:25:03 PM
I didn't know much about French crime patterns, so this was interesting to look up.

France's crime rate is slightly higher than the U.S.'s.

Crime
US  4135 crime victimizations per 100,000 population
France 4244 per 100,000 population
Homicide is higher in US (US 4.280 per 100,000 vs. France 1.737 per 100,000, from official data), but it is the rarest crime so has a more limited impact on total crime and violent crime rates compared to other crimes.  Sexual assualt is higher in U.S., 30.12 victimizations per 100,000 vs. 13.94 France (from victimization surveys).  France's crime rate is increasing, especially drug and human trafficking, organized crime, robbery (i.e. violent theft, the most common violent crime), and crimes involving guns.  In the US, crime rates peaked in early 1990s and declined after.

Incarceration rate
US  756 per 100,000 population
France 96 per 100,000 population
US leads world in incarceration rate, mainly because of much longer sentences than other countries—not difference in crime rate. 

Divorce
US  46% of all marriages are expected to end in divorce at current rate
France  38%
Divorce reform in France is more recent.  Women's labor force participaton is lower in France, but so is men's.  Marriage rate is higher in US, less self-selection to more committed relationships.

At the level of the individual, higher levels of education are associated with lower divorce risk and  lower crime victimization risk in terms of violent crime and non-violent street crime, but these are socioeconomic effects.  It would be more difficult to make a causal link to math knowledge.  Socioeconomic differencess within the society seem to be most important to these risks. The US historically has had a greater degree of social inequality than France, although that may be changing.

Of course, if we are talking abut total losses due to crime in economic or life terms (injury, death), then education is strongly and positively correlated with the costs of crime.  The level of dollar loss, lost wages and healthcare costs, and loss of human life from white-collar individual and corporate crime (fraud, price-fixing, occupational, consumer, and resident health and safety hazards, etc.) exceeds by many times losses from violent and non-violent street crime, and these more respectable crimes are committed by people with more education--and presumably more math knowledge.


Title: Re: assuming too much math knowledge?
Post by: kraken on July 31, 2010, 02:29:43 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.

An interesting way to answer that question is PISA:

http://pisa2000.acer.edu.au/interactive_results.php

If you query it for Korea, and use a school variable of "public/private" you will find that 52% of Korean 8th graders attend private schools and score about 4 points higher than the 48% who attend their public schools.

In most countries, the gap is much bigger: German private schools score 84 points higher in reading, 62 points higher in math, and 59 points higher in science.  American private schools score 41 points higher in reading, 40 points higher in math, and 42 points higher in science.

What we need to worry about is that even at the 8th grade level, before competition in Korea really gets fierce, Korean private school 8th graders already score 60 points higher than our public school 8th graders in math.

What do you think they do right that we do wrong?

Why not ask them?


It may be interesting, but it's not really answering the question.  I was asking whether the processes that select students into public vs. private schools in the US are similar to those in other countries and, if not, whether the data you cite adjust for those differences. 


Title: Re: assuming too much math knowledge?
Post by: johnknight on July 31, 2010, 05:15:39 PM
Quote
Their crime, divorce, incarceration, murder, and rape rates are as much as an order of magnitude lower than ours.

Wouldn't you agree that all of this is consistent with their higher math, science, physics, and calculus scores

Also consistent with lower scores.

You're seriously arguing that studying math and science leads to less crime? - DvF

I like the idea that divorce rates are not only somehow correlated with math and science scores, but also in the same category as crime, incarceration, murder, and rape rates.  I am also amused by the idea that physics and calculus are somehow separate categories from math and science.



Please go back and study all my posts very carefully.  You will then understand that the reason for pointing out specifically our performance in physics and calculus is that, while we do VERY poorly in general math and general science, as well as in math literacy and science literacy, we do EXTREMELY poorly in physics achievement and calculus achievement.

NSF physics students actually do fairly well in math LITERACY and in science LITERACY (meaning that they out-performed a few of the lowest performing countries), but they score LOWER than if they'd just GUESSED on both physics achievement questions and calculus achievement questions.  It was also noted on this forum that Switzerland follows a similar pattern, and immigration was cited as a possible reason.  In addition to that point, we ought to note that about 9% of the test takers in Germany are Turkish immigrants and 8% of the test takers in Ireland are Polish immigrants, which drives down their scores too(and explains why Germany now scores even lower than Sweden, when they used to score much higher not too long ago).

There actually IS a correlation between test scores, divorce rates, and crime rates, but that's not the point.  The point is that our 12th graders seem to score lower than our 8th graders.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on July 31, 2010, 06:52:16 PM
According to the Bureau of Economic Analysis, our rate has been a negative 2-3% for years now.

Me:
Quote
Time to fact check.  The BEA website data is here (http://www.bea.gov/briefrm/saving.htm), and once again shows that you're just making stuff up.
Troll again:
Quote
http://www.bea.gov/national/nipaweb/Nipa-Frb.asp?Freq=Qtr

Comparison of Personal Saving in the National Income and Product Accounts (NIPAs) with Personal Saving in the Flow of Funds Accounts (FFAs)

What this shows is that no matter which way you measure it, our most creative accountants could not conceal that the US has a NEGATIVE personal savings rate

Do you even look at the links you give?  The table on the page you link to has personal savings rate (as percentage of national cash flow indicators) in lines 17 and 18.  The table I gave gives the rate as a flow of disposable income, which is more appropriate for the argument you are trying to make (including comparison to France).  Either way, all positive.

Quote
Please go back and study all my posts very carefully.

US health insurance does not cover exploding heads.  Maybe someone in France should take up this study instead.  - DvF


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 01, 2010, 07:18:25 AM
Quote
Their crime, divorce, incarceration, murder, and rape rates are as much as an order of magnitude lower than ours.

Wouldn't you agree that all of this is consistent with their higher math, science, physics, and calculus scores

Also consistent with lower scores.

You're seriously arguing that studying math and science leads to less crime? - DvF

I like the idea that divorce rates are not only somehow correlated with math and science scores, but also in the same category as crime, incarceration, murder, and rape rates.  I am also amused by the idea that physics and calculus are somehow separate categories from math and science.



Please go back and study all my posts very carefully.  You will then understand that the reason for pointing out specifically our performance in physics and calculus is that, while we do VERY poorly in general math and general science, as well as in math literacy and science literacy, we do EXTREMELY poorly in physics achievement and calculus achievement.

You are trying to persuade me.  That means the burden of proof rests with you to make your points in a way that constructs a logical argument that I can follow.  I am not going to go read your posts very carefully because they are poorly constructed data spews with sweeping generalizations (often wrong or at least not supported by the data I already am familiar with from other sources), not logical, step-by-step arguments leading up to a conclusion.

If you want to make a specific point, give an introduction, show the data, then make the conclusion.  Repeat as necessary to then draw a broader conclusion from a set of subconclusions.

You are on an academic forum speaking to other academics.  Stop giving us middle-school level data dumps with general opinions and construct a solid case for whatever it is your case is.


Title: Re: assuming too much math knowledge?
Post by: conjugate on August 01, 2010, 12:09:09 PM

You are trying to persuade me.  That means the burden of proof rests with you to make your points in a way that constructs a logical argument that I can follow.  I am not going to go read your posts very carefully because they are poorly constructed data spews with sweeping generalizations (often wrong or at least not supported by the data I already am familiar with from other sources), not logical, step-by-step arguments leading up to a conclusion.

If you want to make a specific point, give an introduction, show the data, then make the conclusion.  Repeat as necessary to then draw a broader conclusion from a set of subconclusions.

You are on an academic forum speaking to other academics.  Stop giving us middle-school level data dumps with general opinions and construct a solid case for whatever it is your case is.

And, while we're on the topic, exactly what is it you would have us do?  I asked this before, and got no response.  I'll try again.

If, hypothetically, we were to concede that Edu-geddon is upon us, that ignorance is rampant, that we are a scant half-generation or so away from living in trees and hurling our excreta at the better-educated Europeans and Asians who are going to take over the world and put us in zoos, what should we, as higher education professionals, do about the alleged sad state of the high schools?  The high schools don't listen to us.  Even if they did, it isn't clear what you think we should do about it.

Are we to raise standards and flunk more students?  I picture you as a kind of cut-rate Captain Kirk, shouting from the bridge, "Scotty!  We need more F's in another semester or we're all going to die!!"

"I'm sorry, Cap'n, but me gradebook cannae take much more o' this!  I'm givin' 'em all I've got!"

Right now, all you're doing is the equivalent of running around wearing a sign that says "Repent!  The End is Near!"  If there's nothing we can do about it, then there's no point in worrying; might as well kick back and enjoy a beer until the fall of civilization.  (I've got some good beer, by the way; stop by sometime if you're feeling less distraught.)  If there is something we can do about it, then what (in your opinion) should we do?  Why is that strategy (if you ever enunciate it) better than the various other strategies that are being tried across the country?

Constructive criticism will do a lot more for your case than listing random facts and screaming that the sky is falling.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 02, 2010, 01:19:25 PM
Quote
Their crime, divorce, incarceration, murder, and rape rates are as much as an order of magnitude lower than ours.

Wouldn't you agree that all of this is consistent with their higher math, science, physics, and calculus scores

Also consistent with lower scores.

You're seriously arguing that studying math and science leads to less crime? - DvF

I like the idea that divorce rates are not only somehow correlated with math and science scores, but also in the same category as crime, incarceration, murder, and rape rates.  I am also amused by the idea that physics and calculus are somehow separate categories from math and science.



Please go back and study all my posts very carefully.  You will then understand that the reason for pointing out specifically our performance in physics and calculus is that, while we do VERY poorly in general math and general science, as well as in math literacy and science literacy, we do EXTREMELY poorly in physics achievement and calculus achievement.

You are trying to persuade me.  That means the burden of proof rests with you to make your points in a way that constructs a logical argument that I can follow.  I am not going to go read your posts very carefully because they are poorly constructed data spews with sweeping generalizations (often wrong or at least not supported by the data I already am familiar with from other sources), not logical, step-by-step arguments leading up to a conclusion.

If you want to make a specific point, give an introduction, show the data, then make the conclusion.  Repeat as necessary to then draw a broader conclusion from a set of subconclusions.

You are on an academic forum speaking to other academics.  Stop giving us middle-school level data dumps with general opinions and construct a solid case for whatever it is your case is.

In my small circle of idiots, if the US Department of Education confesses that between 50% to 75% of American high school math teachers neither minored nor majored in math, then we don't need to explain to each other that we need to get rid of all math teachers who never majored nor minored in math and hire those who did.  It is self-evident to them that this would be necessary but it would not be sufficient.  Before a teacher should be allowed to teach math, she should first prove that she understands math, and can teach math.  But what happens right now is just the opposite.  As a related anecdote,  a friend who's a retired Air Force Colonel who does know math wanted to teach math and they said he was "over-qualified".  Another friend who's Hispanic and majored in English (but still can't speak English clearly) was hired by the same school system to teach English, and was surprised that they then asked him to teach math even though he never took math.

Stories like this are repeated endlessly across the country, and our low low and declining test scores are all the evidence you need that this is just the wrong approach.

Another thing that might be useful is if you quit presuming that people are idiots and liars just because they quote data straight from the US Department of Education web site, and other government web sites.  And if you'd actually READ the following study instead of repeating all kinds of education myths which this study positively explodes:

http://eaja.net/Documents/TIMSS_NSFphysicsStudy99.pdf


Another obseravation that they have made, which I agree with, is that if students don't learn calculus in high school, it's too late to learn it in college.  Which is why so many of our global economic competitors make durn sure that as many high school students as possible graduate with calculus behind them.  Which is why so many other countries DID demonstrate wiggling electrons in their cranial cavities while ours seem to be stuck at -273 degrees Celsius.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 02, 2010, 01:30:06 PM
I didn't know much about French crime patterns, so this was interesting to look up.

France's crime rate is slightly higher than the U.S.'s.

Crime
US  4135 crime victimizations per 100,000 population
France 4244 per 100,000 population
Homicide is higher in US (US 4.280 per 100,000 vs. France 1.737 per 100,000, from official data), but it is the rarest crime so has a more limited impact on total crime and violent crime rates compared to other crimes.  Sexual assualt is higher in U.S., 30.12 victimizations per 100,000 vs. 13.94 France (from victimization surveys).  France's crime rate is increasing, especially drug and human trafficking, organized crime, robbery (i.e. violent theft, the most common violent crime), and crimes involving guns.  In the US, crime rates peaked in early 1990s and declined after.

Incarceration rate
US  756 per 100,000 population
France 96 per 100,000 population
US leads world in incarceration rate, mainly because of much longer sentences than other countries—not difference in crime rate. 

Divorce
US  46% of all marriages are expected to end in divorce at current rate
France  38%
Divorce reform in France is more recent.  Women's labor force participaton is lower in France, but so is men's.  Marriage rate is higher in US, less self-selection to more committed relationships.

At the level of the individual, higher levels of education are associated with lower divorce risk and  lower crime victimization risk in terms of violent crime and non-violent street crime, but these are socioeconomic effects.  It would be more difficult to make a causal link to math knowledge.  Socioeconomic differencess within the society seem to be most important to these risks. The US historically has had a greater degree of social inequality than France, although that may be changing.

Of course, if we are talking abut total losses due to crime in economic or life terms (injury, death), then education is strongly and positively correlated with the costs of crime.  The level of dollar loss, lost wages and healthcare costs, and loss of human life from white-collar individual and corporate crime (fraud, price-fixing, occupational, consumer, and resident health and safety hazards, etc.) exceeds by many times losses from violent and non-violent street crime, and these more respectable crimes are committed by people with more education--and presumably more math knowledge.

Without getting too sidetracked from the NSF physics study, if anyone is interested, email me at johnknight@usa.com and I will send you 8 different scholarly studies which point out that, compared to married women, divorced women are:
  • Twice as likely to die of circulatory diseases.

    Twice as likely to die of cancer.


    Three times as likely to die of diabetes.


    Four times as likely to be killed in an accident.


    Four times as likely to be murdered.
       

    Five times as likely to die of respiratory diseases.


    Five times as likely to commit suicide.


    Five times as likely to die of cirrhosis.

So, yes, we should expect crime and other social pathology to track closely with divorce rates, from country to country, from state to state, and from city to city. 

And they do.  While the Catholic Church promotes the idea that they oppose divorce and abortion, it's consistently Catholic states which have the highest divorce and abortion and murder rates. For example, even though almost half the population of New Jersey are Catholics, they have some of the highest abortion, divorce, and murder rates around.  In 1998, their abortion rate per 1,000 women was 35.1 which was six times what it was in South Dakota (at 5.9).  Their muder rate per 100,000 population  has consistently been around 5, which is five times what it is in states like South Dakota, Iowa, and Utah (one year it was 25 times higher than North Dakota because they had a rate of only 0.2).  And their number of divorces as a percentage of their marriages is 57.6%, compared to "only" 36% in North Dakota.  So should we also expect them to score more than 100 SAT math points lower than North Dakota?
 
Do you know which four cities over the last four decades have qualified as the "Murder Capitol of the World"?


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 02, 2010, 01:45:10 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.

An interesting way to answer that question is PISA:

http://pisa2000.acer.edu.au/interactive_results.php

If you query it for Korea, and use a school variable of "public/private" you will find that 52% of Korean 8th graders attend private schools and score about 4 points higher than the 48% who attend their public schools.

In most countries, the gap is much bigger: German private schools score 84 points higher in reading, 62 points higher in math, and 59 points higher in science.  American private schools score 41 points higher in reading, 40 points higher in math, and 42 points higher in science.

What we need to worry about is that even at the 8th grade level, before competition in Korea really gets fierce, Korean private school 8th graders already score 60 points higher than our public school 8th graders in math.

What do you think they do right that we do wrong?

Why not ask them?


It may be interesting, but it's not really answering the question.  I was asking whether the processes that select students into public vs. private schools in the US are similar to those in other countries and, if not, whether the data you cite adjust for those differences. 

Could you please explain?

Why would you want to adjust for the very variable that you want to measure or understand?  There are many reasons you would expect private schools to score higher than public schools, so the only question really is just how much higher they score.  To use the specific example of Louisiana's private schools, which I'm directly familiar with, parents there, even though they must pay taxes to subsidize the public schools (and they pay almost all those costs), would rather pay the extra amount to send their children to private schools rather than send them to public schools.  This is why almost one in five students there are in private schools and not public schools.  So it's not unreasonable to expect them to score 20-35 NAEP math points higher than their public schools.  Do you think they might score even higher if their parents didn't have to bear the extra expenses of public schools which they get no benefit from?  Why would you want to adjust for that variable?


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 02, 2010, 01:50:41 PM
French GNP in PPP dollars: $2.14 trillion  Population 62277432  GNP/Pop=$34,362
US GNP in PPP dollars: $14.7 trillion Population 304060000  GNP/Pop=$48,346
PPP=adjusted to purchasing power
Data from 2008 World Bank via Google

Quote
than we do, plus have a 21% personal savings rate, which is infinitely higher than our negative personal savings rate

According to this (https://econ365.files.wordpress.com/2008/10/gross-savings-rate.pdf), ours is very similar to your model countries, Japan and Korea.  Stop cherry-picking your examples.

Quote
According to the Bureau of Economic Analysis, our rate has been a negative 2-3% for years now.

Time to fact check.  The BEA website data is here (http://www.bea.gov/briefrm/saving.htm), and once again shows that you're just making stuff up.


Quote
Their crime, divorce, incarceration, murder, and rape rates are as much as an order of magnitude lower than ours.

Wouldn't you agree that all of this is consistent with their higher math, science, physics, and calculus scores

Also consistent with lower scores.

You're seriously arguing that studying math and science leads to less crime? - DvF



http://pubdb3.census.gov/macro/031995/hhinc/8_001.htm#pg5

Is U.S. GDP PER CAPITA $41,657, OR $8,488?  The OECD estimates that GDP per capita for the United States is $41,657. However, this is not at all consistent with the 2000 Current Population Survey from the US Census Bureau which put median "total money income" for ALL American households in 2000 at only $32,264 , at $21,027 for all Black households, and $23,421 for Hispanic households.  This is not just wages and salaries, this is ALL money income, which includes welfare and a whole host of social transfer payments to all other "minority" groups. If our GDP per capita actually WAS $41,657, and if there are an average of 2.8 members per household, then our median household income OUGHT to have been $116,340, 3.6 TIMES higher than it actually was.  By what sleight of hand have our great leaders misled us and the world about the true state of our sad economic affairs?

Furthermore, the US Bureau of Labor Statistics estimated that 100.2 million full time American workers earned an average of $29,432 in 2000, with White men earning $34,320, which is 28% higher than the $26,728 earned by full time Black men workers and 70% higher than the $20,176 earned by full time Hispanic men workers.  This is a total income of less than $3 trillion, which is a GDP per capita for 274 million Americans of only $10,610 per year, ONE FOURTH of the OECD estimate. 20,572,000 of those full time employees were government employees who should not be counted in GDP just as they were not until relatively recently, and just as they are not in countries like Japan. Removing them places our REAL GDP per capita at $8,488.  With 2.7 people per household in the US, family (or "household") income is $22,917.

http://www.census.gov/prod/2002pubs/01statab/labor.pdf

In addition to that, more than half of American Blacks and Hispanics are not in the labor force at all, so their actual contributions to wages and salaries for Black and Hispanic households were less than $13,364 and $10,088, respectively.  Social transfer payments from White employees to Black households were ($21,027 - $13,365) $7,662 and to Hispanic households were($23,421 - $10,088) $13,333, a very strong financial disincentive for White employees to produce.  Who wants to work 42 days each year JUST to earn enough to pay JUST the taxes which fund JUST the social transfer payments JUST to Blacks who HATE them for it?  And another 12 days JUST for Hispanics?

Since 2000, major corporations, huge companies, entire industries, our key jobs, have flooded offshore in record numbers and today we'd be LUCKY if per capita incomes are as much as HALF of what they were when this survey was completed a decade ago.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 02, 2010, 01:56:56 PM
JohnKnight,

You are being insulting without making a point as I spend quite a lot of time immersed in literature regarding science and math literacy of the general public and K-12 education.

For example, "few people teaching math in high schools are qualified to do so" is a point.  You can then support that point with data like "according to surveys from the Department of Education, 50-70% of people teaching math in high school do not have math majors or minors as part of their formal education".  You can follow up with the scores on tests

(a) of people taught by people who don't know math
(b) of people taught by people who do know math
(c) of people taught by those who both know math and how to teach it. 

You can then state the conclusion that what needs to be done is to have more people educated in mathematics, more people educated in teaching mathematics, and a stronger will all around to make that happen by having people who are educated in mathematics and wish to teach high school get the help they need to transition into teaching mathematics at the high school level.  That is called constructing a logical argument and is the proper way to go about persuading academics of your points of which I am still in the dark since you don't do anything more than point to a study and yell "Look at how distressing this is!"

Oh, and as long as we're just throwing out anecdotes as though they were data, I am far from the only person I know who did not take calculus in high school and now is proficient in it.  Calculus at the high school level is indicative of nothing more than knowing calculus at a certain age (although, yes, I am very disturbed by people who took calculus classes then not being able to do calculus).  It is not the end of the world as we know it to not know calculus by a certain birthday younger than twenty and has little bearing on what someone might or might not be doing at the age of 25.  Not taking algebra in high school is alarming.  Not taking calculus in high school is just fine.


Title: Re: assuming too much math knowledge?
Post by: duchess_of_malfi on August 02, 2010, 02:39:51 PM
Here are the main problems with the attempt to connect math knowledge, religion, abortion, divorce, and social pathology or decay:

1.  Your facts are wrong on some things about which you are sure you are right. 
For example:
The crime rate in France is slightly higher than in the US--and going up. 
The divorce rate is similar. 
There is no connection between divorce rate and crime rates over time in the US; the divorce rate increased when laws changed and women became economically independent, then it dropped; crime rates increased earlier, when the Baby Boomers entered peak offending years of late adolescence and young adulthood, peaked ten years later than the divorce peak, then dropped as offenders aged out, policies changed, and more people were locked up. 

What, then, makes me inclined to believe that other things about which you are sure you are right have a stronger basis in fact?

2.  It is very difficult to understand the way you see the relationship between correlation and causation. 

People are not randomly selected into marriage or divorce.  Therefore, you need to look closely at all the events and characteristics that lead them to be in one category or another--because those reasons, not the fact of the marriage or divorce itself, are likely to be important to their outcomes.  In the US, divorce risk increases significantly with lower income.  Women with college degrees have a low risk of divorce.  Lower income is also strongly associated with health problems and reduced expectation of life.  If you control for socioeconomic status, many of these differences disappear.  I have no idea if your figures are correct or invented, but for women, the association between life outcomes and divorce is meaningful mainly as a sign of another relationship between the variables.  Divorce, in itself, does increase negative life outcomes for men more significantly, but mostly because they lack the social relationships that buffer women in difficult situations and are more likely to engage in risky behavior after divorce (e.g., alcohol) that lead to negative outcomes.  You also have to consider that there are other differences between people whose marriages end in death and people whose marriages end in divorce.  They aren't the same sorts of people, and the ways they aren't the same make a difference.

Age, gender, race, and income--not marital status--are the primary predictors of homicide victimization.  When comparing abortion rates in NJ and SD, did it occur to you to control for average age and income of women in the two states?  When attempting to draw a connection between crime and religion, did you think of controlling for income, age, or population density?


Following your logic, we would expect these interpretations: 

France has a high crime rate and high math scores.  Therefore, math causes crime.
France's marriage rate is the lowest in Europe, much lower than in the US, and French math scores are good.  Therefore, math lowers the marriage rate. 
Boys typically score higher on math tests than girls do.  Boys and men are far more likely to commit crimes, particularly violent crime, than are girls and women. Victims of violence are most often men.  Therefore, math ability leads to criminal offending and criminal victimization.  Also, in the US, women's criminal offending is increasing.  They must be getting better at math.
Italy is mostly Catholic and France is mostly Catholic.  They have low birth rates.  The US is mostly Protestant and has a much higher birthrate.  Therefore, Protestants like babies better than Catholics.  (Let's not talk about Japan, or the higher Hispanic birth rate in the US.)
New Jersey has a high rate of Catholic residents, and a lot of industrial pollution.  And traffic circles!  Obviously, these things are related.


Let's not forget some of the classics:
Living together before marriage will increase the likelihood that you'll get divorced!
Eating ice cream causes shark attacks!
An individual's height increasing causes his or her vocabulary to increase!
My dog's barking scares away the intruder who puts things in my mailbox.  She has a 100% success rate!


Tell me, do you teach at the college level?  What topic?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on August 02, 2010, 03:23:33 PM
Another thing that might be useful is if you quit presuming that people are idiots and liars just because they quote data straight from the US Department of Education web site, and other government web sites.

You've got it backwards; nobody who correctly quoted such a site was deemed to be an idiot or liar.

Quote
  And if you'd actually READ the following study instead of repeating all kinds of education myths which this study positively explodes:

http://eaja.net/Documents/TIMSS_NSFphysicsStudy99.pdf


Another obseravation that they have made, which I agree with, is that if students don't learn calculus in high school, it's too late to learn it in college.

Where in this document do they say this?  In fact, where in this document does the word "Calculus" appear?

If you'd actually READ the studies you quote, instead of repeating all kinds of uneducated myths which your studies do not support... - DvF


Title: Re: assuming too much math knowledge?
Post by: spork on August 02, 2010, 04:28:16 PM
I never took calculus in high school either.


Title: Re: assuming too much math knowledge?
Post by: kraken on August 03, 2010, 12:07:06 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.

An interesting way to answer that question is PISA:

http://pisa2000.acer.edu.au/interactive_results.php

If you query it for Korea, and use a school variable of "public/private" you will find that 52% of Korean 8th graders attend private schools and score about 4 points higher than the 48% who attend their public schools.

In most countries, the gap is much bigger: German private schools score 84 points higher in reading, 62 points higher in math, and 59 points higher in science.  American private schools score 41 points higher in reading, 40 points higher in math, and 42 points higher in science.

What we need to worry about is that even at the 8th grade level, before competition in Korea really gets fierce, Korean private school 8th graders already score 60 points higher than our public school 8th graders in math.

What do you think they do right that we do wrong?

Why not ask them?


It may be interesting, but it's not really answering the question.  I was asking whether the processes that select students into public vs. private schools in the US are similar to those in other countries and, if not, whether the data you cite adjust for those differences. 

Could you please explain?

Why would you want to adjust for the very variable that you want to measure or understand?  There are many reasons you would expect private schools to score higher than public schools, so the only question really is just how much higher they score.  To use the specific example of Louisiana's private schools, which I'm directly familiar with, parents there, even though they must pay taxes to subsidize the public schools (and they pay almost all those costs), would rather pay the extra amount to send their children to private schools rather than send them to public schools.  This is why almost one in five students there are in private schools and not public schools.  So it's not unreasonable to expect them to score 20-35 NAEP math points higher than their public schools.  Do you think they might score even higher if their parents didn't have to bear the extra expenses of public schools which they get no benefit from?  Why would you want to adjust for that variable?


Simply put, if you select the kinds of students who tend to achieve more in private schools, then they will tend to perform better in academic assessments, regardless of the impact of the school, be it private or public.  Therefore, any comparative assessment of student performance in private and public schools must consider these selection processes in order to make a causal argument that the schools created any performance gap.  To illustrate, if I give one teacher a 10 year old student who possesses an IQ of 175 and was playing Mozart at the age of 2, and I give another teacher a 10 year old student who is still learning the alphabet, it is entirely probable that an academic assessment 8 years later would show greater performance on the part of the first student.  We would be remiss, however, to then conclude that this was entirely the result of differences in teacher efficacy.  Hence, if private schools have a tendency to enroll students with more social advantages than those who attend public schools, and we know these advantages covariates of academic performance, then we would must consider the consequences this selection process has on final assessment in order to make a convincing causal argument.  In addition, we must consider potential selection effects in the kinds of students who are assessed in each country.  Do all students in all countries have an equal probability of being included within the assessment?  If not, do the factors contributing to differences in selection also influence academic performance?


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 12:17:53 PM
Here are the main problems with the attempt to connect math knowledge, religion, abortion, divorce, and social pathology or decay:

1.  Your facts are wrong on some things about which you are sure you are right. 
For example:
The crime rate in France is slightly higher than in the US--and going up. 
The divorce rate is similar. 
There is no connection between divorce rate and crime rates over time in the US; the divorce rate increased when laws changed and women became economically independent, then it dropped; crime rates increased earlier, when the Baby Boomers entered peak offending years of late adolescence and young adulthood, peaked ten years later than the divorce peak, then dropped as offenders aged out, policies changed, and more people were locked up. 

What, then, makes me inclined to believe that other things about which you are sure you are right have a stronger basis in fact?

2.  It is very difficult to understand the way you see the relationship between correlation and causation. 

People are not randomly selected into marriage or divorce.  Therefore, you need to look closely at all the events and characteristics that lead them to be in one category or another--because those reasons, not the fact of the marriage or divorce itself, are likely to be important to their outcomes.  In the US, divorce risk increases significantly with lower income.  Women with college degrees have a low risk of divorce.  Lower income is also strongly associated with health problems and reduced expectation of life.  If you control for socioeconomic status, many of these differences disappear.  I have no idea if your figures are correct or invented, but for women, the association between life outcomes and divorce is meaningful mainly as a sign of another relationship between the variables.  Divorce, in itself, does increase negative life outcomes for men more significantly, but mostly because they lack the social relationships that buffer women in difficult situations and are more likely to engage in risky behavior after divorce (e.g., alcohol) that lead to negative outcomes.  You also have to consider that there are other differences between people whose marriages end in death and people whose marriages end in divorce.  They aren't the same sorts of people, and the ways they aren't the same make a difference.

Age, gender, race, and income--not marital status--are the primary predictors of homicide victimization.  When comparing abortion rates in NJ and SD, did it occur to you to control for average age and income of women in the two states?  When attempting to draw a connection between crime and religion, did you think of controlling for income, age, or population density?


Following your logic, we would expect these interpretations: 

France has a high crime rate and high math scores.  Therefore, math causes crime.
France's marriage rate is the lowest in Europe, much lower than in the US, and French math scores are good.  Therefore, math lowers the marriage rate. 
Boys typically score higher on math tests than girls do.  Boys and men are far more likely to commit crimes, particularly violent crime, than are girls and women. Victims of violence are most often men.  Therefore, math ability leads to criminal offending and criminal victimization.  Also, in the US, women's criminal offending is increasing.  They must be getting better at math.
Italy is mostly Catholic and France is mostly Catholic.  They have low birth rates.  The US is mostly Protestant and has a much higher birthrate.  Therefore, Protestants like babies better than Catholics.  (Let's not talk about Japan, or the higher Hispanic birth rate in the US.)
New Jersey has a high rate of Catholic residents, and a lot of industrial pollution.  And traffic circles!  Obviously, these things are related.


Let's not forget some of the classics:
Living together before marriage will increase the likelihood that you'll get divorced!
Eating ice cream causes shark attacks!
An individual's height increasing causes his or her vocabulary to increase!
My dog's barking scares away the intruder who puts things in my mailbox.  She has a 100% success rate!


Tell me, do you teach at the college level?  What topic?


Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?


Title: Re: assuming too much math knowledge?
Post by: marfa on August 03, 2010, 12:40:35 PM

Another obseravation that they have made, which I agree with, is that if students don't learn calculus in high school, it's too late to learn it in college. 


I never took calculus in high school.  Are you going to revoke my PhD in mathematics??


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 12:44:58 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.

An interesting way to answer that question is PISA:

http://pisa2000.acer.edu.au/interactive_results.php

If you query it for Korea, and use a school variable of "public/private" you will find that 52% of Korean 8th graders attend private schools and score about 4 points higher than the 48% who attend their public schools.

In most countries, the gap is much bigger: German private schools score 84 points higher in reading, 62 points higher in math, and 59 points higher in science.  American private schools score 41 points higher in reading, 40 points higher in math, and 42 points higher in science.

What we need to worry about is that even at the 8th grade level, before competition in Korea really gets fierce, Korean private school 8th graders already score 60 points higher than our public school 8th graders in math.

What do you think they do right that we do wrong?

Why not ask them?


It may be interesting, but it's not really answering the question.  I was asking whether the processes that select students into public vs. private schools in the US are similar to those in other countries and, if not, whether the data you cite adjust for those differences. 

Could you please explain?

Why would you want to adjust for the very variable that you want to measure or understand?  There are many reasons you would expect private schools to score higher than public schools, so the only question really is just how much higher they score.  To use the specific example of Louisiana's private schools, which I'm directly familiar with, parents there, even though they must pay taxes to subsidize the public schools (and they pay almost all those costs), would rather pay the extra amount to send their children to private schools rather than send them to public schools.  This is why almost one in five students there are in private schools and not public schools.  So it's not unreasonable to expect them to score 20-35 NAEP math points higher than their public schools.  Do you think they might score even higher if their parents didn't have to bear the extra expenses of public schools which they get no benefit from?  Why would you want to adjust for that variable?


Simply put, if you select the kinds of students who tend to achieve more in private schools, then they will tend to perform better in academic assessments, regardless of the impact of the school, be it private or public.  Therefore, any comparative assessment of student performance in private and public schools must consider these selection processes in order to make a causal argument that the schools created any performance gap.  To illustrate, if I give one teacher a 10 year old student who possesses an IQ of 175 and was playing Mozart at the age of 2, and I give another teacher a 10 year old student who is still learning the alphabet, it is entirely probable that an academic assessment 8 years later would show greater performance on the part of the first student.  We would be remiss, however, to then conclude that this was entirely the result of differences in teacher efficacy.  Hence, if private schools have a tendency to enroll students with more social advantages than those who attend public schools, and we know these advantages covariates of academic performance, then we would must consider the consequences this selection process has on final assessment in order to make a convincing causal argument.  In addition, we must consider potential selection effects in the kinds of students who are assessed in each country.  Do all students in all countries have an equal probability of being included within the assessment?  If not, do the factors contributing to differences in selection also influence academic performance?

I've been following the progress of the Korean education system and its effect on their technological advancement for quite a while.  So I think I might be able to answer your question based on this direct observation.

It's the quality of the Korean students, and not the quality of their schools, which enables Koreans to outperform us at the 8th grade level by 105 points, and by a much larger margin than this at the 12th grade level, and to graduate 95% of their high school students with calculus already behind them.

While we argue about whether or not calculus is important in high school, China, Germany, Japan, and Korea are already teaching calculus to the vast majority of their students, and now make just about everything WE buy, all the way from cars to semiconductors to shoes.

Someone who understands calculus simply would not argue that calculus is not important for a high school student to learn.  A high school teacher in this country (if there ARE any) simply could not agree that learning calculus in high school is not critical in this technological age.

At the 8th grade level, as measured by PISA, the difference between their public schools and private schools is not that great (about 4 points, both of whom scored more than 70 points higher in math than our public school students and 20 points higher than our private school students).  We don't have the data point for their 12th grade students, but it's between the 8th and 12th grade that competition in schools in Korea really gets fierce, so the difference by then might be 100 points.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 03, 2010, 12:54:41 PM
Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?

What I make of that is that abortions are greatly reduced in big states that have a predominantly rural population and few abortion providers, while abortions are more common in places where abortions can be more readily obtained.  

I can also see a strong correlation with places where small-town, community values against premarital sex predominate having lower abortion rates than places that have more liberal ideas about non-marital sex.

I see a strong correlation between places where people are, in general, anti-abortion based on public polls (hence in part the fewer abortion providers) and a lower abortion rate and places where abortion is more accepted and a higher abortion rate.

As for the Catholic part specifically, I see that places that were settled by people who were Catholic and are now very populous places still have a large proportion of Catholics.

You're still failing on correlation versus causation if your point was to conclude that having a large Catholic population necessarily leads to a higher abortion rate since you have failed to control for some very relevant confounding variables.


Title: Re: assuming too much math knowledge?
Post by: kraken on August 03, 2010, 12:57:36 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.

An interesting way to answer that question is PISA:

http://pisa2000.acer.edu.au/interactive_results.php

If you query it for Korea, and use a school variable of "public/private" you will find that 52% of Korean 8th graders attend private schools and score about 4 points higher than the 48% who attend their public schools.

In most countries, the gap is much bigger: German private schools score 84 points higher in reading, 62 points higher in math, and 59 points higher in science.  American private schools score 41 points higher in reading, 40 points higher in math, and 42 points higher in science.

What we need to worry about is that even at the 8th grade level, before competition in Korea really gets fierce, Korean private school 8th graders already score 60 points higher than our public school 8th graders in math.

What do you think they do right that we do wrong?

Why not ask them?


It may be interesting, but it's not really answering the question.  I was asking whether the processes that select students into public vs. private schools in the US are similar to those in other countries and, if not, whether the data you cite adjust for those differences. 

Could you please explain?

Why would you want to adjust for the very variable that you want to measure or understand?  There are many reasons you would expect private schools to score higher than public schools, so the only question really is just how much higher they score.  To use the specific example of Louisiana's private schools, which I'm directly familiar with, parents there, even though they must pay taxes to subsidize the public schools (and they pay almost all those costs), would rather pay the extra amount to send their children to private schools rather than send them to public schools.  This is why almost one in five students there are in private schools and not public schools.  So it's not unreasonable to expect them to score 20-35 NAEP math points higher than their public schools.  Do you think they might score even higher if their parents didn't have to bear the extra expenses of public schools which they get no benefit from?  Why would you want to adjust for that variable?


Simply put, if you select the kinds of students who tend to achieve more in private schools, then they will tend to perform better in academic assessments, regardless of the impact of the school, be it private or public.  Therefore, any comparative assessment of student performance in private and public schools must consider these selection processes in order to make a causal argument that the schools created any performance gap.  To illustrate, if I give one teacher a 10 year old student who possesses an IQ of 175 and was playing Mozart at the age of 2, and I give another teacher a 10 year old student who is still learning the alphabet, it is entirely probable that an academic assessment 8 years later would show greater performance on the part of the first student.  We would be remiss, however, to then conclude that this was entirely the result of differences in teacher efficacy.  Hence, if private schools have a tendency to enroll students with more social advantages than those who attend public schools, and we know these advantages covariates of academic performance, then we would must consider the consequences this selection process has on final assessment in order to make a convincing causal argument.  In addition, we must consider potential selection effects in the kinds of students who are assessed in each country.  Do all students in all countries have an equal probability of being included within the assessment?  If not, do the factors contributing to differences in selection also influence academic performance?

I've been following the progress of the Korean education system and its effect on their technological advancement for quite a while.  So I think I might be able to answer your question based on this direct observation.

It's the quality of the Korean students, and not the quality of their schools, which enables Koreans to outperform us at the 8th grade level by 105 points, and by a much larger margin than this at the 12th grade level, and to graduate 95% of their high school students with calculus already behind them.

While we argue about whether or not calculus is important in high school, China, Germany, Japan, and Korea are already teaching calculus to the vast majority of their students, and now make just about everything WE buy, all the way from cars to semiconductors to shoes.

Someone who understands calculus simply would not argue that calculus is not important for a high school student to learn.  A high school teacher in this country (if there ARE any) simply could not agree that learning calculus in high school is not critical in this technological age.

At the 8th grade level, as measured by PISA, the difference between their public schools and private schools is not that great (about 4 points, both of whom scored more than 70 points higher in math than our public school students and 20 points higher than our private school students).  We don't have the data point for their 12th grade students, but it's between the 8th and 12th grade that competition in schools in Korea really gets fierce, so the difference by then might be 100 points.


Direct observation is notoriously weak evidence for systemic features, and the patterns you are discussing are systemic.  Your observation also tells us absolutely nothing about the selection processes that determine a) who is going to what school and b) who is being tested in the first place. 


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 01:18:56 PM
According to the Bureau of Economic Analysis, our rate has been a negative 2-3% for years now.

Me:
Quote
Time to fact check.  The BEA website data is here (http://www.bea.gov/briefrm/saving.htm), and once again shows that you're just making stuff up.
Troll again:
Quote
http://www.bea.gov/national/nipaweb/Nipa-Frb.asp?Freq=Qtr

Comparison of Personal Saving in the National Income and Product Accounts (NIPAs) with Personal Saving in the Flow of Funds Accounts (FFAs)

What this shows is that no matter which way you measure it, our most creative accountants could not conceal that the US has a NEGATIVE personal savings rate

Do you even look at the links you give?  The table on the page you link to has personal savings rate (as percentage of national cash flow indicators) in lines 17 and 18.  The table I gave gives the rate as a flow of disposable income, which is more appropriate for the argument you are trying to make (including comparison to France).  Either way, all positive.

Quote
Please go back and study all my posts very carefully.

US health insurance does not cover exploding heads.  Maybe someone in France should take up this study instead.  - DvF


It's meaningless to measure personal savings as a percent of disposable income, for a lot of reasons (the main one of which is that our disposable income is almost nil anyway).  The only way to make a valid comparison is to measure it as a percent of GDP, and when measured that way, nobody disagrees that we have a NEGATIVE personal savings rate and France has a 27% savings rate.  Also, the definition of disposble savings is not consistent from country to country, but the definition of GNP is (almost).

http://www.newyorkfed.org/research/current_issues/ci13-4/ci13-4.html

Personal savings drop to a 73-year low
http://www.msnbc.msn.com/id/16922582/


This is our REAL rate as a percent of GDP (or actually GNP), and it's NEGATIVE:
http://research.stlouisfed.org/publications/review/07/11/Guidolin.pdf
http://eaja.net/Documents/personalsavinggnp.gif


This was BEFORE obamacare, which can do nothing but seal our bankruptcy.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 01:23:10 PM
Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?

What I make of that is that abortions are greatly reduced in big states that have a predominantly rural population and few abortion providers, while abortions are more common in places where abortions can be more readily obtained.  

I can also see a strong correlation with places where small-town, community values against premarital sex predominate having lower abortion rates than places that have more liberal ideas about non-marital sex.

I see a strong correlation between places where people are, in general, anti-abortion based on public polls (hence in part the fewer abortion providers) and a lower abortion rate and places where abortion is more accepted and a higher abortion rate.

As for the Catholic part specifically, I see that places that were settled by people who were Catholic and are now very populous places still have a large proportion of Catholics.

You're still failing on correlation versus causation if your point was to conclude that having a large Catholic population necessarily leads to a higher abortion rate since you have failed to control for some very relevant confounding variables.

The very first thing you must do is calculate the correlation.  Only then should you comment on it:

State,Catholics,Marriages
Utah ,8%,8.6
South Dakota ,21%,8.3
Maine ,15%,7.9
Texas ,29%,7.4
New Hampshire ,24%,7.3
Montana ,12%,7.3
New York ,38%,7
Iowa ,17%,6.9
North Dakota ,22%,6.5
Massachusetts ,43%,6.1
Illinois ,30%,5.8
Connecticut ,39%,5.5
New Jersey ,41%,5


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 01:28:58 PM
I am not an expert in the field, but I'm fairly certain that nothing that has been presented so far actually proves this statement.

Quote
What Korea and Japan proved is that all of our research ought to be handled by the free enterprise system (just as education ought to be).


More to the point, does the following finding account for the processes selecting different kinds of students into private schools in the first place? 


Quote
Correction: I noted previously (from memory) that private school students in Louisiana score 30 points higher than their public school students, but that was actually Texas private school students (who score 31 points higher).  Private school students in Louisiana actually score only 24 points higher than their public school students. That's quite a difference, though, when you realize that the difference between Asians and blacks is only about 60 points.

An interesting way to answer that question is PISA:

http://pisa2000.acer.edu.au/interactive_results.php

If you query it for Korea, and use a school variable of "public/private" you will find that 52% of Korean 8th graders attend private schools and score about 4 points higher than the 48% who attend their public schools.

In most countries, the gap is much bigger: German private schools score 84 points higher in reading, 62 points higher in math, and 59 points higher in science.  American private schools score 41 points higher in reading, 40 points higher in math, and 42 points higher in science.

What we need to worry about is that even at the 8th grade level, before competition in Korea really gets fierce, Korean private school 8th graders already score 60 points higher than our public school 8th graders in math.

What do you think they do right that we do wrong?

Why not ask them?


It may be interesting, but it's not really answering the question.  I was asking whether the processes that select students into public vs. private schools in the US are similar to those in other countries and, if not, whether the data you cite adjust for those differences. 

Could you please explain?

Why would you want to adjust for the very variable that you want to measure or understand?  There are many reasons you would expect private schools to score higher than public schools, so the only question really is just how much higher they score.  To use the specific example of Louisiana's private schools, which I'm directly familiar with, parents there, even though they must pay taxes to subsidize the public schools (and they pay almost all those costs), would rather pay the extra amount to send their children to private schools rather than send them to public schools.  This is why almost one in five students there are in private schools and not public schools.  So it's not unreasonable to expect them to score 20-35 NAEP math points higher than their public schools.  Do you think they might score even higher if their parents didn't have to bear the extra expenses of public schools which they get no benefit from?  Why would you want to adjust for that variable?


Simply put, if you select the kinds of students who tend to achieve more in private schools, then they will tend to perform better in academic assessments, regardless of the impact of the school, be it private or public.  Therefore, any comparative assessment of student performance in private and public schools must consider these selection processes in order to make a causal argument that the schools created any performance gap.  To illustrate, if I give one teacher a 10 year old student who possesses an IQ of 175 and was playing Mozart at the age of 2, and I give another teacher a 10 year old student who is still learning the alphabet, it is entirely probable that an academic assessment 8 years later would show greater performance on the part of the first student.  We would be remiss, however, to then conclude that this was entirely the result of differences in teacher efficacy.  Hence, if private schools have a tendency to enroll students with more social advantages than those who attend public schools, and we know these advantages covariates of academic performance, then we would must consider the consequences this selection process has on final assessment in order to make a convincing causal argument.  In addition, we must consider potential selection effects in the kinds of students who are assessed in each country.  Do all students in all countries have an equal probability of being included within the assessment?  If not, do the factors contributing to differences in selection also influence academic performance?

I've been following the progress of the Korean education system and its effect on their technological advancement for quite a while.  So I think I might be able to answer your question based on this direct observation.

It's the quality of the Korean students, and not the quality of their schools, which enables Koreans to outperform us at the 8th grade level by 105 points, and by a much larger margin than this at the 12th grade level, and to graduate 95% of their high school students with calculus already behind them.

While we argue about whether or not calculus is important in high school, China, Germany, Japan, and Korea are already teaching calculus to the vast majority of their students, and now make just about everything WE buy, all the way from cars to semiconductors to shoes.

Someone who understands calculus simply would not argue that calculus is not important for a high school student to learn.  A high school teacher in this country (if there ARE any) simply could not agree that learning calculus in high school is not critical in this technological age.

At the 8th grade level, as measured by PISA, the difference between their public schools and private schools is not that great (about 4 points, both of whom scored more than 70 points higher in math than our public school students and 20 points higher than our private school students).  We don't have the data point for their 12th grade students, but it's between the 8th and 12th grade that competition in schools in Korea really gets fierce, so the difference by then might be 100 points.


Direct observation is notoriously weak evidence for systemic features, and the patterns you are discussing are systemic.  Your observation also tells us absolutely nothing about the selection processes that determine a) who is going to what school and b) who is being tested in the first place. 

Agreed.

And that's why I trust the data far, far more than any person's personal observation.  And that's why we need both the US and Korea to participate in the 12th grade TIMSS, which neither country did in the last round.  Korea scored so high on GRE that the College Board accused them of cheating, only to discover that they DID score this high without cheating.



Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 03, 2010, 01:34:21 PM
Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?

What I make of that is that abortions are greatly reduced in big states that have a predominantly rural population and few abortion providers, while abortions are more common in places where abortions can be more readily obtained.  

I can also see a strong correlation with places where small-town, community values against premarital sex predominate having lower abortion rates than places that have more liberal ideas about non-marital sex.

I see a strong correlation between places where people are, in general, anti-abortion based on public polls (hence in part the fewer abortion providers) and a lower abortion rate and places where abortion is more accepted and a higher abortion rate.

As for the Catholic part specifically, I see that places that were settled by people who were Catholic and are now very populous places still have a large proportion of Catholics.

You're still failing on correlation versus causation if your point was to conclude that having a large Catholic population necessarily leads to a higher abortion rate since you have failed to control for some very relevant confounding variables.

The very first thing you must do is calculate the correlation.  Only then should you comment on it:

State,Catholics,Marriages
Utah ,8%,8.6
South Dakota ,21%,8.3
Maine ,15%,7.9
Texas ,29%,7.4
New Hampshire ,24%,7.3
Montana ,12%,7.3
New York ,38%,7
Iowa ,17%,6.9
North Dakota ,22%,6.5
Massachusetts ,43%,6.1
Illinois ,30%,5.8
Connecticut ,39%,5.5
New Jersey ,41%,5


No, the very first thing to do is to formulate a hypothesis based on a model of the situation.  Then, you design an experiment identifying likely parameters that will affect the outcome.  As part of the data analysis from the experiment, you look for confounding effects in the data to take them out of correlations or at least account for multiple effects arising from the interaction between independent variables that cannot be otherwise controlled. 

Oh, and units would be useful here since I have no idea whether that final column is a rate that has been normalized in a reasonable manner or just garbage.  I'm also not sure what the second column is since it has no units.

I can do anything I like on random numbers, but if the numbers are meaningless, any correlation is equally meaningless.  That is Rule 1 of science.  Was the point of your repeated posts to demonstrate that you need better education and so you are advocating that other people do as well?


Title: Re: assuming too much math knowledge?
Post by: conjugate on August 03, 2010, 01:39:09 PM

Another obseravation that they have made, which I agree with, is that if students don't learn calculus in high school, it's too late to learn it in college. 


I never took calculus in high school.  Are you going to revoke my PhD in mathematics??
Neither did I, and my PhD is still valid, according to the institutions at which I've worked.

Well, third time's the charm, perhaps:

John Knight:  What are we supposed to do about it?  


The very first thing you must do is calculate the correlation.  Only then should you comment on it:


Okay, you've calculated the correlations.  Now that we know that, what should we, as higher education professionals do about them(in your opinion)?  You've shown links claiming that the personal savings rate is NEGATIVE (your caps) as a percentage of GNP.  What should I as a higher education professional do about that (besides save money for retirement, which I'm doing, by the way)?  


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 02:10:29 PM
Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?

What I make of that is that abortions are greatly reduced in big states that have a predominantly rural population and few abortion providers, while abortions are more common in places where abortions can be more readily obtained.  

I can also see a strong correlation with places where small-town, community values against premarital sex predominate having lower abortion rates than places that have more liberal ideas about non-marital sex.

I see a strong correlation between places where people are, in general, anti-abortion based on public polls (hence in part the fewer abortion providers) and a lower abortion rate and places where abortion is more accepted and a higher abortion rate.

As for the Catholic part specifically, I see that places that were settled by people who were Catholic and are now very populous places still have a large proportion of Catholics.

You're still failing on correlation versus causation if your point was to conclude that having a large Catholic population necessarily leads to a higher abortion rate since you have failed to control for some very relevant confounding variables.

The very first thing you must do is calculate the correlation.  Only then should you comment on it:

State,Catholics,Marriages
Utah ,8%,8.6
South Dakota ,21%,8.3
Maine ,15%,7.9
Texas ,29%,7.4
New Hampshire ,24%,7.3
Montana ,12%,7.3
New York ,38%,7
Iowa ,17%,6.9
North Dakota ,22%,6.5
Massachusetts ,43%,6.1
Illinois ,30%,5.8
Connecticut ,39%,5.5
New Jersey ,41%,5


No, the very first thing to do is to formulate a hypothesis based on a model of the situation.  Then, you design an experiment identifying likely parameters that will affect the outcome.  As part of the data analysis from the experiment, you look for confounding effects in the data to take them out of correlations or at least account for multiple effects arising from the interaction between independent variables that cannot be otherwise controlled. 

Oh, and units would be useful here since I have no idea whether that final column is a rate that has been normalized in a reasonable manner or just garbage.  I'm also not sure what the second column is since it has no units.

I can do anything I like on random numbers, but if the numbers are meaningless, any correlation is equally meaningless.  That is Rule 1 of science.  Was the point of your repeated posts to demonstrate that you need better education and so you are advocating that other people do as well?

Why don't you just amaze yourself by simply figuring the correlation of both sets of data, and THEN learn the details of what you calculated.

Until you do that, you cannot possibly get the point.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 03, 2010, 02:25:45 PM
Why don't you just amaze yourself by simply figuring the correlation of both sets of data, and THEN learn the details of what you calculated.

Until you do that, you cannot possibly get the point.

Fine, I'll play to get you to play.  If I plot column 3 versus column 2, I see a trend that indicates that big numbers in one column indicate big numbers in the other column.  Happy?

Now, you try to follow the scientific reasoning that one cannot draw any conclusion about the Catholic issue in terms of causation (or even necessarily in terms of correlation worth speaking about) for either abortion rate or marriage rate (or whatever your numbers are supposed to have since those units really do matter to be able to draw a conclusion) simply because you haven't designed an experiment that answers that question.  You've taken two sets of numbers based on a third category of state and used them as though they were independent data points collected in such a way that they could answer a question of correlation.  Where I live here in science land and with some knowledge of proper statistical sampling techniques to get a data set to answer a question, that's called garbage and my introductory students in math and science fail their assignments for doing such things.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 05:13:12 PM
Why don't you just amaze yourself by simply figuring the correlation of both sets of data, and THEN learn the details of what you calculated.

Until you do that, you cannot possibly get the point.

Fine, I'll play to get you to play.  If I plot column 3 versus column 2, I see a trend that indicates that big numbers in one column indicate big numbers in the other column.  Happy?

Now, you try to follow the scientific reasoning that one cannot draw any conclusion about the Catholic issue in terms of causation (or even necessarily in terms of correlation worth speaking about) for either abortion rate or marriage rate (or whatever your numbers are supposed to have since those units really do matter to be able to draw a conclusion) simply because you haven't designed an experiment that answers that question.  You've taken two sets of numbers based on a third category of state and used them as though they were independent data points collected in such a way that they could answer a question of correlation.  Where I live here in science land and with some knowledge of proper statistical sampling techniques to get a data set to answer a question, that's called garbage and my introductory students in math and science fail their assignments for doing such things.

Can you guess what your score would have been on TIMSS?

The problem is not to draw any conclusions from this correlation: the problem is to calculate how closely the data correlates, using the mathematical tool of your choice.

Let's do the calculation for you.  The Pearson Coefficient for Catholics vs. abortions is 0.8589 and for Catholics vs. marriages is 0.772.

What does that mean to you?

Can you calculate the Pearson Coefficient for the following data?:


State,Catholics,Cancer
New Jersey ,41%,299.7
Illinois ,30%,292.8
Pennsylvania ,29%,290.9
Massachusetts ,43%,285.7
Texas ,29%,284.2
New York ,38%,274.7
Connecticut ,39%,264.9
North Dakota ,22%,257
Montana ,12%,250.5
Iowa ,17%,248.8
South Dakota ,21%,233.1
Utah ,8%,192.9

Don't draw conclusions from the data: just determine how closely it correlates.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 05:19:36 PM
Correction: the Pearson Coefficient is -0.772, not 0.772.  Why is that significant?  What does that mean about the data, not about the possible causal effects?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on August 03, 2010, 05:41:13 PM
Someone who understands calculus simply would not argue that calculus is not important for a high school student to learn.

Several of us have already done so.  Of course, you might argue that my 30+ years experience of research and teaching in the mathematical sciences (including at 5 State flagship universities) does not mean I have any understanding of the Calculus.

However, you might look at what a colleague at the Mathematical Association of America (http://www.maa.org/columns/launchings/launchings_06_09.html) had to say recently (summarizing several studies, all quoted in the article):
Quote
There is no evidence that taking calculus in high school is of any benefit unless a student learns it well enough to earn college credit for it, and there is some evidence—the high percentage of students who go from calculus in high school to precalculus in college—that an introduction to calculus that builds on an inadequate foundation can be detrimental.

On the other matter:
Quote
It's meaningless to measure personal savings as a percent of disposable income, for a lot of reasons (the main one of which is that our disposable income is almost nil anyway).

This is exactly what the article you now reference does. (Did you even read the title of Chart 1 in your reference (http://www.newyorkfed.org/research/current_issues/ci13-4/chart1.html)?  "Personal Savings Rate: Percentage of Disposable Personal Income").

Good God, I hope you have nothing to do with education, higher or otherwise. - DvF


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 05:45:38 PM

Another obseravation that they have made, which I agree with, is that if students don't learn calculus in high school, it's too late to learn it in college. 


I never took calculus in high school.  Are you going to revoke my PhD in mathematics??
Neither did I, and my PhD is still valid, according to the institutions at which I've worked.

Well, third time's the charm, perhaps:

John Knight:  What are we supposed to do about it?  


The very first thing you must do is calculate the correlation.  Only then should you comment on it:


Okay, you've calculated the correlations.  Now that we know that, what should we, as higher education professionals do about them(in your opinion)?  You've shown links claiming that the personal savings rate is NEGATIVE (your caps) as a percentage of GNP.  What should I as a higher education professional do about that (besides save money for retirement, which I'm doing, by the way)?  

What should "we" do about it?  Why don't *you* apply that Piled High and Deep degree to come up with some explanations for just HOW American students who participated in the NSF physics program managed to score LOWER than if they'd just guessed?  From other forums, I have a list of about 20 possible reasons.  But before I post them here and get censored, why don't YOU present just one idea of how you think this is even possible?

You might take into account that somehow those taking NSF physics courses managed to score lower than American AP students.  The boys scored 49 points lower and the girls scored 50 points lower (and 15 points lower than Greek girls, 42 points lower than Greek boys).


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 03, 2010, 06:27:07 PM
Someone who understands calculus simply would not argue that calculus is not important for a high school student to learn.

Several of us have already done so.  Of course, you might argue that my 30+ years experience of research and teaching in the mathematical sciences (including at 5 State flagship universities) does not mean I have any understanding of the Calculus.

However, you might look at what a colleague at the Mathematical Association of America (http://www.maa.org/columns/launchings/launchings_06_09.html) had to say recently (summarizing several studies, all quoted in the article):
Quote
There is no evidence that taking calculus in high school is of any benefit unless a student learns it well enough to earn college credit for it, and there is some evidence—the high percentage of students who go from calculus in high school to precalculus in college—that an introduction to calculus that builds on an inadequate foundation can be detrimental.

On the other matter:
Quote
It's meaningless to measure personal savings as a percent of disposable income, for a lot of reasons (the main one of which is that our disposable income is almost nil anyway).

This is exactly what the article you now reference does. (Did you even read the title of Chart 1 in your reference (http://www.newyorkfed.org/research/current_issues/ci13-4/chart1.html)?  "Personal Savings Rate: Percentage of Disposable Personal Income").

Good God, I hope you have nothing to do with education, higher or otherwise. - DvF

Would you like me to send you dozens of spreadsheets, graphs, and charts from the BEA which calculate personal savings as a percent of GDP or GNP?  It DOES appear that they are no longer on the BEA web site:

http://www.bea.doc.gov/bea/dn/saverate.htm

So, voila, I go to archive.org to locate the archived copies of those charts and graphs, and it appears that ALL of these archived copies cannot be accessed.  Gee, whiz, I wonder why?

http://web.archive.org/web/*/http://www.bea.doc.gov/bea/dn/saverate.htm

So I go to the US Statistical Abstract and it appears that even THEY have changed the way they calculate personal savings.  However, there IS a table on the following url that's ALMOST consistent with what the BEA previously had on their web site. Table 659. Flow of Funds Accounts—Composition of Individuals’ Savings:  1990 to 2008

http://www.census.gov/prod/2009pubs/10statab/income.pdf

It shows that personal savings was a negative $182 billion in 2000 and a negative $61.2 billion in 2006.  They have sanitized this data immensely since it appeared on the BEA web site.



Title: Re: assuming too much math knowledge?
Post by: tinyzombie on August 03, 2010, 06:56:25 PM
It's bad form to post multiple times in a row, OP. It's worse to do it multiple times.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on August 03, 2010, 07:01:21 PM
Would you like me to send you dozens of spreadsheets, graphs, and charts

No, because pretty near 100% of the time you've given such a citation they haven't said what you said/thought/pretended they did.

Quote
So, voila, I go to archive.org to locate the archived copies of those charts and graphs, and it appears that ALL of these archived copies cannot be accessed.  Gee, whiz, I wonder why?

Because archive.org does not archive your imagination.

Quote
http://www.census.gov/prod/2009pubs/10statab/income.pdf

It shows that personal savings was a negative $182 billion in 2000 and a negative $61.2 billion in 2006.

If you read that chart carefully, what Table 659 actually shows it is a drop in the value of securities (mainly corporate equities) for those two years.  The negative savings numbers that do appear on your chart are numbers that do not include savings in the form of tangible ownership (such as houses or gold), and are only negative for 2 of the 18 years the chart covers.

I do not see how this has any relation to anything at all you are claiming on this thread. - DvF


Title: Re: assuming too much math knowledge?
Post by: spork on August 03, 2010, 08:05:03 PM
It's bad form to post multiple times in a row, OP. It's worse to do it multiple times.

He's a Zombie Poster -- clinically dead, but won't stop.


Title: Re: assuming too much math knowledge?
Post by: marfa on August 04, 2010, 09:49:38 AM
It's bad form to post multiple times in a row, OP. It's worse to do it multiple times.

He's a Zombie Poster -- clinically dead, but won't stop.

I think OP is feeding off this.  I'm out.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 04, 2010, 02:09:27 PM
Would you like me to send you dozens of spreadsheets, graphs, and charts

No, because pretty near 100% of the time you've given such a citation they haven't said what you said/thought/pretended they did.

Quote
So, voila, I go to archive.org to locate the archived copies of those charts and graphs, and it appears that ALL of these archived copies cannot be accessed.  Gee, whiz, I wonder why?

Because archive.org does not archive your imagination.

Quote
http://www.census.gov/prod/2009pubs/10statab/income.pdf

It shows that personal savings was a negative $182 billion in 2000 and a negative $61.2 billion in 2006.

If you read that chart carefully, what Table 659 actually shows it is a drop in the value of securities (mainly corporate equities) for those two years.  The negative savings numbers that do appear on your chart are numbers that do not include savings in the form of tangible ownership (such as houses or gold), and are only negative for 2 of the 18 years the chart covers.

I do not see how this has any relation to anything at all you are claiming on this thread. - DvF

Do you agree or disagree that Table 646 on the following page of the US Stastical Abstract reports that personal saving in 2000 was a NEGATIVE $8.5 billion:

http://www.census.gov/prod/2002pubs/01statab/income.pdf

Do you agree that if personal saving is negative, it makes no sense to measure it as a percent of disposable income?



Title: Re: assuming too much math knowledge?
Post by: johnknight on August 04, 2010, 02:11:48 PM
Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?

What I make of that is that abortions are greatly reduced in big states that have a predominantly rural population and few abortion providers, while abortions are more common in places where abortions can be more readily obtained.  

I can also see a strong correlation with places where small-town, community values against premarital sex predominate having lower abortion rates than places that have more liberal ideas about non-marital sex.

I see a strong correlation between places where people are, in general, anti-abortion based on public polls (hence in part the fewer abortion providers) and a lower abortion rate and places where abortion is more accepted and a higher abortion rate.

As for the Catholic part specifically, I see that places that were settled by people who were Catholic and are now very populous places still have a large proportion of Catholics.

You're still failing on correlation versus causation if your point was to conclude that having a large Catholic population necessarily leads to a higher abortion rate since you have failed to control for some very relevant confounding variables.


If more than 10,000 students just guessed at the answer to the following four part multiple choice question, and if they have no idea what the answer is, and if their answsers are just random guesses, on average, what percentage of them will get it correct:


<begin TIMSS problem>
H.4 Two spheres with masses m and 2m respectivel are connected by a light string and suspended at rest.  The system is released and falls freely, as shown in the figure (the figure can't be posted here, but it shows two spheres connected by a string with one sphere suspended from the other sphere).

if g is the acceleration due to gravity, what is the tension in the string as the system falls?

A. 0

B. mg

C. 2mg

D. 3mg
<end TIMSS problem>



Without worrying about the correct answer, and assuming that 10,000 students merely guessed randomly, what percentage of students do you believe would get this correct, on average?


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 04, 2010, 03:53:47 PM
Would you like me to send you dozens of spreadsheets, graphs, and charts

No, because pretty near 100% of the time you've given such a citation they haven't said what you said/thought/pretended they did.

Quote
So, voila, I go to archive.org to locate the archived copies of those charts and graphs, and it appears that ALL of these archived copies cannot be accessed.  Gee, whiz, I wonder why?

Because archive.org does not archive your imagination.

Quote
http://www.census.gov/prod/2009pubs/10statab/income.pdf

It shows that personal savings was a negative $182 billion in 2000 and a negative $61.2 billion in 2006.

If you read that chart carefully, what Table 659 actually shows it is a drop in the value of securities (mainly corporate equities) for those two years.  The negative savings numbers that do appear on your chart are numbers that do not include savings in the form of tangible ownership (such as houses or gold), and are only negative for 2 of the 18 years the chart covers.

I do not see how this has any relation to anything at all you are claiming on this thread. - DvF

By definition, personal saving does not include housing.  In economics, personal saving has been defined as disposable income minus personal consumption expenditure, as it is on the following page from the Japanese government web site:

http://web.archive.org/web/19990223223925/http://www.stat.go.jp/156.htm


<begin>
Summary of December Survey Results


(1) Expenditure for All Households
         The average monthly living expenditure per household for December 1998 was
    406,682 yen, the same level in nominal but down 0.6% in real terms from the previous year.

(2) Income and Expenditure for Workers' Households
         The average monthly income per household stood at 1,164,785 yen, down 2.2% in
    nominal and 2.8% in real terms from the previous year.
         Living expenditure was 444,211 yen, up 0.5% in nominal but down 0.1% in real
    terms from the previous year.

The  graph which cannot be posted here shows the following:

Workers' households
Income 1,080,114
Disposable income 972,572
Living expenditure 418,221
Average propensity to consume 43%

<end>


iow, personal saving in Japan per worker's household increased that month, December, by 554,351 yen.

This is all very clear.  Each Japanese citizen knows exactly how much he earns, how much he spends for government, and what the AVERAGE per household percent of income was deposited in personal saving that month.  As a percent of disposable income personal saving in Japan was 57%, but they define disposable income very differently than we do, so the only way to make a direct comparison is to calculate it in personal saving as a percent of GDP.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 04, 2010, 03:59:24 PM
It's bad form to post multiple times in a row, OP. It's worse to do it multiple times.

Wouldn't it be worse form to fail to respond to the many excellent inputs?


Title: Re: assuming too much math knowledge?
Post by: kiana on August 04, 2010, 04:00:25 PM
It's bad form to post multiple times in a row, OP. It's worse to do it multiple times.

Wouldn't it be worse form to fail to respond to the many excellent inputs?

That would assume that one is actually responding to the inputs in the first place.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on August 04, 2010, 04:22:12 PM
The Japanese date (a) is not from 2000, the only negative US year, and (b) is not comparable to the US rate, since they are discussing "households" and the US data includes some corporate entities.

I agree with malfa, I'm done. - DvF


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 04, 2010, 05:02:50 PM
The Japanese date (a) is not from 2000, the only negative US year, and (b) is not comparable to the US rate, since they are discussing "households" and the US data includes some corporate entities.

I agree with malfa, I'm done. - DvF

<being quote>
http://www.msnbc.msn.com/id/11098797/
U.S. savings rate hits lowest level since 1933
Consumers depleting savings to buy cars, other big-ticket itemsAdvertisement | ad info
. Douglas Pizac / AP file
Americans have been buying big-ticket items such as cars instead of saving their money.
updated 1/30/2006 12:10:21 PM ET
Share Print Font: +-WASHINGTON — Americans’ personal savings rate dipped into negative territory in 2005, something that hasn’t happened since the Great Depression. Consumers depleted their savings to finance the purchases of cars and other big-ticket items.

The Commerce Department reported Monday that the savings rate fell into negative territory at minus 0.5 percent, meaning that Americans not only spent all of their after-tax income last year but had to dip into previous savings or increase borrowing.

The savings rate has been negative for an entire year only twice before — in 1932 and 1933 — two years when the country was struggling to cope with the Great Depression, a time of massive business failures and job layoffs.

With employment growth strong now, analysts said that different factors are at play. Americans feel they can spend more, given that the value of their homes, the biggest asset for most families, has been rising sharply in recent years.

But analysts cautioned that this behavior was risky at a time when 78 million Americans are on the verge of retirement.

“Americans seem to have the feeling that it is wimpish to save,” said David Wyss, chief economist at Standard & Poor’s in New York. “The idea is to put away money for old age and we are just not doing that.”

The Commerce report said that consumer spending for December rose by 0.9 percent, more than double the 0.4 percent increase in incomes last month.
<end quote>

Furthermore, obamacare will SINK the U.S. economy--you will NEVER see a positive personal savings rate after this.  You have ALL the information you need to calculate both the Japanese and US personal saving rate as a percent of GDP.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 05, 2010, 07:53:06 AM
Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?

What I make of that is that abortions are greatly reduced in big states that have a predominantly rural population and few abortion providers, while abortions are more common in places where abortions can be more readily obtained.  

I can also see a strong correlation with places where small-town, community values against premarital sex predominate having lower abortion rates than places that have more liberal ideas about non-marital sex.

I see a strong correlation between places where people are, in general, anti-abortion based on public polls (hence in part the fewer abortion providers) and a lower abortion rate and places where abortion is more accepted and a higher abortion rate.

As for the Catholic part specifically, I see that places that were settled by people who were Catholic and are now very populous places still have a large proportion of Catholics.

You're still failing on correlation versus causation if your point was to conclude that having a large Catholic population necessarily leads to a higher abortion rate since you have failed to control for some very relevant confounding variables.


If more than 10,000 students just guessed at the answer to the following four part multiple choice question, and if they have no idea what the answer is, and if their answsers are just random guesses, on average, what percentage of them will get it correct:


<begin TIMSS problem>
H.4 Two spheres with masses m and 2m respectivel are connected by a light string and suspended at rest.  The system is released and falls freely, as shown in the figure (the figure can't be posted here, but it shows two spheres connected by a string with one sphere suspended from the other sphere).

if g is the acceleration due to gravity, what is the tension in the string as the system falls?

A. 0

B. mg

C. 2mg

D. 3mg
<end TIMSS problem>



Without worrying about the correct answer, and assuming that 10,000 students merely guessed randomly, what percentage of students do you believe would get this correct, on average?


Assuming pure random sampling from a distribution, four choices leads to a 1/4 expectation for all answers so 25% of the students should get it correct.

However, I expect science students to do better than random guessing on a science question.  Knowing something about how multiple-choice standardized tests are constructed, students who took classes and are working through problems that are far different from those they have previously seen should do worse than chance outcomes would predict if they don't get the right answer.  In fact, I can tell you that in problems of this type, far more people should hone in on a particular wrong answer because that answer logically follows from what most people who have a solid background, but haven't thought about this particular situation will select, including experts who have doctorates in physics, isn't the right one.

Go take a class in teaching science taught by people who focus on critical thinking instead of plug-and-chug math problems.  It's a lot of fun and an eye-opening experience to see what top researchers and educators get wrong for some of these problems on their initial predictions because they haven't thought through all the implications.

Just because someone gives you some data tells you to run a correlation doesn't mean that person was right to do so.  Anyone can be a button-pushing monkey to generate a graph and read off a correlation coefficient and other curve-fit information.  If you don't know how that data was generated, then you don't actually know what kind of statistical analysis to apply to get a useful conclusion, regardless of how near perfect that correlation coefficient is.  That's something I teach my students in statistics (a math class just in case you didn't know).


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 05, 2010, 12:15:46 PM
Would you say the following indicates a strong relationship between being Catholic and having an abortion?



State,Catholics,Abortions
New York ,38%,43.3
New Jersey ,41%,35.1
Connecticut ,39%,31.2
Massachusetts ,43%,30.2
Illinois ,30%,26.4
Texas ,29%,24.8
Pennsylvania ,29%,18.9
New Hampshire ,24%,17.5
Montana ,12%,16.5
Maine ,15%,16.2
North Dakota ,22%,14.9
Iowa ,17%,14.6
Utah ,8%,12.8


What kind of relationship does it represent?  How would you explain or calculate how much these data points correlate with each other?  Does it prove that the Catholic Church has been successful at reducing abortion amongst Catholic women?

What do you make of this?

What I make of that is that abortions are greatly reduced in big states that have a predominantly rural population and few abortion providers, while abortions are more common in places where abortions can be more readily obtained.  

I can also see a strong correlation with places where small-town, community values against premarital sex predominate having lower abortion rates than places that have more liberal ideas about non-marital sex.

I see a strong correlation between places where people are, in general, anti-abortion based on public polls (hence in part the fewer abortion providers) and a lower abortion rate and places where abortion is more accepted and a higher abortion rate.

As for the Catholic part specifically, I see that places that were settled by people who were Catholic and are now very populous places still have a large proportion of Catholics.

You're still failing on correlation versus causation if your point was to conclude that having a large Catholic population necessarily leads to a higher abortion rate since you have failed to control for some very relevant confounding variables.


If more than 10,000 students just guessed at the answer to the following four part multiple choice question, and if they have no idea what the answer is, and if their answsers are just random guesses, on average, what percentage of them will get it correct:


<begin TIMSS problem>
H.4 Two spheres with masses m and 2m respectivel are connected by a light string and suspended at rest.  The system is released and falls freely, as shown in the figure (the figure can't be posted here, but it shows two spheres connected by a string with one sphere suspended from the other sphere).

if g is the acceleration due to gravity, what is the tension in the string as the system falls?

A. 0

B. mg

C. 2mg

D. 3mg
<end TIMSS problem>



Without worrying about the correct answer, and assuming that 10,000 students merely guessed randomly, what percentage of students do you believe would get this correct, on average?


Assuming pure random sampling from a distribution, four choices leads to a 1/4 expectation for all answers so 25% of the students should get it correct.

However, I expect science students to do better than random guessing on a science question.  Knowing something about how multiple-choice standardized tests are constructed, students who took classes and are working through problems that are far different from those they have previously seen should do worse than chance outcomes would predict if they don't get the right answer.  In fact, I can tell you that in problems of this type, far more people should hone in on a particular wrong answer because that answer logically follows from what most people who have a solid background, but haven't thought about this particular situation will select, including experts who have doctorates in physics, isn't the right one.

Go take a class in teaching science taught by people who focus on critical thinking instead of plug-and-chug math problems.  It's a lot of fun and an eye-opening experience to see what top researchers and educators get wrong for some of these problems on their initial predictions because they haven't thought through all the implications.

Just because someone gives you some data tells you to run a correlation doesn't mean that person was right to do so.  Anyone can be a button-pushing monkey to generate a graph and read off a correlation coefficient and other curve-fit information.  If you don't know how that data was generated, then you don't actually know what kind of statistical analysis to apply to get a useful conclusion, regardless of how near perfect that correlation coefficient is.  That's something I teach my students in statistics (a math class just in case you didn't know).

Miracles never cease.  You actually answered a question correctly.  And you even provided a *possible* explanation for why American students, and in particular NSF physics students, scored lower on 12th grade TIMSS than if they'd just guessed.  You ought to supply your theory to the NSF because they seem to be clueless about why their top students score lower than Greek girls, and 50 points lower than AP physics students, and this is surely a possibility.  Another theory which has been advanced on a different forum is that our textbooks, both those used by AP physics students and NSF physics students, are wrong, and intentionally so.  This seems to be a more plausible explanation for why our scores are so low on a nationwide basis while students from so many other countries score so much higher.  AND for why so many American companies have been so unsuccessful at manufacturing semiconductors here while they've been so successful elsewhere.

But your theory certainly is worth further exploration.

On this particular question, only 22% of American students got it right.  And only 13% got question H10 correct, a question about spheres and vectors.



Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 05, 2010, 12:40:07 PM

Miracles never cease.  You actually answered a question correctly. 

How about you answering a question--any question asked by anyone in the last three pages regarding your motivation for posting here and what you expect from us?

I assure you that my track record in answering questions here correctly is higher than yours.

And you even provided a *possible* explanation for why American students, and in particular NSF physics students, scored lower on 12th grade TIMSS than if they'd just guessed.  You ought to supply your theory to the NSF because they seem to be clueless about why their top students score lower than Greek girls, and 50 points lower than AP physics students, and this is surely a possibility.  Another theory which has been advanced on a different forum is that our textbooks, both those used by AP physics students and NSF physics students, are wrong, and intentionally so.  This seems to be a more plausible explanation for why our scores are so low on a nationwide basis while students from so many other countries score so much higher.  AND for why so many American companies have been so unsuccessful at manufacturing semiconductors here while they've been so successful elsewhere.

But your theory certainly is worth further exploration.

On this particular question, only 22% of American students got it right.  And only 13% got question H10 correct, a question about spheres and vectors.

I can answer these questions because, unlike you evidently, I spend quite a lot of time thinking about how American students (and other students in American schools) learn math and science.  I am involved in the community of people (science and math educators and education research people who focus on science and math) who see test scores as indicators of what students still need to learn and we have voluminous discussions about what to do to help students learn more efficiently and be able to apply their learning outside of these tests.  I attend and contribute to workshops to spread that information to other people.  I go to conferences on this topic.  I have nearly daily discussions on this topic.  I am not the ignorant one here or at least all evidence that I have is that I am not ignorant to the extent that you appear to be on this topic.

That is why I am immensely irked by what you have done on this thread in terms of citing random garbage as a data dump, refusing to engage with the issues of teaching and learning of math and science, and a repeatedly refusing to look at the implications of data gathering methods leading to raw numbers, which are useless for getting people to focus on what we know and what we can do.  I am also quite irked by your evident lack of scientific knowledge since you have repeatedly focused on the numbers without thinking about how they were gathered and what factors could be contributing to those numbers, which is contrary to any kind of scientific thinking program that I have ever encountered.

I don't have to tell the NSF and AP people anything because, according to the last discussions I've had with people who are working on those curricula, they are on task and making adjustments that should lead to even better results in things that matter, even if those average test scores on standardized international tests don't go up.  The goal of good science and math education isn't to have high tests scores on standardized tests at the high school level.  Since you don't appear to know even that basic fact, why should anyone continue to take you seriously (assuming anyone still does)?


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 05, 2010, 01:44:33 PM
The Japanese date (a) is not from 2000, the only negative US year, and (b) is not comparable to the US rate, since they are discussing "households" and the US data includes some corporate entities.

I agree with malfa, I'm done. - DvF




So if I agree with you that our personal savings rate is 8%, will that make a difference?

This is from Asia Week:


Country,
,Savings
,% of GDP
,
Singapore,51%
Malaysia,41%
China,40%
South Korea,37%
Indonesia,37%
Thailand,36%
Bhutan,36%
Brunei,35%
Hong Kong,35%
Russia,32%
Japan,31%
Saudi Arabia,30%
Iran,30%
Macau,28%
P. N. Guinea,28%
India,28%
Switzerland,27%
New Zealand,26%
Taiwan,25%
Germany,23%
Italy,22%
France,21%
Canada,21%
Brazil,21%
Kenya,21%
Nigeria,20%
Turkey,20%
South Africa,19%
Mexico,19%
Vietnam,16%
Philippines,16%
Sri Lanka,16%
Britain,15%
Mongolia,14%
Fiji,13%
Pakistan,12%
Maldives,11%
Nepal,11%
Myanmar,11%
Afghanistan,10%
Bangladesh,8%
Egypt,7%
Cambodia,6%
Laos,4%
U.S.,-2%



Even if you change this from a -2% to 8%, we're lower than Afghanistan, equal to Bangladesh, and higher only than Cambodia and Laos.

Does that make you feel better?


Title: Re: assuming too much math knowledge?
Post by: kraken on August 05, 2010, 04:51:32 PM
[Edited by moderator because of personal attack.]


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 05, 2010, 06:39:21 PM

Miracles never cease.  You actually answered a question correctly. 

How about you answering a question--any question asked by anyone in the last three pages regarding your motivation for posting here and what you expect from us?

I assure you that my track record in answering questions here correctly is higher than yours.

And you even provided a *possible* explanation for why American students, and in particular NSF physics students, scored lower on 12th grade TIMSS than if they'd just guessed.  You ought to supply your theory to the NSF because they seem to be clueless about why their top students score lower than Greek girls, and 50 points lower than AP physics students, and this is surely a possibility.  Another theory which has been advanced on a different forum is that our textbooks, both those used by AP physics students and NSF physics students, are wrong, and intentionally so.  This seems to be a more plausible explanation for why our scores are so low on a nationwide basis while students from so many other countries score so much higher.  AND for why so many American companies have been so unsuccessful at manufacturing semiconductors here while they've been so successful elsewhere.

But your theory certainly is worth further exploration.

On this particular question, only 22% of American students got it right.  And only 13% got question H10 correct, a question about spheres and vectors.

I can answer these questions because, unlike you evidently, I spend quite a lot of time thinking about how American students (and other students in American schools) learn math and science.  I am involved in the community of people (science and math educators and education research people who focus on science and math) who see test scores as indicators of what students still need to learn and we have voluminous discussions about what to do to help students learn more efficiently and be able to apply their learning outside of these tests.  I attend and contribute to workshops to spread that information to other people.  I go to conferences on this topic.  I have nearly daily discussions on this topic.  I am not the ignorant one here or at least all evidence that I have is that I am not ignorant to the extent that you appear to be on this topic.

That is why I am immensely irked by what you have done on this thread in terms of citing random garbage as a data dump, refusing to engage with the issues of teaching and learning of math and science, and a repeatedly refusing to look at the implications of data gathering methods leading to raw numbers, which are useless for getting people to focus on what we know and what we can do.  I am also quite irked by your evident lack of scientific knowledge since you have repeatedly focused on the numbers without thinking about how they were gathered and what factors could be contributing to those numbers, which is contrary to any kind of scientific thinking program that I have ever encountered.

I don't have to tell the NSF and AP people anything because, according to the last discussions I've had with people who are working on those curricula, they are on task and making adjustments that should lead to even better results in things that matter, even if those average test scores on standardized international tests don't go up.  The goal of good science and math education isn't to have high tests scores on standardized tests at the high school level.  Since you don't appear to know even that basic fact, why should anyone continue to take you seriously (assuming anyone still does)?


All of this simply because you were asked a simple question on this one single thread, namely, how's it possible for American students to repeatedly score lower in TIMSS physics achievement questions than if they just guessed?  You're the only one to respond, and not even your response is a complete explanation.  If you truly are so concerned about what's going wrong in our high schools, and have spent so much time studying it, don't you think you might have been able to point to just one of the more than 20 other possible explanations which have been provided on another forum?

The reason for making the point about how closely abortion and marriage rates correlate with the percent of Catholics per state is that it seems to be just the opposite of what the Catholic Church stands for.  When abortion rates in the predominately Catholic states are more than three times higher than they are in predominately Protestant states, don't you think you should know how close the correlation is before commenting on why?

Don't you think that if you look into the other social pathologies which appear to emanate from predominately Catholic states that your reply would have been more credible?


Title: Re: assuming too much math knowledge?
Post by: midtownlabgeek on August 05, 2010, 07:48:09 PM
The reason for making the point about how closely abortion and marriage rates correlate with the percent of Catholics per state is that it seems to be just the opposite of what the Catholic Church stands for.  When abortion rates in the predominately Catholic states are more than three times higher than they are in predominately Protestant states, don't you think you should know how close the correlation is before commenting on why?

Don't you think that if you look into the other social pathologies which appear to emanate from predominately Catholic states that your reply would have been more credible?

As was explained to you, you have to know what the data actually represent before worrying about measures of correlation.  And you also can't point to one factor as "the" common element (i.e., a possible cause) until you've at least attempted to examine other possible factors.

For instance, NJ used to have a significant chemical industry.  Other states on your list did not.  Do you suppose that a history of polluting chemical industries might have a connection to cancer?  Some states on your list are sunny (skin cancer), others may have radon problems (lung cancer).  These factors - which are totally ignored in your dataset - are much more likely to affect cancer rates than whatever box someone happens to check on a Census form.  (Or however the dataset defines "Catholic".  You never even explained that!)

There's a whole separate list of other factors to be considered in connection with each "social pathology" that you suspect "emanates from predominately Catholic states".  And not all of those are linked, either.

My students have a hard time with this one also.  Yes, performing statistical tests can give you information about your data.  Sometimes doing statistical tests on data can lead you astray.  The mathematical relationship may be a complete illusion when we add just one more fact.  Actual science is much harder than "measure some stuff and calculate R".

That's why you got so little response to your patiently paternal efforts to lead us by the hand through the deep scary waters of one-variable statistics.  Well, that and your condescending tone, and the lack of apparent point, and the vague-but-unsettling specter of bias against... well, almost everyone, apparently.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 06, 2010, 07:55:11 AM
The reason for making the point about how closely abortion and marriage rates correlate with the percent of Catholics per state is that it seems to be just the opposite of what the Catholic Church stands for.  When abortion rates in the predominately Catholic states are more than three times higher than they are in predominately Protestant states, don't you think you should know how close the correlation is before commenting on why?

Don't you think that if you look into the other social pathologies which appear to emanate from predominately Catholic states that your reply would have been more credible?

As was explained to you, you have to know what the data actually represent before worrying about measures of correlation.  And you also can't point to one factor as "the" common element (i.e., a possible cause) until you've at least attempted to examine other possible factors.

For instance, NJ used to have a significant chemical industry.  Other states on your list did not.  Do you suppose that a history of polluting chemical industries might have a connection to cancer?  Some states on your list are sunny (skin cancer), others may have radon problems (lung cancer).  These factors - which are totally ignored in your dataset - are much more likely to affect cancer rates than whatever box someone happens to check on a Census form.  (Or however the dataset defines "Catholic".  You never even explained that!)

There's a whole separate list of other factors to be considered in connection with each "social pathology" that you suspect "emanates from predominately Catholic states".  And not all of those are linked, either.

My students have a hard time with this one also.  Yes, performing statistical tests can give you information about your data.  Sometimes doing statistical tests on data can lead you astray.  The mathematical relationship may be a complete illusion when we add just one more fact.  Actual science is much harder than "measure some stuff and calculate R".

That's why you got so little response to your patiently paternal efforts to lead us by the hand through the deep scary waters of one-variable statistics.  Well, that and your condescending tone, and the lack of apparent point, and the vague-but-unsettling specter of bias against... well, almost everyone, apparently.


It was a forum on the Boston Globe which first made the observation that, while 37 states had outlawed gay marriage, that it was mostly (and only) Catholic states which were legalizing them.  That naturally got people to think about other social pathologies which are associated with mostly Catholic states.  The fact that within the White Race there is a spread of more than 105 SAT math points and 12 NAEP math points also provides a clue.

Yes, it is nice to know all the details before calculating the correlation.  Since we all have keyboards and the internet, much of that can be confirmed easily without having to post all the gory details here.  Once you learn just how tight the correlation is, and how many other factors are involved, you most likely will form a more complete (and different) opinion about it.

State,Catholics,NAEP
Montana ,12%,287
North Dakota ,22%,286
Texas ,29%,285
Iowa ,17%,285
Maine ,15%,285
Massachusetts ,43%,283
New York ,38%,283
Rhode Island ,59%,275


State,Catholic,1995SAT
Massachusetts ,42.7,477
New Jersey ,41.1,478
Connecticut ,38.7,477
Wisconsin ,29,572
North Dakota ,22.2,592
Minnesota ,21.5,579
South Dakota ,20.5,563
Iowa ,17.1,583


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 06, 2010, 08:02:02 AM


This is all official government data, straight from US and Japanese government sources.  If you have a complaint, take it straight to them, not to me.

Let's look at this data from a different perspective.  This is Personal Savings in Billions of Dollars, Japan vs. U.S.A. 1960 to 2008:





Year,Japan,U.S.A.
1960,653.3,26.4
1961,653.7,31.9
1962,654.0,33.5
1963,654.3,33.1
1964,654.7,40.5
1965,655.0,42.7
1966,655.3,44.5
1967,655.7,54
1968,656.0,52.700
1969,656.3,52.6
1970,656.7,69.5
1971,657.0,80.1
1972,657.3,76.9
1973,657.7,102.5
1974,658.0,114.3
1975,658.3,125.2
1976,658.7,122.1
1977,659.0,125.6
1978,659.3,145.4
1979,659.7,165.8
1980,660.0,205.6
1981,660.3,243.7
1982,660.7,262.2
1983,661.0,227.8
1984,661.3,306.5
1985,661.7,282.6
1986,662.0,267.8
1987,662.3,252.8
1988,662.7,292.3
1989,663.0,301.8
1990,663.3,334.3
1991,663.7,371.7
1992,664.0,413.7
1993,664.3,350.8
1994,664.7,315.5
1995,665.0,302.4
1996,665.3,272.1
1997,665.7,252.9
1998,666.0,301.5
1999,666.3,174
2000,666.7,201.5
2001,667.0,169.7
2002,667.3,159.2
2003,667.7,174.9
2004,668.0,181.7
2005,668.3,32.5
2006,668.7,70.7
2007,669.0,57.4
2008,669.3,192.9



Title: Re: assuming too much math knowledge?
Post by: kraken on August 06, 2010, 08:16:39 AM

This is all official government data, straight from US and Japanese government sources.  If you have a complaint, take it straight to them, not to me.

Let's look at this data from a different perspective.  This is Personal Savings in Billions of Dollars, Japan vs. U.S.A. 1960 to 2008:





Year,Japan,U.S.A.
1960,653.3,26.4
1961,653.7,31.9
1962,654.0,33.5
1963,654.3,33.1
1964,654.7,40.5
1965,655.0,42.7
1966,655.3,44.5
1967,655.7,54
1968,656.0,52.700
1969,656.3,52.6
1970,656.7,69.5
1971,657.0,80.1
1972,657.3,76.9
1973,657.7,102.5
1974,658.0,114.3
1975,658.3,125.2
1976,658.7,122.1
1977,659.0,125.6
1978,659.3,145.4
1979,659.7,165.8
1980,660.0,205.6
1981,660.3,243.7
1982,660.7,262.2
1983,661.0,227.8
1984,661.3,306.5
1985,661.7,282.6
1986,662.0,267.8
1987,662.3,252.8
1988,662.7,292.3
1989,663.0,301.8
1990,663.3,334.3
1991,663.7,371.7
1992,664.0,413.7
1993,664.3,350.8
1994,664.7,315.5
1995,665.0,302.4
1996,665.3,272.1
1997,665.7,252.9
1998,666.0,301.5
1999,666.3,174
2000,666.7,201.5
2001,667.0,169.7
2002,667.3,159.2
2003,667.7,174.9
2004,668.0,181.7
2005,668.3,32.5
2006,668.7,70.7
2007,669.0,57.4
2008,669.3,192.9


[/quote]

My complaint is not with the data you post.  It is with the way in which you choose to mangle them.  


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 06, 2010, 08:23:54 AM
JohnKnight, you just aren't getting it.

Go look at some good rubrics for scientific thinking (http://paer.rutgers.edu/ScientificAbilities/Rubrics/default.aspx) and compare what you have presented here to what is considered adequate in classes.

In particular, go look at conducting an observational experiement (http://paer.rutgers.edu/ScientificAbilities/Downloads/Rubrics/B_ObsStud.pdf), engaging in divergent thinking (http://paer.rutgers.edu/ScientificAbilities/Downloads/Rubrics/H_DivThinkingRub2007.pdf), and collecting and analyzing experimental data (http://paer.rutgers.edu/ScientificAbilities/Downloads/Rubrics/G_DatanalRub2007a.pdf) and get back to us.

Disclaimer: I am not affiliated with Rutgers or this PER group, but they have some of the clearest explanations that I have seen.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 07, 2010, 04:55:29 PM


This is all official government data, straight from US and Japanese government sources.  If you have a complaint, take it straight to them, not to me.

Let's look at this data from a different perspective.  This is Personal Savings in Billions of Dollars, Japan vs. U.S.A. 1960 to 2008:





Year,Japan,U.S.A.
1960,653.3,26.4
1961,653.7,31.9
1962,654.0,33.5
1963,654.3,33.1
1964,654.7,40.5
1965,655.0,42.7
1966,655.3,44.5
1967,655.7,54
1968,656.0,52.700
1969,656.3,52.6
1970,656.7,69.5
1971,657.0,80.1
1972,657.3,76.9
1973,657.7,102.5
1974,658.0,114.3
1975,658.3,125.2
1976,658.7,122.1
1977,659.0,125.6
1978,659.3,145.4
1979,659.7,165.8
1980,660.0,205.6
1981,660.3,243.7
1982,660.7,262.2
1983,661.0,227.8
1984,661.3,306.5
1985,661.7,282.6
1986,662.0,267.8
1987,662.3,252.8
1988,662.7,292.3
1989,663.0,301.8
1990,663.3,334.3
1991,663.7,371.7
1992,664.0,413.7
1993,664.3,350.8
1994,664.7,315.5
1995,665.0,302.4
1996,665.3,272.1
1997,665.7,252.9
1998,666.0,301.5
1999,666.3,174
2000,666.7,201.5
2001,667.0,169.7
2002,667.3,159.2
2003,667.7,174.9
2004,668.0,181.7
2005,668.3,32.5
2006,668.7,70.7
2007,669.0,57.4
2008,669.3,192.9



My complaint is not with the data you post.  It is with the way in which you choose to mangle them.  



"mangle" them?

From my perspective, looking at the long term trends, then comparing them with one widely accepted data point (like the notion that all of a sudden under obamacare our personal savings rate not only climbed out of the negative, but skyrocketed to 8%) is not "mangling" statistics, but understanding them.  If what you're saying is that you'd prefer then to be presented in pretty graphs, then I agree.

Is the personal savings graph on the following page more pleasing from your perspective?  Do you believe you see any errors in it.  If you do, then let me know asap and that error or those errors will be corrected immediately:


http://eaja.net/nsf.aspx


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 07, 2010, 05:25:43 PM
JohnKnight, you just aren't getting it.

Go look at some good rubrics for scientific thinking (http://paer.rutgers.edu/ScientificAbilities/Rubrics/default.aspx) and compare what you have presented here to what is considered adequate in classes.

In particular, go look at conducting an observational experiement (http://paer.rutgers.edu/ScientificAbilities/Downloads/Rubrics/B_ObsStud.pdf), engaging in divergent thinking (http://paer.rutgers.edu/ScientificAbilities/Downloads/Rubrics/H_DivThinkingRub2007.pdf), and collecting and analyzing experimental data (http://paer.rutgers.edu/ScientificAbilities/Downloads/Rubrics/G_DatanalRub2007a.pdf) and get back to us.

Disclaimer: I am not affiliated with Rutgers or this PER group, but they have some of the clearest explanations that I have seen.

You claim to be an expert in education. You claim you have studied the problem of American education closely.  You get all bent out of shape when someone comes along and simply asks the simple question "how's it possible for so many American students to score LOWER on one third of TIMSS questions than if they'd just guessed".  You were complimented when you provided a new perspective to this question, but then proceded to proclaim "you just don't get it".  And in order for me to "get it" better you provide a link to PAER at Rutgers, but then quickly disassociate yourself from them. 

This does not seem to address the question, so it would be greatly appreciated if you'd explain why you provided this reference.  What has this rubric got to do with examining why U.S. students score so low?  Without claiming to be an expert on this Rutgers' rubric, and having viewed only the pages you cited, my off the cuff impression is that it's in the same class as "new math", and could not do anything other than drive our scores down even lower.

To get back on track, please note the following correlation which might be a better way to examine this issue:

State,Catholics,Marriages
State,Catholics,Murder
Pennsylvania,29%,6
Texas,29%,6
Illinois,30%,6
New Jersey,41%,5
New York,38%,5
Montana,12%,2
New Hampshire,24%,1
South Dakota,21%,1
Iowa,17%,1
Maine,15%,1
Utah,8%,1
North Dakota,22%,0.2

Would you like to know what the Pearson Coefficient is?  Good, it's .747.


Title: Re: assuming too much math knowledge?
Post by: midtownlabgeek on August 07, 2010, 06:50:59 PM
To get back on track, please note the following correlation which might be a better way to examine this issue:

You seem to think that a mathematical correlation always reflects some sort of deeper "real world" relationship between two quantities, and that labeled columns of data are enough to "prove" your point.  A lot of my students have this same concept when they enter my class, which is basically all about how to make reliable measurements and deduce certain information about chemicals based on those measurements.

* The data aren't labeled very well.  Now we're onto data labeled "Murder".  Is that total murders per state? per 1000s of residents?  It should be obvious that this makes a difference in how the numbers are interpreted.

* The parameter that you suggest is "causing" all of these "social pathologies" isn't a binary variable.  Nuns and mafiosi might both check "Catholic" on a census form, but their behavior may not have much in common.

* The big one:  The data don't appear to control for any other factors.  One of your tables gave numbers for "Cancer".  Lots of stuff causes cancer, not all of which has any connection to religious belief.  For instance, NJ in particular used to have a good bit of chemical industry; other states on your list have not.  Think that might have some kind of influence?  The EPA sure does.

You've posted N tables like this already.  Do you really think that making it N+1 is suddenly going to convince those of us who are still bothering to read your posts?  Do you really think that we can't do the math?  The correlation (r^2) for "marriages" versus "cancer" from your earlier tables is 0.63, which practically "proves" that marriage cures cancer - right?

Sure, you can do the math to calculate correlation coefficients on the numbers and you'll get a number.  The fact that a calculation can be done doesn't mean that the result has any actual meaning.  For instance, we could take your height and mine, and your post count and mine, and calculate the slope to "prove" something about the "relationship" between height and post count.  Would it mean anything?  I'll let you decide.

Your constant reaction to objections like this - stomp your foot and paste in more tables that "prove" that them Catholics are dragging down the country - might be funnier if only it were less bigoted.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 08, 2010, 06:41:01 AM
This does not seem to address the question, so it would be greatly appreciated if you'd explain why you provided this reference.  What has this rubric got to do with examining why U.S. students score so low?  Without claiming to be an expert on this Rutgers' rubric, and having viewed only the pages you cited, my off the cuff impression is that it's in the same class as "new math", and could not do anything other than drive our scores down even lower.

As Midtownlabgeek explained, I provided the rubrics so that you could look at exactly why your data don't lead anywhere in a scientific sense.  You are not demonstrating scientific thinking on a problem that has been studied at length by people who are both interested in the topic and who have done scientific examination of various things related to the topic at hand regarding American education in science and math.

The key thing that you are missing is this: performance on one test designed for one purpose does not necessarily have anything to do with anything else.  Even if we take all of your posts at face value, you are starting from the premise that standardized tests administered in a form suitable to a global population measures something worth knowing about science and math knowledge.  I, for one, do not accept that premise so your whole reporting of data and harping on scores is completely irrelevant to a discussion on science and math abilities in the American population.

For the random data sets you are posting to illustrate something or other as a secondary or tertiary premise, your "experiments" fail to meet adequate standards for a designed experiment where the conclusion you are either stating or implying could logically be reached.  Thus, we who are scientifically proficient dismiss them out of hand since those data sets as they are presented and as the data were gathered CANNOT demonstrate any of the conclusions you claim they do.

You have not stated a hypothesis based on a model and designed an experiment suitable for testing that hypothesis.  You have not identified all relevant variables and made some effort to control them or use a relevant statistical analysis like a partial factorial design to examine correlations.  You have not even done an adequate job on an observational study as preparation to get the background to state a hypothesis to design an experiment.

Instead, you have taken some numbers and drawn conclusions as though you were doing science without doing the science.  If you checked your performance against those rubrics, then you would realize that you have failed Scientific Thinking 101. Those rubrics aren't wacky New Math; they are simplified explanations of what actual scientists do in words that the average person can understand to help guide students into a more scientific mindset.  My disclaimer was that I didn't have a hand in designing them so that I can't take credit for them.  Academics holding academic discussions care quite a bit about credit and such, another thing that you appear to be missing.

So, JohnKnight, I ask you: what are your qualifications in this discussion?  Why should we take you seriously when all the evidence is that you aren't proficient in science or even the statistics in math beyond being able to do a linear regression?



Title: Re: assuming too much math knowledge?
Post by: spork on August 08, 2010, 07:09:22 AM
How does the Queen of England and the Trilateral Commission figure into all of this?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on August 08, 2010, 09:18:03 AM
So, JohnKnight, I ask you: what are your qualifications in this discussion?

You really want to know?  He's from a thing called the Fathers' Manifesto & Christian Party, a vicious racist and antisemitic organization that might just consist of him:

Here is his wordpress blog. (http://israeliteknight.wordpress.com/)
Here is his hate website. (http://www.eaja.us/knight.htm)
Here is another hate site of his. (http://fathersmanifesto.net/holocaust.htm)
And another one; busy boy! (http://kensingtonmicro.com/ind.htm)

Oh, here's a discussion about him from 10 years ago on the Straight Dope board (http://boards.straightdope.com/sdmb/showthread.php?t=56374).

My favorite bit is the assertion here (http://eaja.us/jewsiq.htm) that Jews are genetically bad at math.

Time to shower. - DvF


Title: Re: assuming too much math knowledge?
Post by: systeme_d_ on August 08, 2010, 09:19:12 AM
I had figured that the "Knight" part referred to the KKK, myself.

His inability to interpret data made his wingnuttiness rather obvious.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 08, 2010, 09:24:12 AM
Thanks for that info, Daniel_von_Flanagan.  That makes some of the data-dump, unreasonable and unrelated-to-the-topic-at-hand examples for correlation calculations make more sense.

Thanks for the warning about the shower.  I only skimmed a couple of posts on those sites so I feel no need to do more than wash my hands and lie down for a bit.


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 08, 2010, 07:14:42 PM
My favorite bit is the assertion here (http://eaja.us/jewsiq.htm) that Jews are genetically bad at math.

And be sure to take five minutes to complete the poll on exiling blacks!

[/vomit]


Title: Re: assuming too much math knowledge?
Post by: conjugate on August 08, 2010, 08:01:42 PM

My favorite bit is the assertion here (http://eaja.us/jewsiq.htm) that Jews are genetically bad at math.


This amazes me.  Think how much more mathematics we'd know if Solomon Lefshetz, John von Neumann, Mark Kac, Stan Ulam, and so forth and so on, had been really good at math instead of being handicapped by their Jewish ancestry!


Title: Re: assuming too much math knowledge?
Post by: kiana on August 08, 2010, 09:20:52 PM
DvF, thanks for the find. It's been so long I didn't even notice that he was the same one who was trolling this topic before.


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on August 08, 2010, 10:10:18 PM
DvF, thanks for the find. It's been so long I didn't even notice that he was the same one who was trolling this topic before.

I didn't notice, either, and thank DvF for the links (that I will not be going to).  I'm not even sure I recall someone trolling the same stuff before, so I'm not sure I should have noticed, at all.  But, it only took a few of his posts before I realized he was nuts.  I am amazed at the patience of some of the forumites here. Truly awe inspiring.  If this is how you deal with your students they have absolutely nothing to complain about if they eventually fail for lack of understanding.


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 09, 2010, 12:40:03 AM
Also, looks like he's been chased away.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 09, 2010, 06:05:57 AM
Also, looks like he's been chased away.

<stern look>

That's because you let some of us get away with being mean to a newbie.  You're falling down on the job.


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 09, 2010, 12:58:16 PM
No, that is a good point.  We should give him a fair chance to repudiate his "statistics" "proving" the inherent mental and moral inferiority of Jews and Blacks (http://www.amazon.com/Jews-Blacks-Dialogue-Religion-Culture/dp/0452275911/ref=sr_1_1?s=books&ie=UTF8&qid=1281376651&sr=1-1) and when he does, welcome him into the fora communities with open arms.

(I thought this book was interesting.)


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 09, 2010, 01:56:00 PM
My favorite bit is the assertion here (http://eaja.us/jewsiq.htm) that Jews are genetically bad at math.

And be sure to take five minutes to complete the poll on exiling blacks!

[/vomit]

Are there any Jews in Israel?  Aren't the majority of the people there, like 90%, Ashkenazi Jews?  If so, then PISA says it's not just math they're no good at--they are also terrible, even worse than US, in reading and science:

Data generated from http://pisaweb.acer.edu.au/oecd/oecd_pisa_data.html



Sex,Country,Reading,Mathematics,Science
Boys,Japan,507,561,547
Boys,Korea,519,559,561
Girls,Japan,537,553,554
Girls,Korea,533,532,541
Boys,Ireland,513,510,511
Boys,Netherlands,485,504,502
Boys,Russia,485,504,502
Boys,Hong Kong,485,504,502
Boys,Thailand,485,504,502
Girls,Ireland,542,497,517
Boys,US,490,497,497
Girls,Netherlands,514,493,503
Girls,Russia,514,493,503
Girls,Hong Kong,514,493,503
Girls,Thailand,514,493,503
Girls,US,518,490,502
Boys,Israel,444,442,446
Girls,Israel,459,430,426
Boys,Mexico,411,393,423
Girls,Mexico,432,382,419


Do you think I just made this up?  Why don't you LOOK at the actual data for a change, rather than sitting around patting each other on the back about how talented Jews are?

Unless you think it's "talent" to score 54 points lower than us in reading, and 55 points lower than us in math, and 51 points lower than us in science, PISA says you have no clue what you're talking about.


Title: Re: assuming too much math knowledge?
Post by: johnknight on August 09, 2010, 02:30:43 PM
My favorite bit is the assertion here (http://eaja.us/jewsiq.htm) that Jews are genetically bad at math.

And be sure to take five minutes to complete the poll on exiling blacks!

[/vomit]

Are there any Jews in Israel?  Aren't the majority of the people there, like 90%, Ashkenazi Jews?  If so, then PISA says it's not just math they're no good at--they are also terrible, even worse than US, in reading and science:

Data generated from http://pisaweb.acer.edu.au/oecd/oecd_pisa_data.html



Sex,Country,Reading,Mathematics,Science
Boys,Japan,507,561,547
Boys,Korea,519,559,561
Girls,Japan,537,553,554
Girls,Korea,533,532,541
Boys,Ireland,513,510,511
Boys,Netherlands,485,504,502
Boys,Russia,485,504,502
Boys,Hong Kong,485,504,502
Boys,Thailand,485,504,502
Girls,Ireland,542,497,517
Boys,US,490,497,497
Girls,Netherlands,514,493,503
Girls,Russia,514,493,503
Girls,Hong Kong,514,493,503
Girls,Thailand,514,493,503
Girls,US,518,490,502
Boys,Israel,444,442,446
Girls,Israel,459,430,426
Boys,Mexico,411,393,423
Girls,Mexico,432,382,419


Do you think I just made this up?  Why don't you LOOK at the actual data for a change, rather than sitting around patting each other on the back about how talented Jews are?

Unless you think it's "talent" to score 54 points lower than us in reading, and 55 points lower than us in math, and 51 points lower than us in science, PISA says you have no clue what you're talking about.


In case you believe it's an anomaly that Israel scores so low in PISA, note that they also score very low in TIMSS math, having succeeded in scoring 463, which is 47 points lower than our already low score of 508, which is 90 points lower than Chinese Taipei:

http://timssandpirls.bc.edu/TIMSS2007/idb_ug.html

This indicates that Ashekanazi Jews in Israel may score even lower than American blacks.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on August 09, 2010, 03:25:28 PM
Setting phasers to shun.

Alan


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 09, 2010, 04:24:12 PM
Shun?  Is there someone here you're shunning, Alan?

Hey, guess what!  Spouse_functional and I had our tenth wedding anniversary this week!  (For real.)


Title: Re: assuming too much math knowledge?
Post by: cc_alan on August 09, 2010, 08:33:44 PM
Shun?  Is there someone here you're shunning, Alan?

Hey, guess what!  Spouse_functional and I had our tenth wedding anniversary this week!  (For real.)

Shun? Huh? I have no idea what you're talking about...

<wanders around in a clueless fog... it's a comfortable feeling>

Congratulations on the anniversary!

Alan


Title: Re: assuming too much math knowledge?
Post by: conjugate on August 09, 2010, 10:41:43 PM
Shun?  Is there someone here you're shunning, Alan?

Hey, guess what!  Spouse_functional and I had our tenth wedding anniversary this week!  (For real.)

Congratulations and many more!


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 09, 2010, 11:20:12 PM
Thanks!


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 10, 2010, 12:04:20 PM
Do you think I just made this up?  Why don't you LOOK at the actual data for a change, rather than sitting around patting each other on the back about how talented Jews are?

One more time for those in the cheap seats: your data cannot support the conclusions you claim to be making based on those data.  The science isn't there in the experimental design.  Thus, I can stipulate that the scores you cite are valid in the sense that you didn't make them up, but that doesn't make them any more useful to discuss.

I will walk you through what you would have to do to be able to draw the conclusions you are claiming (for free, although I usually charge a hefty hourly rate for personal tutoring of reluctant students.  I'm calling this community outreach in my daily activity log).

World model:  X group of people are inherently inferior in terms of mental capacity, where X is any of the groups you have been dinging on this thread.

Hypothesis:  Under the same conditions with the same preparation as other groups, members of X group will do demonstrably worse on standardized tests in math and science.

Experiment:  Taking a group of children who are reasonably average representatives of multiple groups, but with similar previous educational backgrounds and controlled for things like age and language, randomly divide the students into cohorts of students.  Administer a pre-test on the topic to be taught with questions selected from a relevant standardized test.  Then, have an instructor teach each cohort a series of math or science lessons according to best practices for a set of selected topics.  Be sure that the instructor does not know which students belong to which group nor what the hypothesis being tested explicitly is.  The most the instructor needs to know is the common educational level of the children and that the children will be taking a post-instruction standardized test.  The instructor does not get to see the test prior to instruction to prevent any sort of favoritism in instruction.  Administer the post-test with questions selected from a relevant standardized test, ideally different selections from the same test that was used to construct the pre-test.

Data analysis:  Using normalized gains from pre-test to post-test, look at the average gain per group.  Compare differences in average gain among groups to the variation in gain within groups to get an estimate on whether those differences between groups are above chance variation (i.e., are statistically significant).

Replicates: Repeat the experiment and data analysis for multiple topics accompanied by the necessary tests to be sure to minimize sampling bias in kinds of questions asked.  Rotate through different cohorts of students with differing mixes of the groups being tested while making sure that they cannot share information with students who have already taken any of the tests.

Conclusions: Looking at all the data on averages between groups that meet the standard of being above chance, rank the groups by performance if such a pattern can be found to exist.  Only with that information in hand can you possibly make a conclusion about certain groups being automatically inferior that is even worth discussing.

Do you notice how all of the data you have presented here fails to follow this sort of method, which is not at all coincidentally the same points that the rubrics I cited earlier show you fail on?

For all of the numbers I can remember you spewing on this thread, you have made zero effort to control for important factors that are likely to affect the outcome nor have you in any way ever actually looked at the performance of any group X's (Y percentage of the population being an X is not at all the same as 100% of the tested population being a Y) versus any other groups except initially during the discussion about Americans versus other nationalities.

Are you at all familiar with the idea of a confirmation bias in not examining all the possibilities for an illusory correlation?  I ask because that's what you are doing, repeatedly on this thread. 

Consider the following example that I came across in my reading today*.  Many doctors, nurses, and police officers will swear that admissions to psych wards increase during the full moon.  However, we can't evaluate whether that's actually true until we've looked at the relative frequency of 4 cases:

1)  Full moon and psych ward admission
2)  Full moon and no psych ward admission
3)  Non-full moon and psych ward admission
4)  Non-full moon and no psych ward admission

Only looking at admissions to the psych ward during the full moon doesn't tell us anything if we don't have the information about the three cases.  By only considering the first case to draw a correlation means that you are making a logical error.

This logical error is the same kind that you are making when you plot some outcome (e.g., murder, abortion, divorce, or saving rates; test scores; patents) versus percent of population that is X and conclude that X and that rate are correlated.  You don't have enough information to draw that conclusion because you haven't tested observable as a function of X even in a basic way of comparing rates of 100% X populations to 0% X populations and selecting the populations in such a way as minimize other differences in the group that are likely to affect the observable to confuse the issue (also known as confounding variables).  That lack of control of confounding factors is why comparing Americans to anyone else on international standardized tests doesn't work--the huge differences in educational aims and population selected for testing between the nations mean that the populations aren't comparable so that attempting to draw detailed conclusions is not a reasonable activity.

So, in summary, when you present some data gathered in such a way that could possibly support your claims instead of what you have been doing, more of us would be likely to think about the data and discuss it.  In most scientific and academic circles, no one bothers to discuss what results from a flawed methodology since, by definition, it's flawed.  At most, some good ideas that failed in execution might be kicked around to figure out a non-flawed methodology, but that's not the case here.

Oh, for the record, while I don't know that anyone has done exactly as I have described upthread in terms of looking at inherently inferior group X's, I've seen lots of lovely studies done (mostly in the US, although a few in Europe) showing that the primary factors affecting educational achievement through high school are socioeconomic status of the parents, quality and consistency of schooling, and attitude/support of the family toward schooling, not ethnicity, race, religion, or national origin, despite definite differences on standardized tests by those groups when the control for similar schooling and effort is not applied.  Since those researchers did control for as many relevant factors as they could and didn't make claims stronger than their evidence, I would be happy to discuss that data with you.


*Lilienfeld et al.  50 Great Myths of Popular Psychology: Shattering Widespread Misconceptions about Human Behavior, Wiley-Blackwell, 2010


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 10, 2010, 11:38:10 PM
Is this Take Aryan Supremacists Seriously Week?


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 11, 2010, 05:29:37 AM
Is this Take Aryan Supremacists Seriously Week?

Dunno.  However, in my book, it's always Counteract Pseudoscience and Ignorance with Education in Science Week, even if the only hope is to reach the observers instead of the primaries.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on August 11, 2010, 10:40:33 AM
Is this Take Aryan Supremacists Seriously Week?

Seriously? I thought it had something to do with different desserts. I need to get a new calendar.

Alan


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 11, 2010, 04:51:22 PM
Is this Take Aryan Supremacists Seriously Week?

Dunno.  However, in my book, it's always Counteract Pseudoscience and Ignorance with Education in Science Week, even if the only hope is to reach the observers instead of the primaries.

But it only encourages the primates to keep flinging their poo....  If you ignore the primates, sometimes they stop flinging the poo.  Unless you're prepared to uncle this guy through sheer persistence just to prove a point to the observers.  Because he'll just keep coming back and coming back and coming back as long as he's getting attention.  Wouldn't be how I'd want to spend my time, but if it makes you happy, by all means.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 12, 2010, 07:44:14 AM
Is this Take Aryan Supremacists Seriously Week?

Dunno.  However, in my book, it's always Counteract Pseudoscience and Ignorance with Education in Science Week, even if the only hope is to reach the observers instead of the primaries.

But it only encourages the primates to keep flinging their poo....  If you ignore the primates, sometimes they stop flinging the poo.  Unless you're prepared to uncle this guy through sheer persistence just to prove a point to the observers.  Because he'll just keep coming back and coming back and coming back as long as he's getting attention.  Wouldn't be how I'd want to spend my time, but if it makes you happy, by all means.

The question is: what goal are you trying to achieve?  If you are trying to get a particular someone in a particular venue to shut up, I agree that extinction is often the way to go.

However, the standard mindset among people who are trying to combat scientific ignorance and pseudoscience in the general public is that ceding the floor in any public venue by refusing to engage is tantamount to declaring that the vocal pseudoscientists are right and leads to negative consequences in terms of scientific literacy in the general population.

One of the very common logical fallacies is that hearing the same opinion 10 times is the same as having ten people hold that opinion.  Thus, if everytime people turn around, they hear some garbage pseudoscience unchallenged, it's much more likely that they will soon wander around saying things like "Science has proven Q; therefore, the reasonable action to take is blah" when no such thing has ever been proven and the proposed action is costly and will cause many more problems than it solves.  If, on the other hand, every time someone spouts pseudoscience, someone else is on the spot saying, "No, that's not science because X, Y, Z.  What science has shown on that topic is A, B, C", then we have a fighting chance to stem the tide of ignorance. 

The people spewing the pseudoscience almost never publicly say, "Hmm. I didn't know that.  You are right and I recant", but the evidence we have on public attitudes indicates that engaging with the pseudoscientists as politely as possible while hammering on evidence and scientific thinking is viewed favorably by people who are open to the science, but haven't before seen the counterarguments presented in a calm way.  Those people may not fully get on board with all the science or even the particular issue at hand.  However, merely calling names and being immediately dismissive of anyone who is spewing pseudoscience has been shown to be ineffective on changing general public attitudes toward science to the positive and often actually moves people to more firmly gain new pseudoscience beliefs; we often hear: it's all opinion and those scientists are all arrogant, atheists jerks who don't understand normal people and real life so who cares if they think this is stupid?  If there's even a 1% possibility, then we should do it. 

In terms of raising the scientific literacy of the general public, allowing pseudoscience to go unchallenged in public venues while only concentrating on fighting the battle in schools means that more school battles occur.  More people will bring up the idea of teaching pseudoscience in schools since they don't know any better and want their children to learn that pseudoscience in a coherent manner.  The categories of environmentalism and "going green" are prime examples of ideas that are commonly in the public eye in which good science exists, but the good science is often ignored in favor of pseudoscience pushed by the general public based on some very vocal proponents who offer simplistic solutions to real problems.

In summary, I've already chosen to fight the good fight for science whenever I can and I don't see it as a waste of my time to do so in this particular venue since, ideally, it will eventually make the teaching in the classroom I do easier with more people having a solid scientific background as they come out of K-12 education and have scientifically literate adults around them.

Also, since I've seen some scary pseudoscience ideas, evidence of lack of scientific literacy, and actively hostile toward science attitudes put forth by DSM's on these fora, I don't think even here among educated people that it's safe to let pseudoscience go unchallenged.


Title: Re: assuming too much math knowledge?
Post by: post_functional on August 12, 2010, 04:08:40 PM
You know, polly, not everything is about science.  You sometimes sound like the proverbial carpenter who only has a hammer and thus everything looks like a nail.  John Knight's pseudoscience offends you more than his white supremacism?  Really?  

If your goal is to correct every instance of pseudoscience you find, more power to you.  To me, the far more egregious offense is not the pseudoscience itself, but of what it's being used in service--- blatant and undisguised white supremacy.  This guy doesn't even bother to couch his views in the barely acceptable guise of polite-society conservatism.  He's an out and out acknowledged racist.

My realpolitik goal is to keep the crazy neo-Nazi racists marginalized.  And to do that, you ignore them.  You don't grant them the legitimating capacity of your audience.  Now, any old garden variety proponent of copper bracelets and ley lines, but who is otherwise unoffending, fine.  Argue them down until the cows come home.  But with this clown I think it's a mistake to engage.  $0.02.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 12, 2010, 04:29:04 PM
You know, polly, not everything is about science.  You sometimes sound like the proverbial carpenter who only has a hammer and thus everything looks like a nail.  John Knight's pseudoscience offends you more than his white supremacism?  Really?  

Yes, I really am much more offended by pseudoscience to justify that racism than having him be a racist spouting racist views.  Remember who you are talking to.

I am very much more concerned about the fact that this guy is wandering around using the trappings of science to dazzle the unwary into possibly agreeing with him and confirming what others already think than being confronted with the fact that some people are racist.  People who are racist simply through a lack of contact with a diverse enough population can often eventually be convinced by enough examples of "oh, but that one isn't like that" to maybe give up on the racism.  People who are convinced that not only are they right to be racist, but that science says they are right go out and do horrible things.

Since the reasons that are most convincing to me against racism are primarily the actual science underlying human differences, I will fight tooth and nail to make sure that no racist gets a free pass on spouting pseudoscience in an attempt to gain followers to the racist cause.

I, for one, am not convinced by any sort of fairness argument that doesn't have an underlying component of human potential, which has to be established by science.  Being an atheist, the religious "all men are endowed by their creator" doesn't do anything for me.

For you to question the foundations of my worldview on an issue that clearly has a scientific basis just doesn't make sense to me.  Not everything is science, but whether true differences exist in human potential based on genetics (which is what inherently inferior has to mean to these racists) is definitely 100% a science question answerable by good science.

In my world, if you ignore racists, they don't give up.  Instead, they just say bad words against those liberal, out-of-touch academics who don't live in the real world and form more cells of like-minded people who then at a minimum discriminate and at a maximum commit crimes to cleanse the world.  I would far rather spend a lot of time arguing with a nut-bar to expose him as a nut bar to the people on the fence than send him out into the world to start the cleansing since we are all too polluted to see the truth.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 12, 2010, 04:35:46 PM
P.S.
My realpolitik goal is to keep the crazy neo-Nazi racists marginalized.  And to do that, you ignore them.  You don't grant them the legitimating capacity of your audience.  Now, any old garden variety proponent of copper bracelets and ley lines, but who is otherwise unoffending, fine.  Argue them down until the cows come home.  But with this clown I think it's a mistake to engage.  $0.02.

If you think the copper-bracelet-ley-line people are any less harmful to society in terms of pushing public policy and harming the common good than racists, then we don't have anything to talk about.  I'd much rather have a racist who is otherwise in touch with reality than a ley-liner who is going to push for health dollars to be wasted on garbage in the name of "alternative medicine", argue against vaccines, and do atmospheric cleansing with who-knows-what.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 12, 2010, 04:42:27 PM
<stupid editing window and multiple thoughts>
In case I wasn't clear "a racist who is otherwise in touch with reality" is exactly comparable to saying something like "proponent of copper bracelets and ley lines, but who is otherwise unoffending".  If you don't see that, then you are one of the members of the general public whose science literacy needs to be raised.


Title: Re: assuming too much math knowledge?
Post by: spork on August 12, 2010, 04:44:33 PM
You know, polly, not everything is about science.  

[. . .]


Yes it is.

Quote

My realpolitik goal is to keep the crazy neo-Nazi racists marginalized.  And to do that, you ignore them.  You don't grant them the legitimating capacity of your audience.  Now, any old garden variety proponent of copper bracelets and ley lines, but who is otherwise unoffending, fine.  Argue them down until the cows come home.  But with this clown I think it's a mistake to engage.  $0.02.

Sunlight is the best disinfectant, and the best sunlight is science.  Refuse to counter pseudoscience with science, and you get large numbers of people thinking that vaccines cause autism, just because that's all they read/hear/see in the media.


Title: Re: assuming too much math knowledge?
Post by: polly_mer on August 12, 2010, 05:01:50 PM
You know, polly, not everything is about science.  

[. . .]


Yes it is.

Now, now. 

Post_functional, I distinctly remember being on a thread not too long ago where I argued the case for science not being able to answer all questions that arise in human minds because some questions are not scientific.  How soon they forget.  While not all things are science, everything that is science has to be answered by science.  What we "should" do if people are the same or if they are different is a non-scientific question.  However, if any part of your argument relies on needing to judge individuals because the groups aren't essentially different on the relevant factors, then that is indeed science.


Title: Re: assuming too much math knowledge?
Post by: anthroid on August 12, 2010, 05:36:54 PM
You know, polly, not everything is about science.  You sometimes sound like the proverbial carpenter who only has a hammer and thus everything looks like a nail.  John Knight's pseudoscience offends you more than his white supremacism?  Really?  

Yes, I really am much more offended by pseudoscience to justify that racism than having him be a racist spouting racist views.  Remember who you are talking to.

I am very much more concerned about the fact that this guy is wandering around using the trappings of science to dazzle the unwary into possibly agreeing with him and confirming what others already think than being confronted with the fact that some people are racist.  People who are racist simply through a lack of contact with a diverse enough population can often eventually be convinced by enough examples of "oh, but that one isn't like that" to maybe give up on the racism.  People who are convinced that not only are they right to be racist, but that science says they are right go out and do horrible things.

Since the reasons that are most convincing to me against racism are primarily the actual science underlying human differences, I will fight tooth and nail to make sure that no racist gets a free pass on spouting pseudoscience in an attempt to gain followers to the racist cause.

I, for one, am not convinced by any sort of fairness argument that doesn't have an underlying component of human potential, which has to be established by science.  Being an atheist, the religious "all men are endowed by their creator" doesn't do anything for me.

For you to question the foundations of my worldview on an issue that clearly has a scientific basis just doesn't make sense to me.  Not everything is science, but whether true differences exist in human potential based on genetics (which is what inherently inferior has to mean to these racists) is definitely 100% a science question answerable by good science.

In my world, if you ignore racists, they don't give up.  Instead, they just say bad words against those liberal, out-of-touch academics who don't live in the real world and form more cells of like-minded people who then at a minimum discriminate and at a maximum commit crimes to cleanse the world.  I would far rather spend a lot of time arguing with a nut-bar to expose him as a nut bar to the people on the fence than send him out into the world to start the cleansing since we are all too polluted to see the truth.

Polly, I completely and totally agree with you.  I know that I have said more than once in these fora that I don't care what people (to whom I have no connection) think or feel.  Really, I don't.  I'm not interested in being "politically correct" and I'm not interested in "realpolitik" as a first principle.  I am interested in facts and accuracy.  The guy on this thread had no clue about what constitutes actual evidence and accurate interpretation of facts--indeed, if a fact the size of a grand piano dropped on his head he would not have been able to recognize it. It is my job, as someone who knows the science behind evolution, human difference, and so forth, to correct misstatements or out and out lies.  I didn't do it here because you guys were doing such a great job and, frankly, I didn't have the patience for this particular wingnut.


Title: Re: assuming too much math knowledge?
Post by: benami on September 14, 2010, 05:53:06 PM
Do you think I just made this up?  Why don't you LOOK at the actual data for a change, rather than sitting around patting each other on the back about how talented Jews are?

One more time for those in the cheap seats: your data cannot support the conclusions you claim to be making based on those data.  The science isn't there in the experimental design.  Thus, I can stipulate that the scores you cite are valid in the sense that you didn't make them up, but that doesn't make them any more useful to discuss.

I will walk you through what you would have to do to be able to draw the conclusions you are claiming (for free, although I usually charge a hefty hourly rate for personal tutoring of reluctant students.  I'm calling this community outreach in my daily activity log).

World model:  X group of people are inherently inferior in terms of mental capacity, where X is any of the groups you have been dinging on this thread.

Hypothesis:  Under the same conditions with the same preparation as other groups, members of X group will do demonstrably worse on standardized tests in math and science.

Experiment:  Taking a group of children who are reasonably average representatives of multiple groups, but with similar previous educational backgrounds and controlled for things like age and language, randomly divide the students into cohorts of students.  Administer a pre-test on the topic to be taught with questions selected from a relevant standardized test.  Then, have an instructor teach each cohort a series of math or science lessons according to best practices for a set of selected topics.  Be sure that the instructor does not know which students belong to which group nor what the hypothesis being tested explicitly is.  The most the instructor needs to know is the common educational level of the children and that the children will be taking a post-instruction standardized test.  The instructor does not get to see the test prior to instruction to prevent any sort of favoritism in instruction.  Administer the post-test with questions selected from a relevant standardized test, ideally different selections from the same test that was used to construct the pre-test.

Data analysis:  Using normalized gains from pre-test to post-test, look at the average gain per group.  Compare differences in average gain among groups to the variation in gain within groups to get an estimate on whether those differences between groups are above chance variation (i.e., are statistically significant).

Replicates: Repeat the experiment and data analysis for multiple topics accompanied by the necessary tests to be sure to minimize sampling bias in kinds of questions asked.  Rotate through different cohorts of students with differing mixes of the groups being tested while making sure that they cannot share information with students who have already taken any of the tests.

Conclusions: Looking at all the data on averages between groups that meet the standard of being above chance, rank the groups by performance if such a pattern can be found to exist.  Only with that information in hand can you possibly make a conclusion about certain groups being automatically inferior that is even worth discussing.

Do you notice how all of the data you have presented here fails to follow this sort of method, which is not at all coincidentally the same points that the rubrics I cited earlier show you fail on?

For all of the numbers I can remember you spewing on this thread, you have made zero effort to control for important factors that are likely to affect the outcome nor have you in any way ever actually looked at the performance of any group X's (Y percentage of the population being an X is not at all the same as 100% of the tested population being a Y) versus any other groups except initially during the discussion about Americans versus other nationalities.

Are you at all familiar with the idea of a confirmation bias in not examining all the possibilities for an illusory correlation?  I ask because that's what you are doing, repeatedly on this thread. 

Consider the following example that I came across in my reading today*.  Many doctors, nurses, and police officers will swear that admissions to psych wards increase during the full moon.  However, we can't evaluate whether that's actually true until we've looked at the relative frequency of 4 cases:

1)  Full moon and psych ward admission
2)  Full moon and no psych ward admission
3)  Non-full moon and psych ward admission
4)  Non-full moon and no psych ward admission

Only looking at admissions to the psych ward during the full moon doesn't tell us anything if we don't have the information about the three cases.  By only considering the first case to draw a correlation means that you are making a logical error.

This logical error is the same kind that you are making when you plot some outcome (e.g., murder, abortion, divorce, or saving rates; test scores; patents) versus percent of population that is X and conclude that X and that rate are correlated.  You don't have enough information to draw that conclusion because you haven't tested observable as a function of X even in a basic way of comparing rates of 100% X populations to 0% X populations and selecting the populations in such a way as minimize other differences in the group that are likely to affect the observable to confuse the issue (also known as confounding variables).  That lack of control of confounding factors is why comparing Americans to anyone else on international standardized tests doesn't work--the huge differences in educational aims and population selected for testing between the nations mean that the populations aren't comparable so that attempting to draw detailed conclusions is not a reasonable activity.

So, in summary, when you present some data gathered in such a way that could possibly support your claims instead of what you have been doing, more of us would be likely to think about the data and discuss it.  In most scientific and academic circles, no one bothers to discuss what results from a flawed methodology since, by definition, it's flawed.  At most, some good ideas that failed in execution might be kicked around to figure out a non-flawed methodology, but that's not the case here.

Oh, for the record, while I don't know that anyone has done exactly as I have described upthread in terms of looking at inherently inferior group X's, I've seen lots of lovely studies done (mostly in the US, although a few in Europe) showing that the primary factors affecting educational achievement through high school are socioeconomic status of the parents, quality and consistency of schooling, and attitude/support of the family toward schooling, not ethnicity, race, religion, or national origin, despite definite differences on standardized tests by those groups when the control for similar schooling and effort is not applied.  Since those researchers did control for as many relevant factors as they could and didn't make claims stronger than their evidence, I would be happy to discuss that data with you.


*Lilienfeld et al.  50 Great Myths of Popular Psychology: Shattering Widespread Misconceptions about Human Behavior, Wiley-Blackwell, 2010

This illustrates ZERO understanding of math and science.  It's absurd to the max for you to proclaim that it's others who practice "pseudoscience".  You might just as well claim that the only reason people with higher SAT scores earn more than those with lower SAT scores is because of "discrimination", and that it has nothing to do with being more qualified.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 14, 2010, 07:14:04 PM
<head suddenly pops up the desk>

<wipes drool from notebook>

Huh? Sorry... did I miss something? Should I have written that down? Will it be on the test?

<goes back to sleep>

Alan


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 15, 2010, 09:31:10 AM
This illustrates ZERO understanding of math and science.  It's absurd to the max for you to proclaim that it's others who practice "pseudoscience".  You might just as well claim that the only reason people with higher SAT scores earn more than those with lower SAT scores is because of "discrimination", and that it has nothing to do with being more qualified.
Oh, really? It sounds like a pretty good understanding of statistical experimental design to me. However, I'm only a mathematician, so what do I know? Of course, I know Polly's qualifications in regards to science and have seen her demonstrate significant statistical understanding on these fora. However, given that this is your VERY FIRST post, I don't know your qualifications, Benami. Time to 'fess up. What are your qualifications to be pronouncing such judgments?


Title: Re: assuming too much math knowledge?
Post by: john_proctor on September 15, 2010, 01:05:29 PM
Are there any Jews in Israel?  Aren't the majority of the people there, like 90%, Ashkenazi Jews? 

In order:

Yes.

No.

But do continue to insist on making arguments based on data. 

The irony makes my nose feel all tingly.


Title: Re: assuming too much math knowledge?
Post by: kiana on September 15, 2010, 04:24:11 PM
What are your qualifications to be pronouncing such judgments?

Being jacob/john's new sock?


Title: Re: assuming too much math knowledge?
Post by: benami on September 15, 2010, 04:33:11 PM
Do you think I just made this up?  Why don't you LOOK at the actual data for a change, rather than sitting around patting each other on the back about how talented Jews are?
Oh, for the record, while I don't know that anyone has done exactly as I have described upthread in terms of looking at inherently inferior group X's, I've seen lots of lovely studies done (mostly in the US, although a few in Europe) showing that the primary factors affecting educational achievement through high school are socioeconomic status of the parents, quality and consistency of schooling, and attitude/support of the family toward schooling, not ethnicity, race, religion, or national origin, despite definite differences on standardized tests by those groups when the control for similar schooling and effort is not applied.  Since those researchers did control for as many relevant factors as they could and didn't make claims stronger than their evidence, I would be happy to discuss that data with you.


Why is it that the biggest racists are those who claim that socioeconomic status and test scores are related?



Title: Re: assuming too much math knowledge?
Post by: benami on September 15, 2010, 04:35:29 PM
Are there any Jews in Israel?  Aren't the majority of the people there, like 90%, Ashkenazi Jews? 

In order:

Yes.

No.

But do continue to insist on making arguments based on data. 

The irony makes my nose feel all tingly.


Isn't it anti-Semitic to claim that Jews have a higher IQ than Whites?


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 15, 2010, 08:29:16 PM
Zzzzzzz....

<clueless poster's ramblings wake me up>

42!

Makes more sense than Benami. Do I get relative points?

Alan


Title: Re: assuming too much math knowledge?
Post by: conjugate on September 15, 2010, 09:09:10 PM
Are there any Jews in Israel?  Aren't the majority of the people there, like 90%, Ashkenazi Jews? 

In order:

Yes.

No.

But do continue to insist on making arguments based on data. 

The irony makes my nose feel all tingly.


Isn't it anti-Semitic to claim that Jews have a higher IQ than Whites?

Did you know that many Jews are white?  Did you know that no one here made such a claim?


Title: Re: assuming too much math knowledge?
Post by: mouseman on September 15, 2010, 09:53:13 PM

Am I the only one who is amused that the new troll has taken a Hebrew name?  What's even more amusing is that it is also the name of the son born to Lot and his daughter.  So the troll has chosen a name that evokes drunken, incestuous sex.


Title: Re: assuming too much math knowledge?
Post by: keev_o_matic on September 16, 2010, 09:23:39 AM
Article from a Canadian perspective on math skills of first-year university students:

http://www.universityaffairs.ca/big-drop-in-math-skills-of-entering-students.aspx

The last paragraph of the article reminded me of a friend's story about going to an office supply store recently.  He wanted to buy eight manila folders (or somesuch), listed at 50 cents each.  At the checkout, the young clerk got out a calculator and announced that the cost would be 40 dollars.  When my friend asked how that could possibly be right, the clerk held up the device and said "because the calculator says so", and kept insisting the cost was 40 dollars.   My friend had to get the manager to sort it out.  


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 16, 2010, 10:18:39 AM
Article from a Canadian perspective on math skills of first-year university students:

http://www.universityaffairs.ca/big-drop-in-math-skills-of-entering-students.aspx

The last paragraph of the article reminded me of a friend's story about going to an office supply store recently.  He wanted to buy eight manila folders (or somesuch), listed at 50 cents each.  At the checkout, the young clerk got out a calculator and announced that the cost would be 40 dollars.  When my friend asked how that could possibly be right, the clerk held up the device and said "because the calculator says so", and kept insisting the cost was 40 dollars.   My friend had to get the manager to sort it out.  

Your friend should not have chosen the rhinestone-encrusted folders.

Sorry... I just felt a weird urge to type the word "encrusted".

Alan


Title: Re: assuming too much math knowledge?
Post by: benami on September 16, 2010, 12:32:33 PM


Oh, for the record, while I don't know that anyone has done exactly as I have described upthread in terms of looking at inherently inferior group X's, I've seen lots of lovely studies done (mostly in the US, although a few in Europe) showing that the primary factors affecting educational achievement through high school are socioeconomic status of the parents, quality and consistency of schooling, and attitude/support of the family toward schooling, not ethnicity, race, religion, or national origin, despite definite differences on standardized tests by those groups when the control for similar schooling and effort is not applied.  Since those researchers did control for as many relevant factors as they could and didn't make claims stronger than their evidence, I would be happy to discuss that data with you.


*Lilienfeld et al.  50 Great Myths of Popular Psychology: Shattering Widespread Misconceptions about Human Behavior, Wiley-Blackwell, 2010

The World Health Organization recently released a report on the number of cars per traffic fatality for most countries around the world.  It showed that the most dangerous cars are in the Central Republic of Africa where a car is 1,447 times more likely to kill someone than a car in Switzerland, and 85 times more likely than a car in Congo.

Do you think this correlation is with socioeconomic status, or with race as this report claims?


Country   Vehicles per death
San Marino   51,590
Malta   24,723
Switzerland   14,476
Japan   13,764
Germany   11,217
Netherlands   11,205
Norway   11,158
Sweden   8,983
Spain   7,661
Italy   7,632
Canada   7,148
England, Wales   7,141
Uruguay   6,566
USA   5,896
Korea   2,954
Marshall Is.   2,487
Thailand   2,051
United Arab Emirates   1,661
China   1,503
Iraq   1,161
Libya   854
Congo   854
Eriteria   751
India   688
S. Africa   573
Ghana   502
Gaza Strip   418
Afghanistan   411
Guinea-Bisau   381
Angola   285
Egypt   269
Gambia   268
Kenya    267
Tanzania   223
Niger   133
Uganda   128
Sao Tome   61
Ethiopia   61
Central African Republic   10


Title: Re: assuming too much math knowledge?
Post by: duchess_of_malfi on September 16, 2010, 12:43:43 PM
I don't know about other countries, but in the U.S., declining auto fatality rates over time are usually explained as an outcome of safer automobiles and with the decreasing prevalence of 2-lane highways in comparison to multi-lane, single-direction highways.  Improvements in medical care in the U.S. have led to increased survivor probability of potentially fatal injuries in gunshot incidents, so I assume this is true for auto injuries as well.  I don't see why the same forces would not be present elsewhere.  

I guess the bottom-line message of this thread is that it is easy to assume that people have more math knowledge, or simply more knowledge, than they do.


Title: Re: assuming too much math knowledge?
Post by: benami on September 16, 2010, 12:52:27 PM
Is this Take Aryan Supremacists Seriously Week?

Dunno.  However, in my book, it's always Counteract Pseudoscience and Ignorance with Education in Science Week, even if the only hope is to reach the observers instead of the primaries.


The following is science.  What you believe, or at least write, is pseudoscience:


http://www.minnesotamedicine.com/PastIssues/February2009/ClinicalJonesWebbFebruary2009/tabid/2827/Default.aspx

Discussion
We found support for our hypothesis that the association between race and premature mortality varied by socioeconomic status. Black men and women who lived in poorer neighborhoods had greater odds of dying prematurely than white men and women who lived in similar neighborhoods. Racial differences were most striking, however, for men and women who lived in more affluent neighborhoods, and especially for women. Our results suggest that both race and socioeconomic position are important in understanding the differences in mortality between blacks and whites.

♦ Strengths and Limitations
Our findings should be viewed in light of certain methodological limitations of our study. First, neighborhood poverty and educational status, our 2 proxy measures of socioeconomic status, were coded based on the person’s residence at the time of death. Many diseases have long induction periods and, thus, it may be equally important to know where a person lived most of his or her life. Researchers may wish to encourage health departments to include such information on death records in the future.

Second, the socioeconomic characteristics of some neighborhoods may have changed between the time of the census and the time of the individual’s death. We do not expect this to introduce significant bias because it generally takes a number of years for neighborhoods to change significantly.7

Third, statistical power to detect significant interaction effects was limited by the small number of deaths in certain subgroups (eg, the number of deaths among black men who lived in census tracts with higher educational status). Despite this limitation, we found a significant interaction effect between race and neighborhood poverty on premature mortality among both men and women. To increase power, we pooled data from 1992 through 1998 and dichotomized the neighborhood poverty and education variables. Future studies may wish to confirm the findings from this study using mortality data across multiple states that have similar demographic characteristics.

Our analyses also did not take into account the effects of living in a poor census tract that is adjacent to one like it versus one that is more affluent.8 Nor did our study include individual measures of socioeconomic status. We note, however, that other studies using area-based and individual-level socioeconomic data have yielded findings similar to ours.9

Finally, it may not be possible to generalize our findings to populations outside of Minnesota. The 5-county metro area we studied is highly segregated and has one of the highest percentages of minority children living in poverty in the United States.10 Future studies may wish to include both urban and rural samples of blacks and whites to confirm our findings.






Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 16, 2010, 03:51:59 PM
Ah. Spit out large sets of data. Post large amounts of summaries. Mouseman's observation.

Where have I seen this before? Hmm...

Alan


Title: Re: assuming too much math knowledge?
Post by: wet_blanket on September 16, 2010, 06:48:01 PM
Benami, would you be so kind as to provide a citation for the WHo traffic report you mention?  I ask because I had a look around the WHO website and couldn't find a report containing the data you quote.  I did find some data from which it would be possible to calculate  registered cars/1000 deaths, but that can't be what you used.  How do I know this?  Because:

1)  The number (whether calculated using the actual number of reported deaths or the number based on statistical modelling) in many cases are not those which you presented.  Given your undoubted excellence as a mathemitician, statistician and scientist, it is inconceivable that your numbers are incorrect.

2)  The cases presented are a fraction of the 150+ available.  Amongst those cases included are countries such as San Martin, which had a single road fatality.  I know that you would never cherry pick such extreme cases just to make a point, nor make generalizations based on outliers.

3)  The data available to make the calculation is the number of cars registered in each country.  You would of course be aware that the number of cars registered is not the same as the number of cars on the road, and that the differences between the two numbers of cars will vary by country, making the caluclation of cars/road death meaningless.  Someone of your calibre would never make such an elementary mistake.

But, since you of course have a different source to refer me to and did not make any of those basic errors, I'll answer the question you posed:


The World Health Organization recently released a report on the number of cars per traffic fatality for most countries around the world.  It showed that the most dangerous cars are in the Central Republic of Africa where a car is 1,447 times more likely to kill someone than a car in Switzerland, and 85 times more likely than a car in Congo.

Do you think this correlation is with socioeconomic status, or with race as this report claims?


Firstly, it would be nice to have a reference for the report to judge for myself what it claims.  But, I would point out that if race had anything to do with the issue (and stepping around the debate of what race means and the relative roles of biology and socialization in defining the concept) then I would expect to see similar numbers of deaths in the Central African Republic (which I assume you meant by Central Republic of Africa) and the Congo.  (Which Congo, by the way?  Did you know there are two countries with that name?)

Secondly, the correlation could be between either or both.  What you are really asking, I believe, is whether socioeconomic status or race offers a better explanation of the pattern of road traffic fatalities around the world.  The WHO seems to think SES, and I agree.  Road traffic deaths are caused not only by road traffic accidents, but also by a lack of medical attention after an accident.  It seems obvious to me that even if the pattern of traffic accidents were identical (number/population, severity, etc) in, say Switzerland and the CAR, the number of deaths would be far greater in the CAR because of the difference in availability of medical care.  I consider access to medical care to be a function of SES.


Title: Re: assuming too much math knowledge?
Post by: benami on September 17, 2010, 10:56:27 AM
I don't know about other countries, but in the U.S., declining auto fatality rates over time are usually explained as an outcome of safer automobiles and with the decreasing prevalence of 2-lane highways in comparison to multi-lane, single-direction highways.  Improvements in medical care in the U.S. have led to increased survivor probability of potentially fatal injuries in gunshot incidents, so I assume this is true for auto injuries as well.  I don't see why the same forces would not be present elsewhere.  

I guess the bottom-line message of this thread is that it is easy to assume that people have more math knowledge, or simply more knowledge, than they do.

How does this explain why it is that an American car is 9 times more dangerous than a car in San Marino, 4 times more dangerous than one in Malta, twice as dangerous as a car in Switzerland, or Japan, or Germany, or the Netherlands, or Norway, and even more dangerous than a car in Italy, Spain, Canada, and England?


For the same reason that "improvements in medical care in the US" have left us with a life expectancy 4 years shorter than many other countries which, as a percent of GDP, spend one fourth as much as we do?


Title: Re: assuming too much math knowledge?
Post by: benami on September 17, 2010, 11:14:28 AM
Benami, would you be so kind as to provide a citation for the WHo traffic report you mention?  I ask because I had a look around the WHO website and couldn't find a report containing the data you quote.  I did find some data from which it would be possible to calculate  registered cars/1000 deaths, but that can't be what you used.  How do I know this?  Because:

1)  The number (whether calculated using the actual number of reported deaths or the number based on statistical modelling) in many cases are not those which you presented.  Given your undoubted excellence as a mathemitician, statistician and scientist, it is inconceivable that your numbers are incorrect.

2)  The cases presented are a fraction of the 150+ available.  Amongst those cases included are countries such as San Martin, which had a single road fatality.  I know that you would never cherry pick such extreme cases just to make a point, nor make generalizations based on outliers.

3)  The data available to make the calculation is the number of cars registered in each country.  You would of course be aware that the number of cars registered is not the same as the number of cars on the road, and that the differences between the two numbers of cars will vary by country, making the caluclation of cars/road death meaningless.  Someone of your calibre would never make such an elementary mistake.

But, since you of course have a different source to refer me to and did not make any of those basic errors, I'll answer the question you posed:


The World Health Organization recently released a report on the number of cars per traffic fatality for most countries around the world.  It showed that the most dangerous cars are in the Central Republic of Africa where a car is 1,447 times more likely to kill someone than a car in Switzerland, and 85 times more likely than a car in Congo.

Do you think this correlation is with socioeconomic status, or with race as this report claims?


Firstly, it would be nice to have a reference for the report to judge for myself what it claims.  But, I would point out that if race had anything to do with the issue (and stepping around the debate of what race means and the relative roles of biology and socialization in defining the concept) then I would expect to see similar numbers of deaths in the Central African Republic (which I assume you meant by Central Republic of Africa) and the Congo.  (Which Congo, by the way?  Did you know there are two countries with that name?)

Secondly, the correlation could be between either or both.  What you are really asking, I believe, is whether socioeconomic status or race offers a better explanation of the pattern of road traffic fatalities around the world.  The WHO seems to think SES, and I agree.  Road traffic deaths are caused not only by road traffic accidents, but also by a lack of medical attention after an accident.  It seems obvious to me that even if the pattern of traffic accidents were identical (number/population, severity, etc) in, say Switzerland and the CAR, the number of deaths would be far greater in the CAR because of the difference in availability of medical care.  I consider access to medical care to be a function of SES.


Why certainly:

http://www.who.int/violence_injury_prevention/road_traffic/global_status_report/en/index.html

It's not at all true that "The data available to make the calculation is the number of cars registered in each country.  You would of course be aware that the number of cars registered is not the same as the number of cars on the road, and that the differences between the two numbers of cars will vary by country, making the caluclation of cars/road death meaningless."


First of all, none of this, even if it were 100% correct, would make the data "meaningless", unless you can prove that there are orders of magnitude differences between the way various countries count vehicles on the road.

This of course is impossible, so the data is far from "meaningless".

If you're implying that we somehow do a better job than other countries (at least most other countries) of keeping track of  the number of cars on the road or of the number of registered cars, I would have to disagree that the single nation which managed to score dead last in 16 of 32 12th Grade TIMSS items could possibly accomplish this.  Lastly, even if this were a factor, it would have an extremely minor effect on the data, considering that there are four orders of magnitude differences between the safest and most dangerous drivers/cars.



Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 17, 2010, 11:34:38 AM
Benami, we have been through the TIMSS debate before, and I will not rehash it again. Suffice it to say that I find very few conclusions that can actually be drawn from TIMSS on a scientific, statistical basis.

You still haven't answered the question about your qualifications to make judgments on other people's understandings of mathematics, statistics, and science when those same people have demonstrated a significant understanding over the course of YEARS on these fora. So, I will ask one more time before assuming that you are Jacobisrael's sock and ignoring you for eternity: What are your qualifications to be passing judgment on others' understandings of these subjects?


Title: Re: assuming too much math knowledge?
Post by: marfa on September 17, 2010, 12:31:14 PM
I can't believe I made the mistake of reading this thread again.

Can someone please tell me how to get a thread (that I so mistakenly posted to once) off the "show new replies to your posts" listing?

Thanks.

<I realize this post is a hijacking, but I think  a hijack would be appropriate about now>


Title: Re: assuming too much math knowledge?
Post by: slinger on September 17, 2010, 01:36:53 PM
I can't believe I made the mistake of reading this thread again.

Can someone please tell me how to get a thread (that I so mistakenly posted to once) off the "show new replies to your posts" listing?

Thanks.

<I realize this post is a hijacking, but I think  a hijack would be appropriate about now>

Is it possible to hijack a thread that's long since been hijacked at least once already?


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 17, 2010, 01:42:37 PM
I can't believe I made the mistake of reading this thread again.

Can someone please tell me how to get a thread (that I so mistakenly posted to once) off the "show new replies to your posts" listing?

Thanks.

<I realize this post is a hijacking, but I think  a hijack would be appropriate about now>

Is it possible to hijack a thread that's long since been hijacked at least once already?
Hijacking the hijack. I like it!


Title: Re: assuming too much math knowledge?
Post by: benami on September 17, 2010, 06:37:00 PM
Benami, we have been through the TIMSS debate before, and I will not rehash it again. Suffice it to say that I find very few conclusions that can actually be drawn from TIMSS on a scientific, statistical basis.

You still haven't answered the question about your qualifications to make judgments on other people's understandings of mathematics, statistics, and science when those same people have demonstrated a significant understanding over the course of YEARS on these fora. So, I will ask one more time before assuming that you are Jacobisrael's sock and ignoring you for eternity: What are your qualifications to be passing judgment on others' understandings of these subjects?

Would you say that the following [as yet unidentified] individual disagrees with you?

"Once the results for all grades are considered, we see that U.S. students in the early school years have reasonable levels of achievement when compared with other countries--in science they are actually rated near the top--but performance lags by grade 8 and becomes even poorer at grade 12. The report's new information about advanced students should be reviewed carefully by college and university policy makers as well as those who influence coursetaking and career decisions made during the high school years.

"Results of the advanced mathematics test reveal some unexpected weaknesses. Despite the fact that about one-quarter of the test related to calculus and that one-half of the U.S. advanced mathematics students were actually studying calculus, it was in geometry, not calculus, where U.S. students performed worst. This is consistent with performance in grades 4 and 8, but unexpected because these advanced students have all had formal geometry coursework. The results show that both geometry and algebra need to be key subjects of study throughout the curriculum.

"For me, as a physicist with a keen interest in education, the science results are even more troubling. Students performed poorly in most sub-areas of physics, with the poorest performance coming on items on mechanics and electricity/magnetism (areas that account for about 75 percent of American physics textbooks). Even students who took an Advanced Placement physics course scored below the international norm.

"These studies suggest that students appear to disengage from learning critical mathematics and science content as they progress through the school system. The sources of disengagement may include the classroom environment, the quality of instruction, and parental and community support for the value of science and mathematics to our children's future."


Title: Re: assuming too much math knowledge?
Post by: benami on September 17, 2010, 06:41:16 PM
Or how about this one?  Did you all ever consult with him?  Did he agree with your assessment?

"I am confident that Americans -- and American students -- have the ability to be competitive with the best students in the world. Consider, for example, the most recent TIMSS measurement of U.S. 4th graders. It showed that our students are well above the international average in mathematics and very near the top in achievement in science. This and other assessments show that we are making progress. Unfortunately, we are not gaining fast enough -- and the rest of the world is not standing still.

"We give our children a good foundation in the basics. Unfortunately, math and science education gets "stuck in a rut" in the middle grades. We run in place and then allow the majority of our students to "check out" of rigorous math and science courses in high school.

"The U.S. was the only country in TIMSS whose students dropped in ranking from above average performance in mathematics at the fourth grade to slightly below average performance at the eighth grade.

"By the 12th grade, our students' standing has fallen even further. We must recognize why the drop-off occurred and act aggressively to fix it.

"The first reason, and the real core of the problem, is the low expectations and low standards we have for what our students can and should learn in math and science from 4th to 12th grade. At the 8th grade, for example, many state standards and tests are far less rigorous than national and international standards of excellence."


Title: Re: assuming too much math knowledge?
Post by: polly_mer on September 17, 2010, 07:43:31 PM
I can't believe I made the mistake of reading this thread again.

Can someone please tell me how to get a thread (that I so mistakenly posted to once) off the "show new replies to your posts" listing?

Thanks.

<I realize this post is a hijacking, but I think  a hijack would be appropriate about now>

Unfortunately, no way currently exists to get any thread off your list.  Once you've responded, you're stuck with it for eternity or until you decide to ditch your moniker and start over.

Mr. Trolling Sock,  I have given dozens of free statistical analysis lessons over the years.  I have given several of them on this thread.  If you refuse to do the required reading, then I cannot help you any more.  I've got 20 students who paid good money for my teaching them statistics on which to spend my time.  Students who show no evidence of having done the reading don't get to have individual tutoring.


Title: Re: assuming too much math knowledge?
Post by: marfa on September 18, 2010, 09:27:52 AM


Unfortunately, no way currently exists to get any thread off your list.  Once you've responded, you're stuck with it for eternity or until you decide to ditch your moniker and start over.


Thanks, polly.  That's a sad little lesson for me.


Title: Re: assuming too much math knowledge?
Post by: benami on September 18, 2010, 01:19:27 PM

Mr. Trolling Sock,  I have given dozens of free statistical analysis lessons over the years.  I have given several of them on this thread.  If you refuse to do the required reading, then I cannot help you any more.  I've got 20 students who paid good money for my teaching them statistics on which to spend my time.  Students who show no evidence of having done the reading don't get to have individual tutoring.


Your free lessons and a dime won't buy you a cup of coffee.

Anyone who would accept your lessons as fact would score LOWER on TIMSS than if they'd just guessed.  And clearly lots of American 12th grade girls HAVE accepted lessons like yours, which is the only real explanation for why a THIRD of them scored lower than if they's just guessed.

Your free lesson on this thread has more than a dozen factual and logical errors which would lead those who follow it into negative IQ territory.


Title: Re: assuming too much math knowledge?
Post by: benami on September 18, 2010, 01:29:13 PM
Benami, we have been through the TIMSS debate before, and I will not rehash it again. Suffice it to say that I find very few conclusions that can actually be drawn from TIMSS on a scientific, statistical basis.

You still haven't answered the question about your qualifications to make judgments on other people's understandings of mathematics, statistics, and science when those same people have demonstrated a significant understanding over the course of YEARS on these fora. So, I will ask one more time before assuming that you are Jacobisrael's sock and ignoring you for eternity: What are your qualifications to be passing judgment on others' understandings of these subjects?


Everyone I know wholeheartedly agrees with the following accurate (if not politically correct) assessment, and vehemently disagrees with your above assertions.

"TIMSS released achievement results comparing general mathematics and science knowledge among typical graduating seniors in several countries. They also released results on more advanced, specialized achievement tests for graduating seniors studying physics or calculus (including Advanced Placement courses in one or both of those areas) and their counterparts in other countries.

"TIMSS showed very low results for US students compared to those in the other countries giving the tests, both for general knowledge by average graduating seniors and for advanced performance by seniors studying physics and calculus. A recent report, Facing the Consequences, from the US TIMSS Research Center suggested that these results were certainly to be expected. It pointed out that there was a consistent decline in our relative standing from fourth grade to eighth grade in both mathematics and science. Of the almost 40 topics examined in both mathematics and science, none showed improved standing relative to other TIMSS countries from fourth to eighth grade. Most topics showed a decline over the middle school years.

"Schmidt said, "It could hardly be a surprise to find this decline continuing on through high school. As we discussed in Facing the Consequences and in our earlier report A Splintered Vision, US curricula through eighth grade do not focus on any key topics or give them significantly more attention. Those curricula and our textbooks are highly repetitive and unchallenging in grade after grade of the middle school years. How could they provide a sound foundation on which to build during the high school years?" The middle school curricula in most TIMSS countries cover topics from algebra, geometry, physics and chemistry. For most US students these are first studied, if at all, in high school. Many students (about 15 percent) never study algebra, geometry (about 30 percent), advanced algebra (40 percent), other advanced mathematics (around 80 percent), chemistry (about 45 percent) or physics (almost 75 percent).

"Schmidt indicated, "US students frequently opt out of advanced study of mathematics and science in high school or are placed in less demanding courses even if they do continue to take mathematics and science courses. So high school mathematics and science is unlikely to overcome the poor foundation provided during US middle school education and reverse the downward trend in comparative performance for average students."

"The US is also selective about who takes what courses, especially in mathematics. We do this even before high school and are essentially unique among TIMSS countries in doing so. As early as middle school we offer different content to different groups of students. We presumably do this to improve our educational 'efficiency' and increase learning for all students or, at least, for the students in our most demanding courses. It doesn't work. Facing the Consequences used TIMSS results to examine these practices in some detail and found that they did little to help most students learn mathematics. The report also found that this practice contributed to exaggerating achievement differences among US students. The new twelfth grade results make it clear that tracking also fails to provide satisfactory achievement for either average or advanced students."


Title: Re: assuming too much math knowledge?
Post by: benami on September 18, 2010, 01:35:10 PM
Benami, we have been through the TIMSS debate before, and I will not rehash it again. Suffice it to say that I find very few conclusions that can actually be drawn from TIMSS on a scientific, statistical basis.

You still haven't answered the question about your qualifications to make judgments on other people's understandings of mathematics, statistics, and science when those same people have demonstrated a significant understanding over the course of YEARS on these fora. So, I will ask one more time before assuming that you are Jacobisrael's sock and ignoring you for eternity: What are your qualifications to be passing judgment on others' understandings of these subjects?



Was the following person consulted prior to your reaching those conclusions?  Do you think they agree with you?  Do you know who wrote this?

"The dramatic results are: U.S. twelfth-graders performed among the lowest of 21 countries on the assessment of mathematical and scientific general knowledge. In math, U.S. students were outperformed by those in 14 other countries, had similar scores to students in four countries, and performed better than students in only two countries, Cyprus and South Africa. In science, U.S. students were outperformed by students in 11 countries, performed similarly to those in seven countries, and again outperformed only students in Cyprus and South Africa. The U.S.'s lower relative ranking in general math (worse than 14 countries and similar to four) than in general science (worse than 11 countries and similar to 7) continues the same pattern found in both the fourth- and eighth-grade assessments. The U.S. was one of 3 countries that did not demonstrate a significant gender gap in general math. Although all the participating nations except South Africa showed a gender gap in science, favoring males, the U.S. had one of the smallest differences between male and female achievement.

"The TIMSS questions were designed to assess "how well students had acquired the mathematical and scientific skills and knowledge judged by an international committee of experts to be necessary for all citizens in their daily life," and were "given to a random sample of all students at whatever grade their nation or program of studies set as the end of their secondary schooling, regardless of whether or not they were currently taking mathematics or science at the time of the study."

"A subset of advanced students, from fewer countries, also participated in a comparison of higher-level mathematics and physics. The advanced mathematics assessment included the categories of calculus; numbers, equations and functions; and geometry. In a comparison of achievement among 16 nations, U.S. twelfth-grade students were bested by students in 11 countries, and did not perform better than a single country. Among the content areas, U.S. students were relatively weakest in geometry. Eight countries, including the U.S., showed a significant gender gap, favoring males, in all three content areas.

"The physics categories included mechanics; electricity and magnetism; particle, quantum, and modern physics; heat; and wave phenomena. U.S. students again did not outperform any of the 15 other countries, and 14 of them outperformed the U.S. While among the lowest performers in all five content areas, U.S. students performed relatively most poorly in mechanics, and electricity and magnetism. In all the participating nations except Latvia, males outperformed females in physics. For U.S. students, this gender gap existed in all of the content areas except heat.

"The report also looks for factors in the students' schooling and lives that might account for differing achievement levels, focusing specifically on the general math results. For example, it finds that the proportion of graduating students currently taking mathematics or science was lower in the United States than the average for all participating countries. U.S. twelfth-graders spent fewer hours per day studying or doing homework than the international average; more of those U.S. twelfth-graders worked at paid jobs, and worked longer hours, than did students in any other TIMSS nation. Students in the U.S. spent the same amount of time watching TV and videos as the international average. The report concludes that while there may be differences across countries, "few appear to be systematically related to our performance in twelfth grade compared to the other countries participating in TIMSS."


Title: Re: assuming too much math knowledge?
Post by: polly_mer on September 18, 2010, 02:41:09 PM
Benami, we have been through the TIMSS debate before, and I will not rehash it again. Suffice it to say that I find very few conclusions that can actually be drawn from TIMSS on a scientific, statistical basis.

You still haven't answered the question about your qualifications to make judgments on other people's understandings of mathematics, statistics, and science when those same people have demonstrated a significant understanding over the course of YEARS on these fora. So, I will ask one more time before assuming that you are Jacobisrael's sock and ignoring you for eternity: What are your qualifications to be passing judgment on others' understandings of these subjects?


Everyone I know wholeheartedly agrees with the following accurate (if not politically correct) assessment, and vehemently disagrees with your above assertions.

You need to get out more.  I spend large chunks of my time dealing with people deeply concerned about the state of math and science education in the United States.  There are excellent reasons to be concerned about the scientific and mathematical abilities (or lack thereof) of the general public in the United States but the TIMSS data is worthless for drawing that conclusion.

The whole problem with your arguments is that little or nothing of what you have presented supports your arguments because for anyone who knows statistics and how experimental design works, you are spouting nonsense.  It is beyond old to have spent the morning reading student work in statistics class where the students post examples of "bad statistics" when they mean "outcomes I don't like" and then come over here to have you whine about being ignored when you harp on the outcomes without doing the proper statistical analyses that could lead to the outcomes you claim.

In summary, I am sick and tired of reading your lengthy posts that do nothing more than add anecdotal data to the need for better math and science education in the general public.

Go pass a statistics class or a quantitative methods class in sociology or other relevant field and then come back when you can contribute to the conversation.



Title: Re: assuming too much math knowledge?
Post by: marfa on September 19, 2010, 10:00:00 AM

Mr. Trolling Sock,  I have given dozens of free statistical analysis lessons over the years.  I have given several of them on this thread.  If you refuse to do the required reading, then I cannot help you any more.  I've got 20 students who paid good money for my teaching them statistics on which to spend my time.  Students who show no evidence of having done the reading don't get to have individual tutoring.


Your free lessons and a dime won't buy you a cup of coffee.

Anyone who would accept your lessons as fact would score LOWER on TIMSS than if they'd just guessed.  And clearly lots of American 12th grade girls HAVE accepted lessons like yours, which is the only real explanation for why a THIRD of them scored lower than if they's just guessed.

Your free lesson on this thread has more than a dozen factual and logical errors which would lead those who follow it into negative IQ territory.

Benami,

Do not attribute that quote to me.  I did not, and will not, respond to your arguments.

~marfa


Title: Re: assuming too much math knowledge?
Post by: polly_mer on September 19, 2010, 11:14:32 AM
Another free lesson, Benami, because it's Sunday and I'm feeling generous:

Check the preview before you post, see that too many headers are in the quoted material, and then delete the one that doesn't apply.

Mr. Trolling Sock,  I have given dozens of free statistical analysis lessons over the years.  I have given several of them on this thread.  If you refuse to do the required reading, then I cannot help you any more.  I've got 20 students who paid good money for my teaching them statistics on which to spend my time.  Students who show no evidence of having done the reading don't get to have individual tutoring.


Your free lessons and a dime won't buy you a cup of coffee.

Anyone who would accept your lessons as fact would score LOWER on TIMSS than if they'd just guessed.  And clearly lots of American 12th grade girls HAVE accepted lessons like yours, which is the only real explanation for why a THIRD of them scored lower than if they's just guessed.

Your free lesson on this thread has more than a dozen factual and logical errors which would lead those who follow it into negative IQ territory.

Benami,

Do not attribute that quote to me.  I did not, and will not, respond to your arguments.

~marfa

One more story for the readers at home to consider, Benami.  I give my students a lab that consists of a panful of pennies and a balance.  The students are to weigh a sample of the pennies, record the mass, and then plot the mass of the pennies as a function of year minted.  A minor complicating factor is that the materials that make up the penny changed in the mid-1980's.  Thus, the data, if all of the pennies were mint-condition and uncirculated, would show a dramatic step function in the mid-80's.  However, due to wear, corrosion, gunk build-up, and inaccurate weighings by students, almost no graphs show that step function.  Yet, I always have students write as their conclusion something that includes the change in materials in the mid-1980's for the effect of age on the mass of a penny.  They have done no tests that would provide them that information since all they did was weigh the pennies; they didn't do chemical assays.  Their data doesn't support that conclusion; usually the data shows that the age of a penny has no affect on the mass since the data are so scattered with no step function even when I squint and know what I should be looking for.  A poorly conducted study cannot lead to the true answer by definition.  Thus, just like my students who lose points for drawing a conclusion that cannot be supported by the data in front of them, citing the TIMSS data as support for anything merely indicates that one's own ability to conduct and/or interpret a statistical experiment is in need of remediation.

I am extremely curious as to what you think the "dozen factual and logical errors" are in my previous lesson.  I would love to use them as examples of faulty thinking by the general public in my statistics classes this semester.


Title: Re: assuming too much math knowledge?
Post by: benami on September 19, 2010, 01:01:38 PM
Another free lesson, Benami, because it's Sunday and I'm feeling generous:



I am extremely curious as to what you think the "dozen factual and logical errors" are in my previous lesson.  I would love to use them as examples of faulty thinking by the general public in my statistics classes this semester.

Your first and foremost error is to accept a "study" which would draw the conclusion that there IS no correlation between full moons and psych ward admissions, then attempt to equate that to an assertion that there could be no correlation between test scores and race, or test scores and education quality, or test scores and nations, in the very same breath you claim that there IS a correlation between test scores and socioeconomic status.


Your claim that "That lack of control of confounding factors is why comparing Americans to anyone else on international standardized tests doesn't work--the huge differences in educational aims and population selected for testing between the nations mean that the populations aren't comparable so that attempting to draw detailed conclusions is not a reasonable activity" is PRECISELY what TIMSS set out to do, PRECISELY what they SUCCEEDED in doing, precisely what ALL the experts unanimously agreed they did, and precisely what everyone I know agrees happened.

Educators, and many other people, have agreed and maintained for a long time that we have a good, or even an adequate, education system, yet TIMSS is precisely the statistical evidence you need to understand your position is a MUCH greater and more serious fallacy than the correlation between full moons and psych wards.

How exactly do you believe TIMSS did not accomplish its objective?  They did everything, plus some, that you claim they did not do.


Title: Re: assuming too much math knowledge?
Post by: benami on September 19, 2010, 01:05:38 PM

Secondly, the correlation could be between either or both.  What you are really asking, I believe, is whether socioeconomic status or race offers a better explanation of the pattern of road traffic fatalities around the world.  The WHO seems to think SES, and I agree.  Road traffic deaths are caused not only by road traffic accidents, but also by a lack of medical attention after an accident.  It seems obvious to me that even if the pattern of traffic accidents were identical (number/population, severity, etc) in, say Switzerland and the CAR, the number of deaths would be far greater in the CAR because of the difference in availability of medical care.  I consider access to medical care to be a function of SES.


Would you be surprised to hear that traffic fatality rates by nation like this track perfectly with the average IQ of each nation?  Would you think this would track more closely than SES? Would you care to guess how close the correlation is with IQ?  Or how close it is when only 6 outliers out of 50 data points are removed?  Or how much the IQ of each nation must be adjusted to reach a perfectly linear correlation?  Or what happens to the data when you try to adjust IQ for a number of African nations where the number of traffic fatalities exceeds one for every 200 cars, EACH year?  Wouldn't this be a better measure of the condition of a country than SES? Or is this precisely how we might assign a numerical value for the SES of each country?


Title: Re: assuming too much math knowledge?
Post by: benami on September 19, 2010, 01:18:55 PM

One more story for the readers at home to consider, Benami.  I give my students a lab that consists of a panful of pennies and a balance.  The students are to weigh a sample of the pennies, record the mass, and then plot the mass of the pennies as a function of year minted.  A minor complicating factor is that the materials that make up the penny changed in the mid-1980's.  Thus, the data, if all of the pennies were mint-condition and uncirculated, would show a dramatic step function in the mid-80's.  However, due to wear, corrosion, gunk build-up, and inaccurate weighings by students, almost no graphs show that step function.  Yet, I always have students write as their conclusion something that includes the change in materials in the mid-1980's for the effect of age on the mass of a penny.  They have done no tests that would provide them that information since all they did was weigh the pennies; they didn't do chemical assays.  Their data doesn't support that conclusion; usually the data shows that the age of a penny has no affect on the mass since the data are so scattered with no step function even when I squint and know what I should be looking for.  A poorly conducted study cannot lead to the true answer by definition.  Thus, just like my students who lose points for drawing a conclusion that cannot be supported by the data in front of them, citing the TIMSS data as support for anything merely indicates that one's own ability to conduct and/or interpret a statistical experiment is in need of remediation.


And while you're wasting your and your students' time on such trivial nonsense, take a look at a direct observation of the performance of Japanese students in learning calculus in the same country I learned calculus--in high school:

<begin quote>
High School Calculus in the United States and in Japan
by Thomas W. Judson
In Japan, as in the United States, calculus is a gateway course that students must pass to study science or engineering. Japanese educators often voice complaints similar to those that we made about students' learning of calculus in the 1970s and 1980s. They believe that many students learn methods and templates for working entrance-examination problems without learning the concepts of calculus. University professors report that the mathematical preparation of students is declining and that even though Japanese middle school students excelled in mathematics in TIMSS-R, these same students expressed a strong dislike for the subject.

Japan has a national curriculum that is tightly controlled by the Ministry of Education and Science. In Japan, grades K–12 are divided into elementary school, middle school, and high school; students must pass rigorous entrance examinations to enter good high schools and universities. After entering high school, students choose either a mathematics and science track or a humanities and social science track. Students in the science track take suugaku 3 (calculus) during their last year of high school; most of them take a more rigorous calculus course at the university.

The course curricula for AP Calculus BC and suugaku 3 are very similar. The most noticeable differences are that Japanese students study only geometric series and do not study differential equations. The epsilon-delta definition of limit does not appear in either curriculum.

In the spring and summer of 2000, Professor Toshiyuki Nishimori of Hokkaido University and I studied United States and Japanese students' understanding of the concepts of calculus and their ability to solve traditional calculus problems. We selected two above-average high schools for our study, one in Portland, Oregon, and one in Sapporo, Japan. Our investigation involved 18 students in Portland and 26 students in Japan. Of the 16 Portland students who took the BC examination, six students scored a 5. We tested 75 calculus students in Sapporo; however, we concentrated our study on 26 students in the A class. The other two classes, the B and C groups, were composed of students of lower ability. Each student took two written examinations. The two groups of students that we studied were not random samples of high school calculus students from Japan and the United States, but we believe that they are representative of above-average students. We interviewed each student about his or her background, goals, and abilities and carefully discussed the examination problems with them.

Since we did not expect Japanese students to be familiar with calculators, we prohibited their use on the examinations. However, the students in Portland had made significant use of calculators in their course and might have been at a disadvantage if they did not have access to calculators. For that reason, we attempted to choose problems that were calculator independent. However, some problems on the second examinations required a certain amount of algebraic calculation.

We used problems from popular calculus-reform textbooks on the first examination. These problems required a sound understanding of calculus but little or no algebraic computation. For example, in one problem from the Harvard Calculus Project, a vase was to be filled with water at a constant rate. We asked students to graph the depth of the water against time and to indicate the points at which concavity changed. We also asked students where the depth grew most quickly and most slowly and to estimate the ratio between the two growth rates at these depths.

We found no significant difference between the two groups on the first examination. The Portland students performed as expected on calculus-reform-type problems; however, the Sapporo A students did equally well. Indeed, the Sapporo A group performed better than we had expected. We were somewhat surprised, since the Japanese students had no previous experience with such problems. The performance of Japanese students on the first examination may suggest that bright students can perform well on conceptual problems if they have sufficient training and experience in working such problems as those on the university entrance examinations.

The problems on the second examination were more traditional and required good algebra skills. For example, we told students that the function f(x) = x3+ ax2 + bx assumes the local minimum value—(2 )/9 at x = 1/—and asked them to determine a and b. We then asked them to find the local maximum value of f(x) and to compute the volume generated by revolving the region bounded by the x-axis and the curve y = f(x) about the x-axis. The Sapporo A students scored much higher than the Portland students did on the second examination. In fact, the Portland group performed at approximately the same level as the Sapporo C group and significantly below the Sapporo B group. Several Japanese students said in interviews that they found that certain problems on the second examination were routine, yet no American student was able to completely solve these problems. The Portland students had particular difficulty with algebraic expressions that contained radicals. Several students reported that they worked slowly to avoid making mistakes, possibly because they were accustomed to using calculators instead of doing hand computations.

Students from both countries were intelligent and highly motivated, and they excelled in mathematics; however, differences were evident in their performances, especially in algebraic calculation. One of the best Portland students correctly began to solve a problem on the second examination but gave up when he was confronted with algebraic calculations that involved radicals. On his examination paper he wrote, "Need calculator again."

Perhaps the largest difference between the two groups lies in the different high school cultures. Japanese students work hard to prepare for the university entrance examinations and are generally discouraged from holding part-time jobs. In contrast, students in the United States often hold part-time jobs in high school, and many are involved in such extracurricular activities as sports or clubs.
<end quote>

Did you catch that?  Our BEST students score on par with the THIRD TIER of Japanese high school students?



Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 20, 2010, 12:42:26 AM
Did you catch that?  Our BEST students score on par with the THIRD TIER of Japanese high school students?

Though based on your quote the US students would likely have done better with a different mix of problems, eg some including differential equations.  The study also seems to bear out what the Japanese educators were complaining about, that
"many [Japanese] students learn methods and templates for working entrance-examination problems without learning the concepts of calculus." 

As you surely know, since you are such an adept student of STEM fields, using calculus to compute volumes of rotation (such as the non-mechanical problem on the second exam) was an innovation of Kepler, who was doing consulting at the time for winemakers and needed to compute the volumes of wine barrels.  As this is no longer a major industry in the US, many American Calculus instructors skip that section of the text (usually somewhere in chapter 6,7, or 8 in modern Calc texts).

Since you like to ask questions, here's one for you:  Why have you started posting under a new name?  Is it because you've seen the error of your ways an no longer want to associate yourself with the offensive views you posted as John Knight?  - DvF


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 20, 2010, 01:43:55 AM
Did you catch that?  Our BEST students score on par with the THIRD TIER of Japanese high school students?

Though based on your quote the US students would likely have done better with a different mix of problems, eg some including differential equations.  The study also seems to bear out what the Japanese educators were complaining about, that
"many [Japanese] students learn methods and templates for working entrance-examination problems without learning the concepts of calculus." 

Warning-anecdote ahead. Proceed with caution. I hope I'm not repeating myself since I have told this story multiple times so it's still fresh in my head

I recently attended a presentation by some Chinese students attending college and they shared stories about their experiences. One thing that stood out was their initial reactions to their professors. They stated that in the schools they attended in their homeland that the professors would press them for answers but not how they decided upon the answer.

Their reactions were close to fear when their US professors followed-up by asking them how they decided upon the answer. One student told us that she couldn't answer because she wasn't used to a professor wanting to know more than just the answer to the question. To paraphrase her, she said that all of her professors here were-

"Why? Why? Why? Why?"

She stated that it was a very difficult transition for her to make to not just come up a solution but also to explain it.

Alan


Title: Re: assuming too much math knowledge?
Post by: polly_mer on September 20, 2010, 06:20:18 AM
Another free lesson, Benami, because it's Sunday and I'm feeling generous:



I am extremely curious as to what you think the "dozen factual and logical errors" are in my previous lesson.  I would love to use them as examples of faulty thinking by the general public in my statistics classes this semester.

Your first and foremost error is to accept a "study" which would draw the conclusion that there IS no correlation between full moons and psych ward admissions, then attempt to equate that to an assertion that there could be no correlation between test scores and race, or test scores and education quality, or test scores and nations, in the very same breath you claim that there IS a correlation between test scores and socioeconomic status.

No, I did not state that there could be no correlation between test scores and race or anything else.  I merely stated that the studies you were claiming showed such correlations could not possibly do so because they were not conducted in such a way as to yield that information.  Without proper controls for confounding variables like socioeconomic status, conclusions based on race alone by comparing populations with significant variation in socioeconomic status are meaningless.

Your claim that "That lack of control of confounding factors is why comparing Americans to anyone else on international standardized tests doesn't work--the huge differences in educational aims and population selected for testing between the nations mean that the populations aren't comparable so that attempting to draw detailed conclusions is not a reasonable activity" is PRECISELY what TIMSS set out to do, PRECISELY what they SUCCEEDED in doing, precisely what ALL the experts unanimously agreed they did, and precisely what everyone I know agrees happened.

Define ALL for me because where I live over here in STEM land populated by statisticians and scientists, the edu-wonks and politicians claim that TIMSS is a good study while people who have the capability to do scientific design see serious flaws in TIMSS.  Yes, the goal was to make a comparison between diverse populations using quantitative methods.  However, inadequate controls were applied in terms of populations sampled and in terms of reasonable comparison samples (for example, German students majoring in calculus are not at all the same as American students who are going to be English majors), making the study meaningless for that purpose.  Anyone can write a test that anyone else can fail, even an expert in the field (go look at what Rutgers has done for physics education where tenured full professors in physics and engineering sometimes fail the tests because of the way the questions are asked). 

Oh, and one further fun idea to consider: people can lie, unlike measuring physical phenonmena.  Eventually, some students hit test fatigue and simply bomb a test that has no consequences for them (like a random measuring test that doesn't come with a grade) because it's a free blow-off couple of hours and they are just freakin' tired.  Thus, your test is completely worthless under those conditions and people will do worse than chance because they are purposely bombing it (after all, if I can do all the problems, I can pick out a wrong answer with no problem).  I have no data to support my conclusions, but anecdotally I can tell you that some American students do do this.  I, myself, as a high school student capable of scoring a near perfect score on the standardized test in front of me did it as part of a pact with other high performers as a protest against taking a zillion stupid tests.  We were done being guinea pigs.  We wanted to learn, but we had taken plenty of tests already to gauge our knowledge in a meaningful way, thank you very much.  Where are the controls in TIMSS for that?

The strongest conclusion that one can draw from the data are that some populations of students in some countries didn't do well at the exact problems put on the test using the tools available to them at that time.  That's a far cry from the conclusions that have been bandied about by those ALL you mention.



One more story for the readers at home to consider, Benami.  I give my students a lab that consists of a panful of pennies and a balance.  The students are to weigh a sample of the pennies, record the mass, and then plot the mass of the pennies as a function of year minted.  A minor complicating factor is that the materials that make up the penny changed in the mid-1980's.  Thus, the data, if all of the pennies were mint-condition and uncirculated, would show a dramatic step function in the mid-80's.  However, due to wear, corrosion, gunk build-up, and inaccurate weighings by students, almost no graphs show that step function.  Yet, I always have students write as their conclusion something that includes the change in materials in the mid-1980's for the effect of age on the mass of a penny.  They have done no tests that would provide them that information since all they did was weigh the pennies; they didn't do chemical assays.  Their data doesn't support that conclusion; usually the data shows that the age of a penny has no affect on the mass since the data are so scattered with no step function even when I squint and know what I should be looking for.  A poorly conducted study cannot lead to the true answer by definition.  Thus, just like my students who lose points for drawing a conclusion that cannot be supported by the data in front of them, citing the TIMSS data as support for anything merely indicates that one's own ability to conduct and/or interpret a statistical experiment is in need of remediation.


And while you're wasting your and your students' time on such trivial nonsense, take a look at a direct observation of the performance of Japanese students in learning calculus in the same country I learned calculus--in high school:


Explain to me exactly why learning how to design an experiment from which one can draw useful conclusions is a waste of time.

Explain to me exactly why learning to draw conclusions from the data in front of you (not what you think the data ought to show, but what the data actually show) is a waste of time.

Being able to do calculus as a set of given problems is nice.  Being able to do the science to figure out what the problems are to be able to set them up to solve is even better.  If one has to, one can look up a given type of equation in a book or use a program to solve it if it turns out that that the particular equation in front of one doesn't immediately come to mind (one of the huge drawbacks of using a timed standardized test as the primary gauge of learning). 

It's nearly impossible to look up how to design an experiment for a specific situation and construct the necessary equations from the data when one doesn't know how to do those things.  Math can be done with the help of reference books as necessary; science requires knowing how to set up problems that can be solved.  The fact that you appear to be confused on this point doesn't make me want to adopt whatever learning strategy you think is superior because the world is filled with problems that aren't tidy.  Those are the problems that I want my college freshmen science students to be able to solve, not isolated math problems that someone else has already set up for them.


Title: Re: assuming too much math knowledge?
Post by: benami on September 20, 2010, 08:02:24 AM
No, I did not state that there could be no correlation between test scores and race or anything else.  I merely stated that the studies you were claiming showed such correlations could not possibly do so because they were not conducted in such a way as to yield that information.  Without proper controls for confounding variables like socioeconomic status, conclusions based on race alone by comparing populations with significant variation in socioeconomic status are meaningless.

This is completely silly.

This is exactly like saying that once you control for height, pygmies are no shorter than normal people.

NO data is "meaningless" just because you don't control for "confounding variables" like socioeconomic status.

Furthermore, there is a DIRECT correlation between race and sex, and socioeconomic status, so if a factor correlates with socioeconoic status, it MUST also correlate with race and sex.

Every single standardized math test ever developed in the entire world shows precisely the same hierarchy between races and sexes as is seen in socioeconomic status.  They all put Asian men at the top of the hierarchy and black women at the bottom, separated by two to three standard deviations.  All Hispanics (whether Puerto Ricans, Cubans, Mexicans, Latin American, South American, Central American, Latino, or "White" Hispanics) score one standard deviation lower than Whites and one quarter of a standard deviation higher than blacks.  American Indians score in between Whites and blacks, and Asians score one quarter of a standard deviation higher than Whites.  Within each race, boys score about half a standard deviation higher than girls.  This is exactly the pattern from state to state, city to city, and country to country.

And it's precisely the pattern in wages and salaries reported by the Census Bureau in their Annual Demographic Survey which is the only valid method for measuring socioeconomic status:

http://pubdb3.census.gov/macro/031995/hhinc/8_001.htm#pg5
http://ferret.bls.census.gov/macro/032002/perinc/toc.htm



Title: Re: assuming too much math knowledge?
Post by: ptarmigan on September 20, 2010, 08:09:59 AM
Another free lesson, Benami, because it's Sunday and I'm feeling generous:

Check the preview before you post, see that too many headers are in the quoted material, and then delete the one that doesn't apply.

Mr. Trolling Sock,  I have given dozens of free statistical analysis lessons over the years.  I have given several of them on this thread.  If you refuse to do the required reading, then I cannot help you any more.  I've got 20 students who paid good money for my teaching them statistics on which to spend my time.  Students who show no evidence of having done the reading don't get to have individual tutoring.


Your free lessons and a dime won't buy you a cup of coffee.

Anyone who would accept your lessons as fact would score LOWER on TIMSS than if they'd just guessed.  And clearly lots of American 12th grade girls HAVE accepted lessons like yours, which is the only real explanation for why a THIRD of them scored lower than if they's just guessed.

Your free lesson on this thread has more than a dozen factual and logical errors which would lead those who follow it into negative IQ territory.

Benami,

Do not attribute that quote to me.  I did not, and will not, respond to your arguments.

~marfa

One more story for the readers at home to consider, Benami.  I give my students a lab that consists of a panful of pennies and a balance.  The students are to weigh a sample of the pennies, record the mass, and then plot the mass of the pennies as a function of year minted.  A minor complicating factor is that the materials that make up the penny changed in the mid-1980's.  Thus, the data, if all of the pennies were mint-condition and uncirculated, would show a dramatic step function in the mid-80's.  However, due to wear, corrosion, gunk build-up, and inaccurate weighings by students, almost no graphs show that step function.  Yet, I always have students write as their conclusion something that includes the change in materials in the mid-1980's for the effect of age on the mass of a penny.  They have done no tests that would provide them that information since all they did was weigh the pennies; they didn't do chemical assays.  Their data doesn't support that conclusion; usually the data shows that the age of a penny has no affect on the mass since the data are so scattered with no step function even when I squint and know what I should be looking for.  A poorly conducted study cannot lead to the true answer by definition.  Thus, just like my students who lose points for drawing a conclusion that cannot be supported by the data in front of them, citing the TIMSS data as support for anything merely indicates that one's own ability to conduct and/or interpret a statistical experiment is in need of remediation.

I am extremely curious as to what you think the "dozen factual and logical errors" are in my previous lesson.  I would love to use them as examples of faulty thinking by the general public in my statistics classes this semester.

Polly, the sentence bolded above sounds like you instruct your students ("have them") to do this, but I think what you're saying is that some students draw this conclusion in their reports because they know it is expected, and that you disapprove.  Is that right?


Title: Re: assuming too much math knowledge?
Post by: wet_blanket on September 20, 2010, 08:25:56 AM
This is completely silly.
Well, yes.  Just not in the way you think.

Furthermore, there is a DIRECT correlation between race and sex, and socioeconomic status, so if a factor correlates with socioeconoic status, it MUST also correlate with race and sex.

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.


Every single standardized math test ever developed in the entire world shows precisely the same hierarchy between races and sexes as is seen in socioeconomic status.  They all put Asian men at the top of the hierarchy and black women at the bottom, separated by two to three standard deviations.  All Hispanics (whether Puerto Ricans, Cubans, Mexicans, Latin American, South American, Central American, Latino, or "White" Hispanics) score one standard deviation lower than Whites and one quarter of a standard deviation higher than blacks.  American Indians score in between Whites and blacks, and Asians score one quarter of a standard deviation higher than Whites.  Within each race, boys score about half a standard deviation higher than girls. 

Interesting.  I'd be surprised if you had a list of every single standardized math test ever developed in the entire world.  I would be more surprised if every administration of every test even had test takers of the populations you mention - not many Native Americans taking a test administered in say, Hong Kong, I bet.  Not to mention that the races mentioned don't include all people on this planet who have ever taken a standardized math test.

And why is "white" capitalized and "black" not?


Title: Re: assuming too much math knowledge?
Post by: benami on September 20, 2010, 08:30:45 AM
Did you catch that?  Our BEST students score on par with the THIRD TIER of Japanese high school students?

Though based on your quote the US students would likely have done better with a different mix of problems, eg some including differential equations.  The study also seems to bear out what the Japanese educators were complaining about, that
"many [Japanese] students learn methods and templates for working entrance-examination problems without learning the concepts of calculus." 

Warning-anecdote ahead. Proceed with caution. I hope I'm not repeating myself since I have told this story multiple times so it's still fresh in my head

I recently attended a presentation by some Chinese students attending college and they shared stories about their experiences. One thing that stood out was their initial reactions to their professors. They stated that in the schools they attended in their homeland that the professors would press them for answers but not how they decided upon the answer.

Their reactions were close to fear when their US professors followed-up by asking them how they decided upon the answer. One student told us that she couldn't answer because she wasn't used to a professor wanting to know more than just the answer to the question. To paraphrase her, she said that all of her professors here were-

"Why? Why? Why? Why?"

She stated that it was a very difficult transition for her to make to not just come up a solution but also to explain it.

Alan

It's good that you issued that anecdote warning.  Your anecdote is completely worthless.  It contradicts a thousand anecdotes I could quote, plus contradicts the data, plus an anecdote about China has nothing to do with how students are taught calculus in Japan, and it ignores that the differences across China in academic skills and teaching methods are even more dramatic than the 220 SAT point difference from North Dakota to Rhode Island.

Here's my worthless anecdote.  The last day the US competed effectively in the semiconductor industry was 1983.  Yet even then, 100% of the design engineers in this "American" semiconductor company were Chinese, mostly from Taiwan, Hong Kong, and Singapore.  Yet even then, even before seeing the raw test scores, it was obvious that design engineers from Singapore were heads and shoulders above those from  Taiwan, who were head and shoulders above the nonexistent "American" design engineers.  One thing these uncreative Chinese could do was design all our chips for us, but not even they compete today with Japanese design engineers, who are also a generation behind Korea.

At the 8th grade level ALL of them scored more than 100 TIMSS points higher than us and Singapore scored 150 points higher.  But by the 12th grade, the differences in math skills are so big that the College Board accused them all of cheating on the Graduate Record Exam--only to discover that they actually KNEW the subject that well.

Singapore teaches calculus in elementary school.  95% of Japanese and Korean students, and 65% of German students, graduate from high school with calculus behind them.  Even the 5% in this country who actually DO complete calculus in high school score one letter grade higher in advanced math in college than students who wait until college to take calculus.


Title: Re: assuming too much math knowledge?
Post by: zharkov on September 20, 2010, 08:38:55 AM

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.


Chime.  As the saying goes, "correlation does not equal causation."  At the risk of dating myself, my favorite example of a strong (and more or less social scientifically incomplete) correlation was from the S manual (S was a stats programming language, the precursor to R).  US data showed that literacy rate was strongly correlated with murder rate (by state).  But it wasn't because the illiterate blast away because they can't be lured to read Dickens.  It was that there are other social factors at play (natch).

So how does one get from correlation to causation?  You need to do the social research, read the lit, understand the theories, and so on.  The math ladder -- as valuable as it is -- doesn't reach that far.


 



Title: Re: assuming too much math knowledge?
Post by: benami on September 20, 2010, 08:54:32 AM

Singapore teaches calculus in elementary school.  95% of Japanese and Korean students, and 65% of German students, graduate from high school with calculus behind them.  Even the 5% in this country who actually DO complete calculus in high school score one letter grade higher in advanced math in college than students who wait until college to take calculus.


One more worthless anecdote, since you're so fond of anecdotes.  Having just returned from a class reunion where I majored in physics, I'm itching to tell this story.  I was standing in front of the Jackson Hope Memorial (which at the time I knew nothing about) when a classmate who I just barely remembered walked up.  We got reacquainted by discussing our experiences in physics lab and the problems he had with calculus, as he wasn't able to complete it in high school.  Because I was in Japan, not only did I complete calculus in high school, but I got a dose of other very valuable math that appears to be virtually unknown in the US.  I figured out then that he had never discovered what his problem with calculus was, so he was (naturally) shocked and incredulous when I told him  what it was.

He mentioned that he knew one of our underclassmen who was listed on that memorial, which I later learned was awarded to the top academic student in the entire school that year.  We said good bye, he walked away, so I went over to the memorial to figure out what it was all about.  And guess whose name was on the memorial from our class year.  The guy who just walked away without even mentioning it!

The moral of the story?  THE top student in one of America's (once) top physics and engineering colleges didn't even know calculus.

Do you wanna know why?


Title: Re: assuming too much math knowledge?
Post by: benami on September 20, 2010, 09:08:18 AM

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.




I'm not in the business of defining or redefining terms. I accept the term "correlation" as it's defined in every math book you can get your hands on.  Yes, lots of data correlates without ever even implying cause.  But when an education system says "we can't do our jobs without more money", and we discover that, city to city, state to state, and country, almost without exception, there's an INVERSE correlation between test scores and dollars per student, then certainly we deserve to know why, eh?


Title: Re: assuming too much math knowledge?
Post by: benami on September 20, 2010, 09:35:57 AM

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.


Chime.  As the saying goes, "correlation does not equal causation."  At the risk of dating myself, my favorite example of a strong (and more or less social scientifically incomplete) correlation was from the S manual (S was a stats programming language, the precursor to R).  US data showed that literacy rate was strongly correlated with murder rate (by state).  But it wasn't because the illiterate blast away because they can't be lured to read Dickens.  It was that there are other social factors at play (natch).

So how does one get from correlation to causation?  You need to do the social research, read the lit, understand the theories, and so on.  The math ladder -- as valuable as it is -- doesn't reach that far.


 



Well, it appears that nobody else on this forum wants to even think about the possibility that people in different parts of the country or the world actually are different.  As you evidently understand, when there's a 400 fold difference in the murder rate from state to state, we need to know why.  As all the other social pathology (incarceration, divorce, poverty, drug abuse, illegitimacy, high education and health care spending, poor academic skills, welfare abuse, etc.) tracks perfectly state to state and city to city with murder rates, the answer's not too far off.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 20, 2010, 10:33:18 AM

Singapore teaches calculus in elementary school.  95% of Japanese and Korean students, and 65% of German students, graduate from high school with calculus behind them.  Even the 5% in this country who actually DO complete calculus in high school score one letter grade higher in advanced math in college than students who wait until college to take calculus.

One more worthless anecdote, since you're so fond of anecdotes.  Having just returned from a class reunion where I majored in physics, I'm itching to tell this story.  I was standing in front of the Jackson Hope Memorial (which at the time I knew nothing about) when a classmate who I just barely remembered walked up.  We got reacquainted by discussing our experiences in physics lab and the problems he had with calculus, as he wasn't able to complete it in high school.  Because I was in Japan, not only did I complete calculus in high school, but I got a dose of other very valuable math that appears to be virtually unknown in the US.  I figured out then that he had never discovered what his problem with calculus was, so he was (naturally) shocked and incredulous when I told him  what it was.

He mentioned that he knew one of our underclassmen who was listed on that memorial, which I later learned was awarded to the top academic student in the entire school that year.  We said good bye, he walked away, so I went over to the memorial to figure out what it was all about.  And guess whose name was on the memorial from our class year.  The guy who just walked away without even mentioning it!

The moral of the story?  THE top student in one of America's (once) top physics and engineering colleges didn't even know calculus.

Do you wanna know why?


Please learn to quote properly.

Alan


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 20, 2010, 11:25:56 AM
 Even the 5% in this country who actually DO complete calculus in high school score one letter grade higher in advanced math in college than students who wait until college to take calculus.
This happens to not be true, but even if it was all it would imply is that people identified as the best math students in high school are the best math students in college.  Not a surprise.  Deciding based on this to change the curriculum is cargo cult mentality.

You haven't answered my question.  Why did you change your posting name? - DvF


Title: Re: assuming too much math knowledge?
Post by: benami on September 20, 2010, 01:38:25 PM

One more story for the readers at home to consider, Benami.  I give my students a lab that consists of a panful of pennies and a balance.  The students are to weigh a sample of the pennies, record the mass, and then plot the mass of the pennies as a function of year minted.  A minor complicating factor is that the materials that make up the penny changed in the mid-1980's.  Thus, the data, if all of the pennies were mint-condition and uncirculated, would show a dramatic step function in the mid-80's.  However, due to wear, corrosion, gunk build-up, and inaccurate weighings by students, almost no graphs show that step function.  Yet, I always have students write as their conclusion something that includes the change in materials in the mid-1980's for the effect of age on the mass of a penny.  They have done no tests that would provide them that information since all they did was weigh the pennies; they didn't do chemical assays.  Their data doesn't support that conclusion; usually the data shows that the age of a penny has no affect on the mass since the data are so scattered with no step function even when I squint and know what I should be looking for.  A poorly conducted study cannot lead to the true answer by definition.  Thus, just like my students who lose points for drawing a conclusion that cannot be supported by the data in front of them, citing the TIMSS data as support for anything merely indicates that one's own ability to conduct and/or interpret a statistical experiment is in need of remediation.


Polly, the sentence bolded above sounds like you instruct your students ("have them") to do this, but I think what you're saying is that some students draw this conclusion in their reports because they know it is expected, and that you disapprove.  Is that right?

My question exactly.  It sounds like her students lose points if they know that the material in coins changed, found no test results which indicate that the material changed, then note in their report that their measurements didn't indicate that the material had changed.

Besides all that, this is a bad analogy (in fact a fatally flawed analogy) to the TIMSS study which DID CONSISTENTLY find huge differences in student performance across nations, continents, sexes, and races [code-named socioeconomic status] without using trick questions like this, results which are consistent with tests like IAEP, PISA, and Pirls.


Title: Re: assuming too much math knowledge?
Post by: ptarmigan on September 20, 2010, 05:59:59 PM

One more story for the readers at home to consider, Benami.  I give my students a lab that consists of a panful of pennies and a balance.  The students are to weigh a sample of the pennies, record the mass, and then plot the mass of the pennies as a function of year minted.  A minor complicating factor is that the materials that make up the penny changed in the mid-1980's.  Thus, the data, if all of the pennies were mint-condition and uncirculated, would show a dramatic step function in the mid-80's.  However, due to wear, corrosion, gunk build-up, and inaccurate weighings by students, almost no graphs show that step function.  Yet, I always have students write as their conclusion something that includes the change in materials in the mid-1980's for the effect of age on the mass of a penny.  They have done no tests that would provide them that information since all they did was weigh the pennies; they didn't do chemical assays.  Their data doesn't support that conclusion; usually the data shows that the age of a penny has no affect on the mass since the data are so scattered with no step function even when I squint and know what I should be looking for.  A poorly conducted study cannot lead to the true answer by definition.  Thus, just like my students who lose points for drawing a conclusion that cannot be supported by the data in front of them, citing the TIMSS data as support for anything merely indicates that one's own ability to conduct and/or interpret a statistical experiment is in need of remediation.


Polly, the sentence bolded above sounds like you instruct your students ("have them") to do this, but I think what you're saying is that some students draw this conclusion in their reports because they know it is expected, and that you disapprove.  Is that right?

My question exactly.  It sounds like her students lose points if they know that the material in coins changed, found no test results which indicate that the material changed, then note in their report that their measurements didn't indicate that the material had changed.

Besides all that, this is a bad analogy (in fact a fatally flawed analogy) to the TIMSS study which DID CONSISTENTLY find huge differences in student performance across nations, continents, sexes, and races [code-named socioeconomic status] without using trick questions like this, results which are consistent with tests like IAEP, PISA, and Pirls.

No, I'm sure that's not what she's saying at all.


Title: Re: assuming too much math knowledge?
Post by: kraken on September 20, 2010, 07:55:36 PM

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.






I'm not in the business of defining or redefining terms. I accept the term "correlation" as it's defined in every math book you can get your hands on.  Yes, lots of data correlates without ever even implying cause.  But when an education system says "we can't do our jobs without more money", and we discover that, city to city, state to state, and country, almost without exception, there's an INVERSE correlation between test scores and dollars per student, then certainly we deserve to know why, eh?


Citation?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 21, 2010, 01:11:12 AM
Quote from: aryan supremacy dude wrote
I'm not in the business of defining or redefining terms. I accept the term "correlation" as it's defined in every math book you can get your hands on.

Citation?

"Most Of 'Em...All Of 'Em...Any Of 'Em"   - DvF


Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 05:15:34 AM

Singapore teaches calculus in elementary school.  95% of Japanese and Korean students, and 65% of German students, graduate from high school with calculus behind them.  Even the 5% in this country who actually DO complete calculus in high school score one letter grade higher in advanced math in college than students who wait until college to take calculus.

One more worthless anecdote, since you're so fond of anecdotes.  Having just returned from a class reunion where I majored in physics, I'm itching to tell this story.  I was standing in front of the Jackson Hope Memorial (which at the time I knew nothing about) when a classmate who I just barely remembered walked up.  We got reacquainted by discussing our experiences in physics lab and the problems he had with calculus, as he wasn't able to complete it in high school.  Because I was in Japan, not only did I complete calculus in high school, but I got a dose of other very valuable math that appears to be virtually unknown in the US.  I figured out then that he had never discovered what his problem with calculus was, so he was (naturally) shocked and incredulous when I told him  what it was.

He mentioned that he knew one of our underclassmen who was listed on that memorial, which I later learned was awarded to the top academic student in the entire school that year.  We said good bye, he walked away, so I went over to the memorial to figure out what it was all about.  And guess whose name was on the memorial from our class year.  The guy who just walked away without even mentioning it!

The moral of the story?  THE top student in one of America's (once) top physics and engineering colleges didn't even know calculus.

Do you wanna know why?


Please learn to quote properly.

Alan



Did you intentionally misquote your instructions to quote properly, Alan, or was that a Freudian Slip?


Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 06:12:16 AM


Define ALL for me because where I live over here in STEM land populated by statisticians and scientists, the edu-wonks and politicians claim that TIMSS is a good study while people who have the capability to do scientific design see serious flaws in TIMSS.  Yes, the goal was to make a comparison between diverse populations using quantitative methods.  However, inadequate controls were applied in terms of populations sampled and in terms of reasonable comparison samples (for example, German students majoring in calculus are not at all the same as American students who are going to be English majors), making the study meaningless for that purpose.  Anyone can write a test that anyone else can fail, even an expert in the field (go look at what Rutgers has done for physics education where tenured full professors in physics and engineering sometimes fail the tests because of the way the questions are asked). 


You don't live in STEM land.  Your statement "for example, German students majoring in calculus are not at all the same as American students who are going to be English majors" is all the proof we need that you live in Alice in Wonderland. 

TIMSS is completely open with the data and anyone, particularly an education expert living in STEM land, wanting to know how German students taking calculus stack up to American English majors could find out instantly.  On top of that, PISA's open and searchable data base, which is consistent with the TIMSS data, enables you to discover without even leaving your keyboard that a German boy in a private school who agrees "When I do mathematics, I sometimes get totally absorbed" scores 560 in math, compared to 470 for an American girl in public schools who disagrees, and 597 for a Korean boy who agrees "Mathematics is important to me personally."

Did you not know this?  Have you not seen this data base, or searached it?  Or did you not understand it?  Your statement is FALSE.

Each time TIMSS is conducted, dozens of countries meet the strict sampling requirements and none of them have the complaints you claim our educators have.  The US is one of the only countries who evidently can't meet the sampling requirements, which by itself is an indictment our education system, probably even worse than our amazingly low 12th grade scores.  We probably would have scored even lower had we met those strict statistical requirements.  As a courtesy, TIMSS reported our 12th grade scores with the caveat that the data was suspect because we did not meet the sampling requirements (in the range of 14% compared to the required 85%).

Your argument MIGHT have some weight had it not been for the fact that this is precisely the same pattern we've seen on all the other international standardized tests we've participated in (or at least released to the public), like IAEP, PIRLS (and of course PISA).  We've also administered tests like GRE, SAT, and ACT to foreign countries and confirmed the same pattern.

Crying "wolf" usually only works once.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 21, 2010, 12:15:44 PM
Did you intentionally misquote your instructions to quote properly, Alan, or was that a Freudian Slip?

I prefer boxer briefs over slips.

Alan


Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 12:46:14 PM

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.






I'm not in the business of defining or redefining terms. I accept the term "correlation" as it's defined in every math book you can get your hands on.  Yes, lots of data correlates without ever even implying cause.  But when an education system says "we can't do our jobs without more money", and we discover that, city to city, state to state, and country, almost without exception, there's an INVERSE correlation between test scores and dollars per student, then certainly we deserve to know why, eh?


Citation?

Citation? Why don't you cite a source which disagrees with the way this word has been used here?  Because you can't?

If you really want to learn about correlation, take a look at the Beaton Gonzalez correlation between NAEP and IAEP.  Or you might start with the following correlation which shows a perfect match between SAT scores and NAEP scores:

http://www.cse.ucla.edu/products/Reports/TECH375.pdf

What you should be asking is how closely does data correlate, and what are the reasons for the correlation.  For example, should we expect states' SAT math scores to correlate with states' SAT Verbal scores?  Of course.  How closely should we expect them to correlate?  The Pearson coefficient exceeds 0.97 which is a very high rate of correlation.  When just one outlier, Hawaii, is removed, it increases to 0.976, an even stronger correlation.

Does such a high degree of correlation imply causation?  Of course.  There's no question about it.

But what factors are involved?  Other forums have produced more than 20 possibilities.



Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 12:48:40 PM
Did you intentionally misquote your instructions to quote properly, Alan, or was that a Freudian Slip?

I prefer boxer briefs over slips.

Alan


Ah, so, that explains your position perfectly.


Title: Re: assuming too much math knowledge?
Post by: zharkov on September 21, 2010, 12:54:47 PM

Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


Causation is a property of science, not of mathematics.




Title: Re: assuming too much math knowledge?
Post by: conjugate on September 21, 2010, 01:01:02 PM
Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.

Finally, I still don't know what you think we could do about it in any case.  I mean, you spew statistics at us, chide us because we aren't making as many suggestions as the other "forums" (your word), and still haven't said what we should do about any of it.  You didn't give a coherent answer in your other ID either, so I suspect the sock puppet you're now using will be similarly unresponsive.

If these other forums are giving you so many possibilities, why don't you go bother them some more and leave us alone?

On preview: Or, what Zharkov said.


Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 01:20:21 PM
German students majoring in calculus are not at all the same as American students who are going to be English majors), making the study meaningless for that purpose.  Anyone can write a test that anyone else can fail, even an expert in the field (go look at what Rutgers has done for physics education where tenured full professors in physics and engineering sometimes fail the tests because of the way the questions are asked). 


The goal of TIMSS was not to compare English majors to "calculus majors" (nor should it ever be), but to assess (which it did perfectly well) the relative math skills of students at all levels of math in countries all around the world.  However, both TIMSS and PISA went into much greater detail and analysis than this to search for reasons for good and poor math skills.
 
For example, the following PISA math scores for 8th graders in the Netherlands (BEFORE their scores skyrocketed, which they did between 8th and 12th grade), gives us a hint about what factors might improve math skills, or what types of students perform better in math, or both:

http://pisa2000.acer.edu.au/interactive.php

"math is important" = 499
"well in tests" = 522
"Mathematics is one of my best subjects" = 516
"Because doing mathematics is fun, I wouldn't want to give it up" = 491
"I get good marks in mathematics" = 522
"Because reading is fun, I wouldn't want to give it up" = 504
"When I do mathematics, I sometimes get totally absorbed" = 506
"Use calculator several times a week" = 513 (compared to 512 for never use calculator)
"use science lab several times per month" = 528
"three or more computers in home" = 549
"we have books of poetry in my home" = 511
"we have a dishwasher" = 516
"father usually lives at home with you" = 507 (compared to 475 for "no")
"go to ballet 3 or 4 times per year" - 541
"boy in private school" = 535 (vs. 484 for girl in public school)
"private school" = 530 (compared to 489 for public school)
"internet in home" = 530 (compared to 473 for "no"_

Is this a suggestion that buying three or more computers for your children is a better way to improve their math skills than taking them to a ballet several times per year, or that dishwashers are better than books of poetry?  Of course not--these are indicators that such parents would naturally be expected to have more intelligent children.

What score do you believe a boy in a private school in the Netherlands would have if he never used a calculator, believed he "got good marks in math", had a dishwasher, five computers and the internet in his home, used a science lab several times per month, and went to the ballet several times per year?

Would a book on poetry improve his score?

What you claim these tests don't do is PRECISELY what they DO!



Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 01:27:11 PM

Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


Causation is a property of science, not of mathematics.






Sure.  The math only proves that the data correlates.

Should we expect SAT math scores and SAT verbal scores to have such a high degree of correlation.

No.

Why should they?


Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 01:38:19 PM
Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.




If you rely on Wikipedia as your source for mathematics principles (or scientific facts of any kind, or actually for ANY information), you're in a HEAP of trouble.  Not even most of our textbooks are accurate, but they're a lightyear ahead of Wikipedia, particularly when it comes to statistics.

That's the LAST source you should cite as a reference for probabilities and statistics (a subject which a vast majority of our students scored lower on than if they'd just GUESSED on almost all the questions).


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on September 21, 2010, 01:44:15 PM
Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.




If you rely on Wikipedia as your source for mathematics principles (or scientific facts of any kind, or actually for ANY information), you're in a HEAP of trouble.  Not even most of our textbooks are accurate, but they're a lightyear ahead of Wikipedia, particularly when it comes to statistics.

That's the LAST source you should cite as a reference for probabilities and statistics (a subject which a vast majority of our students scored lower on than if they'd just GUESSED on almost all the questions).


I believe conjugate pointed you toward Wikipedia in the hope that it was written at an elementary enough level that even you might be capable of comprehending it.


Title: Re: assuming too much math knowledge?
Post by: pollinate on September 21, 2010, 02:13:23 PM
Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.




If you rely on Wikipedia as your source for mathematics principles (or scientific facts of any kind, or actually for ANY information), you're in a HEAP of trouble.  Not even most of our textbooks are accurate, but they're a lightyear ahead of Wikipedia, particularly when it comes to statistics.

That's the LAST source you should cite as a reference for probabilities and statistics (a subject which a vast majority of our students scored lower on than if they'd just GUESSED on almost all the questions).


I believe conjugate pointed you toward Wikipedia in the hope that it was written at an elementary enough level that even you might be capable of comprehending it.

We can dream, can't we?

I wonder if there is any correlation between being unable to stop trying to educate the obviously ineducable and being in the teaching profession?


Title: Re: assuming too much math knowledge?
Post by: benami on September 21, 2010, 02:26:43 PM
Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.




If you rely on Wikipedia as your source for mathematics principles (or scientific facts of any kind, or actually for ANY information), you're in a HEAP of trouble.  Not even most of our textbooks are accurate, but they're a lightyear ahead of Wikipedia, particularly when it comes to statistics.

That's the LAST source you should cite as a reference for probabilities and statistics (a subject which a vast majority of our students scored lower on than if they'd just GUESSED on almost all the questions).


I believe conjugate pointed you toward Wikipedia in the hope that it was written at an elementary enough level that even you might be capable of comprehending it.



Here's a good question for you.  Did you know that American girls scored 426 in advanced math, and that no other race, sex, or country scored lower?  Did you know that American boys scored 457 and no other race or country scored lower, and only girls in Austria and the Czech Republic scored lower?  Did you know that Russian and French and and Swiss boys scored 559 or higher, which is  102 points higher than our boys and 133 points higher than our girls, and this doesn't even include the highest scoring Asian nations in the 8th grade test, like Japan, Korea, and Singapore?  Assuming that probabilities and statistics is counted as "advanced math" (which it's not in most other countries), which source do you believe most of  these students got their FALSE information from (these scores are LOWER than if they'd just guessed):



1) Wikipedia?

2) American textbooks?



If you believe even TEN PERCENT of them got their information from text books, then exactly what do you believe is wrong with these books?







Title: Re: assuming too much math knowledge?
Post by: mystictechgal on September 21, 2010, 02:58:12 PM
Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.




If you rely on Wikipedia as your source for mathematics principles (or scientific facts of any kind, or actually for ANY information), you're in a HEAP of trouble.  Not even most of our textbooks are accurate, but they're a lightyear ahead of Wikipedia, particularly when it comes to statistics.

That's the LAST source you should cite as a reference for probabilities and statistics (a subject which a vast majority of our students scored lower on than if they'd just GUESSED on almost all the questions).


I believe conjugate pointed you toward Wikipedia in the hope that it was written at an elementary enough level that even you might be capable of comprehending it.



Here's a good question for you.  Did you know that American girls scored 426 in advanced math, and that no other race, sex, or country scored lower?  Did you know that American boys scored 457 and no other race or country scored lower, and only girls in Austria and the Czech Republic scored lower?  Did you know that Russian and French and and Swiss boys scored 559 or higher, which is  102 points higher than our boys and 133 points higher than our girls, and this doesn't even include the highest scoring Asian nations in the 8th grade test, like Japan, Korea, and Singapore?  Assuming that probabilities and statistics is counted as "advanced math" (which it's not in most other countries), which source do you believe most of  these students got their FALSE information from (these scores are LOWER than if they'd just guessed):



1) Wikipedia?

2) American textbooks?



If you believe even TEN PERCENT of them got their information from text books, then exactly what do you believe is wrong with these books?







"American girls" and "American boys" are races? No wonder you have difficulties understanding the difference between correlation and causation. Apparently you are definitionally challenged. That might explain why you are incapable of constructing a cogent, logical argument. I suggest you seek remediation.


Title: Re: assuming too much math knowledge?
Post by: wet_blanket on September 21, 2010, 04:07:53 PM

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.






I'm not in the business of defining or redefining terms. I accept the term "correlation" as it's defined in every math book you can get your hands on.  Yes, lots of data correlates without ever even implying cause.  But when an education system says "we can't do our jobs without more money", and we discover that, city to city, state to state, and country, almost without exception, there's an INVERSE correlation between test scores and dollars per student, then certainly we deserve to know why, eh?


Citation?

Citation? Why don't you cite a source which disagrees with the way this word has been used here?  Because you can't?


I think the request for a citation was for your claim that within cities, states, and countries, "almost without exception" increasing speending on education per student is related to lower test scores.


Title: Re: assuming too much math knowledge?
Post by: anthroid on September 21, 2010, 09:20:07 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.


Title: Re: assuming too much math knowledge?
Post by: kraken on September 22, 2010, 06:36:00 AM


Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


No.  It doesn't.  Magnitude has nothing to do with causation.  Correlation is one of three criteria generally accepted for causation.  Do you know the other two? 


Title: Re: assuming too much math knowledge?
Post by: zharkov on September 22, 2010, 07:33:55 AM

Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


Causation is a property of science, not of mathematics.





Sure.  The math only proves that the data correlates.


No, the math shows that the data are correlated.  Proof only occurs within mathematics, not in science.  In science, we examine and create theories, and test hypotheses.  We never prove anything.

You seem to have done some exploratory data analysis (EDA) and come up with a hunch about underlying relationships or causation about your data sets.  Fine.  If you were really interested in the topic, your next step would be a trip to the library to get up to speed with the journal lit on the topic.   Then you would be closer to a position to do hypothesis testing and so on.  Continuing to do EDA over and over in an attempt to show some causation is a misunderstanding of how math and science work.

 








Title: Re: assuming too much math knowledge?
Post by: tinyzombie on September 22, 2010, 08:49:50 AM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

I love Anthroid.


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 22, 2010, 09:41:19 AM
Benami, I have ___ pieces of advice for you.

1.  Quit quoting TIMSS to prove something that TIMSS doesn't prove. TIMSS, as a comparison between nations, uses a fundamentally flawed design that anyone who has passed a reasonably rigorous statistical design course can see. Therefore, drawing conclusions about distinctions between nations using TIMSS is a fool's game.

2.  Take an introductory statistics course so that you understand the BASICS of experimental design. The fact that you don't understand anything about it indicates that you don't live in STEMLand or even in SocialScienceLand, while I know that Polly does live in STEMLand with several others of us.

3.  While you're taking the introductory statistics course, pay close attention to the sections on correlation. Trust me on this: you don't understand it AT ALL.

4.  Try paying attention to the social scientists the next time you talk to them. You are trying to play a game that is unacceptable to most of us, because the social science behind your game is WRONG.

Once you are done with these, feel free to come back and discuss these ideas with us again. However, don't come back until you have completed these assignments. Otherwise, you should be ignored.

Oh, and you still haven't told us your qualifications to pass judgment on the forumites here who have demonstrated over the years that they understand the statistics that you don't.


Title: Re: assuming too much math knowledge?
Post by: anthroid on September 22, 2010, 09:47:57 AM
Benami, I have ___ pieces of advice for you.

1.  Quit quoting TIMSS to prove something that TIMSS doesn't prove. TIMSS, as a comparison between nations, uses a fundamentally flawed design that anyone who has passed a reasonably rigorous statistical design course can see. Therefore, drawing conclusions about distinctions between nations using TIMSS is a fool's game.

2.  Take an introductory statistics course so that you understand the BASICS of experimental design. The fact that you don't understand anything about it indicates that you don't live in STEMLand or even in SocialScienceLand, while I know that Polly does live in STEMLand with several others of us.

3.  While you're taking the introductory statistics course, pay close attention to the sections on correlation. Trust me on this: you don't understand it AT ALL.

4.  Try paying attention to the social scientists the next time you talk to them. You are trying to play a game that is unacceptable to most of us, because the social science behind your game is WRONG.

Once you are done with these, feel free to come back and discuss these ideas with us again. However, don't come back until you have completed these assignments. Otherwise, you should be ignored.

Oh, and you still haven't told us your qualifications to pass judgment on the forumites here who have demonstrated over the years that they understand the statistics that you don't.

I love Cgfunmathguy.


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 22, 2010, 09:54:47 AM
I love Cgfunmathguy.
Thank you, Anthroid. You do realize that goes both ways, right? ;-)


Title: Re: assuming too much math knowledge?
Post by: benami on September 22, 2010, 01:50:07 PM
Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.




If you rely on Wikipedia as your source for mathematics principles (or scientific facts of any kind, or actually for ANY information), you're in a HEAP of trouble.  Not even most of our textbooks are accurate, but they're a lightyear ahead of Wikipedia, particularly when it comes to statistics.

That's the LAST source you should cite as a reference for probabilities and statistics (a subject which a vast majority of our students scored lower on than if they'd just GUESSED on almost all the questions).


I believe conjugate pointed you toward Wikipedia in the hope that it was written at an elementary enough level that even you might be capable of comprehending it.



Here's a good question for you.  Did you know that American girls scored 426 in advanced math, and that no other race, sex, or country scored lower?  Did you know that American boys scored 457 and no other race or country scored lower, and only girls in Austria and the Czech Republic scored lower?  Did you know that Russian and French and and Swiss boys scored 559 or higher, which is  102 points higher than our boys and 133 points higher than our girls, and this doesn't even include the highest scoring Asian nations in the 8th grade test, like Japan, Korea, and Singapore?  Assuming that probabilities and statistics is counted as "advanced math" (which it's not in most other countries), which source do you believe most of  these students got their FALSE information from (these scores are LOWER than if they'd just guessed):



1) Wikipedia?

2) American textbooks?



If you believe even TEN PERCENT of them got their information from text books, then exactly what do you believe is wrong with these books?







"American girls" and "American boys" are races? No wonder you have difficulties understanding the difference between correlation and causation. Apparently you are definitionally challenged. That might explain why you are incapable of constructing a cogent, logical argument. I suggest you seek remediation.

Are you trying to prove that you can't read either?

"no other race, sex, or country scored lower"


No, "we" are a country, not a race.  But Russians and Germans and most other European countries consider themselves to be not just a country, but a race.  For example 3.3% of the German population (and of those now taking TIMSS in Germany) are Turks, not Germans, even though they now live in Germany.  Ditto for Ireland where 7% of those taking PISA are Poles who will never be considered of the Irish race.


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 22, 2010, 02:00:20 PM
You obviously haven't completed your assignments.


Title: Re: assuming too much math knowledge?
Post by: benami on September 22, 2010, 02:08:49 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".

"Racist"?  What does that mean?  If you look up the definition in the OED, you'll discover that YOU are the racist.

Agreed, The Bell Curve was discredited: it was written in such a politically correct manner as to be almost meaningless.  Some of the data was useful, but much of it was fabricated to make certain races appear  to be more intelligent than the international test scores and driving safety records indicate.





Title: Re: assuming too much math knowledge?
Post by: benami on September 22, 2010, 02:15:21 PM

Ah ha!  I get the problem now: people have been saying "there is no correlation" as shorthand for "the correlation observed can be better explained by other factors than by a causal relationship.  I will concede that you, Benami, can probably find data suggesting a correlation between any two or more sets of variables, such as the color of cars in Taiwan and the number of diet cokes consumed daily in Tajikistan, if you will concede that explanations of that correlation include chance, bias, and confounding, along with an actual relationship.






I'm not in the business of defining or redefining terms. I accept the term "correlation" as it's defined in every math book you can get your hands on.  Yes, lots of data correlates without ever even implying cause.  But when an education system says "we can't do our jobs without more money", and we discover that, city to city, state to state, and country, almost without exception, there's an INVERSE correlation between test scores and dollars per student, then certainly we deserve to know why, eh?


Citation?

Citation? Why don't you cite a source which disagrees with the way this word has been used here?  Because you can't?


I think the request for a citation was for your claim that within cities, states, and countries, "almost without exception" increasing speending on education per student is related to lower test scores.

ok.

The following is from the perspective of a California voter who kept hearing that the only way to improve our schools was to spend ever more for education.  Well, we kept on doing that only to end up almost dead last in the nation in SAT and NAEP scores, as well as in the world in TIMSS scores.  Many of the following links are missing or broken, so let me know if you want the original tables.  The following is what the data from the tables tells us.

In 1973 California scored 75 SAT verbal points and 81 SAT math points (156 points total) lower than North Dakota even though we spent more than 26% more per student for education than North Dakota ($867 vs. $690).  So we increased education spending almost 9 fold by 2005 (to $7,673 per student) only to end up in 1995 scoring 98 SAT verbal and 107 SAT math points (205 total points) behind North Dakota.  During this time, the entire nation was on an education spending spree, having in 1994 spent 41% more per student for secondary education than Japan ($5,993 vs. $4,227) and more than four times as much as Korea ($5,993 vs. $1,296), and for primary education, 11% more than Japan ($4,669 vs. $4,186), and 2 1/2 times as much as Korea ($4,669 vs. $1,893).

SOURCE: College Entrance Examination Board, "College-Bound Seniors: 1995 Profile of SAT Program Test Takers," Copyright @ 1995 by the College


We thought at the time that we were getting something for our money, until TIMSS came along and proved that at the EIGHTH GRADE level we were already more than 105 TIMSS math points behind those countries.  On top of that, we outspent the highest scoring European nation, the Netherlands (who scored 41 points higher than us in 8th grade math, but by 12th grade 99 points higher in math literacy and 78 points higher in science) by 57% in primary education ($4,669 vs. $2,996), and 51% in secondary education ($5,993 vs. $3,956), another indicator that it's something besides money that improves education.

http://nces.ed.gov/pubs98/condition98/c9820d05.html

States which did much worse in education were those who spent MORE for education. In 2004, DC spent 69% more per student ($12,959 vs. $7,673), New Jersey spent 71% more ($13,338), Rhode Island spent 41% more ($11,078), and New York spent 65% more ($12,638), yet managed to score even lower than us in SAT (45, 4, 14, and 10 points lower, respectively).  Money's not the answer.

NAEP math scores are a bit more difficult to compare state to state because of the different proportions of lower scoring minority races.  It makes more sense when we confine this to a discussion of the scores of Whites, who in California do score 4 points higher than Whites in Rhode Island and New Jersey (279 vs. 275), but they score six points or more lower than Whites in Iowa, North Dakota, South Dakota, Montana, and Wisconsin, who spend the LEAST per student for education, far less than California:

http://nces.ed.gov/nationsreportcard/mathematics/results/stateavgscale-g8.asp 9/2/01

When SAT scores of Whites are compared, we see that by 2008, these states managed to increase the gap between them and states like Iowa and North Dakota.  Whites in Iowa now score 190 points higher than Whites in Rhode Island, 172 points higher than Whites in New Jersey, and 170 points higher than Whites in New York:

http://professionals.collegeboard.com/profdownload/Iowa_CBS_08.pdf

How exactly did they accomplish that?  You guessed it--they increased education spending in just FOUR YEARS by more than 30%, to a whopping $17,620 per student in New Jersey, $16,794 in New York, $14,459 in Rhode Island, and $16,353 in DC:

http://nces.ed.gov/pubs2006/Expenditures/tables/table_3.asp

http://nces.ed.gov/pubs2001/digest/tables/XLS/Tab168.xls

http://nces.ed.gov/pubs2010/expenditures/tables/table_03.asp

It's simply not true that these test scores and education spending data, and correlations between them, are "meaningless".  These are dramatic exceptions to the public misperception that increasing education spending improves something.  Those who claim this have no clue about what they're talking about, are in a chronic state of denial, or are just plain too stupid to understand what all this means anyway.


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 22, 2010, 02:15:21 PM
Wow!! You need to quit digging, Benami. You obviously don't understand anything about which you're talking.

Seriously, now. What are your qualifications? (I'm actually afraid to find out the answer.)


Title: Re: assuming too much math knowledge?
Post by: tinyzombie on September 22, 2010, 02:17:36 PM
Fiiiiioooooonnnnnaaaaaaaa!


Title: Re: assuming too much math knowledge?
Post by: anthroid on September 22, 2010, 02:19:24 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".

"Racist"?  What does that mean?  If you look up the definition in the OED, you'll discover that YOU are the racist.

Agreed, The Bell Curve was discredited: it was written in such a politically correct manner as to be almost meaningless.  Some of the data was useful, but much of it was fabricated to make certain races appear  to be more intelligent than the international test scores and driving safety records indicate.


You haven't read my post.  Indeed, I doubt you've ever read anything of a scholarly nature, based on how you dump data as though it makes sense.

"Race" is a cultural category and hardly fixed at that.  To argue that Hispanic is a "race," which people like you, apparently, believe is a biological category, is flat out wrong.  Wrong, wrong, wrong.  There is no "Hispanic" "race."  It is a linguistic category.  And if you think the Census Bureau knows more about biological classification than those who actually study it--not you, apparently--then you're wrong, wrong, wrong.

And if you think The Bell Curve was politically correct, then you are far over on the racist side.  Way far over there.  The Bell Curve was poorly written and even more poorly researched.  Its arguments were incomplete, based on incredibly incorrect assumptions about ethnicity and class, almost identical to the huge mistakes you're making in your posts when you aren't posting random lists of numbers.


Title: Re: assuming too much math knowledge?
Post by: benami on September 22, 2010, 03:18:01 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".

"Racist"?  What does that mean?  If you look up the definition in the OED, you'll discover that YOU are the racist.

Agreed, The Bell Curve was discredited: it was written in such a politically correct manner as to be almost meaningless.  Some of the data was useful, but much of it was fabricated to make certain races appear  to be more intelligent than the international test scores and driving safety records indicate.


You haven't read my post.  Indeed, I doubt you've ever read anything of a scholarly nature, based on how you dump data as though it makes sense.

"Race" is a cultural category and hardly fixed at that.  To argue that Hispanic is a "race," which people like you, apparently, believe is a biological category, is flat out wrong.  Wrong, wrong, wrong.  There is no "Hispanic" "race."  It is a linguistic category.  And if you think the Census Bureau knows more about biological classification than those who actually study it--not you, apparently--then you're wrong, wrong, wrong.

And if you think The Bell Curve was politically correct, then you are far over on the racist side.  Way far over there.  The Bell Curve was poorly written and even more poorly researched.  Its arguments were incomplete, based on incredibly incorrect assumptions about ethnicity and class, almost identical to the huge mistakes you're making in your posts when you aren't posting random lists of numbers.

I did read your post.  The only point I'm making is that I disagree with it 100%.  And as I said, what you say or think, no matter how many slurs you manage to throw in, has zero effect on me and mine.

It's interesting that you're now redefining racists to include those who point out the huge 200 SAT point difference from state to state WITHIN the White Race, though.  Can you please point me to the dictionary which makes THAT claim?

This is not MY data.  This is straight from the College Board, the US Census Bureau, and goes all the way back to 3,000 years before Jesus.  If you think they are racists, or are in error for using the term race, talk to them, not me.


Title: Re: assuming too much math knowledge?
Post by: benami on September 22, 2010, 03:19:32 PM
Wow!! You need to quit digging, Benami. You obviously don't understand anything about which you're talking.

Seriously, now. What are your qualifications? (I'm actually afraid to find out the answer.)

Do you think there ought to be some kind of correlation between the amount of money we spend for education and higher test scores?  What kind of correlation would you expect?  An inverse correlation?

At the time we participated in 12th grade TIMSS, wherein we scored dead last in 16 of 32 TIMSS subjects, we spent four times as much for education as Hungary whose boys scored 19 points higher than our boys, 14% more than Austria who scored 74 points higher, 2 1/2 times as much as the Czech Republic who scored 22 points higher, 21% more than Italy who scored 24 points higher, 39% more than Germany who scored 43 points higher, 8% more than France who scored 78 points higher, 4% more than Sweden who scored 107 points higher, and twice as much as Spain who didn't take 12th grade TIMSS but scored only 13 points lower in the 8th grade.

From your obviously erudite perspective, cgfunmathguy, does it sound to you like spending more for education is the answer?  Or is it the problem?

What kind of correlation do you see in this data?  What do you EXPECT to see?



Title: Re: assuming too much math knowledge?
Post by: mouseman on September 22, 2010, 03:37:48 PM


Am I the only one that thinks that there is a very lonely bridge out there? 


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 22, 2010, 06:30:45 PM
And if you think The Bell Curve was politically correct, then you are far over on the racist side.
He likes the part of the Bell Curve that says that blacks are genetically inferior, but not the part which says that Jews are superior.  Adolf faced much the same predicament in Mein Kampf (his arguments for why Jewish intelligence is not 'real' intelligence are very tortured), and the predicament has plagued all his acolytes, down to and including Benami. - DvF


Title: Re: assuming too much math knowledge?
Post by: benami on September 22, 2010, 07:03:20 PM
And if you think The Bell Curve was politically correct, then you are far over on the racist side.
He likes the part of the Bell Curve that says that blacks are genetically inferior, but not the part which says that Jews are superior.  Adolf faced much the same predicament in Mein Kampf (his arguments for why Jewish intelligence is not 'real' intelligence are very tortured), and the predicament has plagued all his acolytes, down to and including Benami. - DvF


Absolutely FALSE on every point.

There was NOTHING in The Bell Curve that said anything new about blacks.  Every single point they made about blacks was published thousands of times before they wrote this book.

What REALLY discredits this book was for them to claim that the *average* IQ of Jews was 117.  NO race has an AVERAGE IQ almost two standard deviations higher than East Asians, and you know it.  This is a ridiculous and impossible claim.

Claiming any American is an acolyte of Hitler, who was responsible for the death or disappearance of 264 million fellow Christians around the world, is also absurd, not to mention an insult, not to mention inflammatory.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 22, 2010, 07:17:41 PM
I think your first two points fairly clearly support my assertion.

As to the third, by all means report me to the moderators.  I would love an excuse to direct them to your websites and blogs, where you freely refer to Jews as "k***s" and African-Americans as "N*****s" and (for example) refer to these two groups as "animals at best, or beasts".  - DvF


Title: Re: assuming too much math knowledge?
Post by: benami on September 22, 2010, 07:21:47 PM


Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


No.  It doesn't.  Magnitude has nothing to do with causation.  Correlation is one of three criteria generally accepted for causation.  Do you know the other two? 

If the Pearson Coefficient for the correlation between state to state SAT verbal and SAT math scores was zero, then it would have a zero probability of correlating.  If the Pearson Coefficient was 1, it would have a 100% probability of correlating.  That says nothing about WHY the data correlates, but you cannot deny these two facts.

So it's not true that "Magnitude has nothing to do with causation" because regardless of the cause, if the Pearson Coefficient is zero there is NO relationship to any cause.  For the Pearson Coefficient to be 1 for 50 separate but closely associated data points like this, there would have to be a very distinct and obvious and easily identifiable cause.

What do you believe is the obvious reason that so many of the states with the lowest SAT math scores are the same states with the lowest SAT verbal scores?


Title: Re: assuming too much math knowledge?
Post by: anthroid on September 22, 2010, 07:22:07 PM
And if you think The Bell Curve was politically correct, then you are far over on the racist side.
He likes the part of the Bell Curve that says that blacks are genetically inferior, but not the part which says that Jews are superior.  Adolf faced much the same predicament in Mein Kampf (his arguments for why Jewish intelligence is not 'real' intelligence are very tortured), and the predicament has plagued all his acolytes, down to and including Benami. - DvF


Absolutely FALSE on every point.

There was NOTHING in The Bell Curve that said anything new about blacks.  Every single point they made about blacks was published thousands of times before they wrote this book.

What REALLY discredits this book was for them to claim that the *average* IQ of Jews was 117.  NO race has an AVERAGE IQ almost two standard deviations higher than East Asians, and you know it.  This is a ridiculous and impossible claim.

Claiming any American is an acolyte of Hitler, who was responsible for the death or disappearance of 264 million fellow Christians around the world, is also absurd, not to mention an insult, not to mention inflammatory.


Oh for pity's sake.  You say "the blacks" (charming, by the way, to put "black" in lower case and "White" in upper case--you are telegraphing your attitudes big time) as though this is an isolated grouping in the US.  Wrong, wrong, wrong.  The history of slavery tells us that African-Americans are not that isolated gene pool that you, and your little friends, keep claiming that it is.  That's why Murray and Hernnstein's initial hypothesis was completely flawed from the outset.  You just don't understand the nuance.  

Let's do a thought experiment.  Would you agree, in your own...er....unique way that the Irish are "white" in the same way that the English are "white"?  I'm going to assume that you will say yes.  How, then, do you explain that the Irish score 15 points lower on IQ tests when newly immigrated to England than the English do?  This is exactly the same IQ point difference that Hernnstein and Murray say is so significant between African-Americans and European-Americans, and what they say is "racial."  The argument is, of course, complete bullsh!t.  It has to do with class, discrimination, and SES far more than their very inaccurate assumptions (and, thus, yours) about "race" as a real category rather than acknowledging the very real fact that the "one-drop" rule means that people whose ancestors are largely European-Americans are still identified by people like you as "black" belong in more complex categories.  President Obama is a good example as someone who is European-American as much as he is African-American, but in this country, he has to be pigeonholed, quite inaccurately, as "Black."

By the way, unlike you, I did not call YOU racist.  I called your ideas and your posts "racist."  Personal name-calling is against the rules in these fora, though of course ideas can and should be attacked.  You have called me a racist, so I will be reporting you to the moderators.  Mainly, though, you have no idea what you're talking about and you clearly are in way over your head.  


Title: Re: assuming too much math knowledge?
Post by: janewales on September 22, 2010, 07:58:28 PM

I think it's time to stop, folks. It isn't possible to reason with someone like this. You've all shown the patience of Job in trying, again and again, to explain the flaws in his posts; you make one proud to be a member of the teaching profession. I accept the argument that one must counter ignorance and prejudice head-on, but it's clear that every response to benami simply leads to further outbursts, effectively giving him a platform for his irrational antics. So, I'm out of here; perhaps if we all leave, he will too.


Title: Re: assuming too much math knowledge?
Post by: anthroid on September 22, 2010, 09:02:31 PM

I think it's time to stop, folks. It isn't possible to reason with someone like this. You've all shown the patience of Job in trying, again and again, to explain the flaws in his posts; you make one proud to be a member of the teaching profession. I accept the argument that one must counter ignorance and prejudice head-on, but it's clear that every response to benami simply leads to further outbursts, effectively giving him a platform for his irrational antics. So, I'm out of here; perhaps if we all leave, he will too.

Yeah.  I was late to the game and I'm hardly breaking a sweat.  Not worth the tiny effort.  Adolph has the epic fail. 

Buh-bye.

ETA:  I did report him to the mods, however, for name-calling.


Title: Re: assuming too much math knowledge?
Post by: ptarmigan on September 22, 2010, 09:33:55 PM
And if you think The Bell Curve was politically correct, then you are far over on the racist side.
He likes the part of the Bell Curve that says that blacks are genetically inferior, but not the part which says that Jews are superior.  Adolf faced much the same predicament in Mein Kampf (his arguments for why Jewish intelligence is not 'real' intelligence are very tortured), and the predicament has plagued all his acolytes, down to and including Benami. - DvF


Absolutely FALSE on every point.

There was NOTHING in The Bell Curve that said anything new about blacks.  Every single point they made about blacks was published thousands of times before they wrote this book.

What REALLY discredits this book was for them to claim that the *average* IQ of Jews was 117.  NO race has an AVERAGE IQ almost two standard deviations higher than East Asians, and you know it.  This is a ridiculous and impossible claim.

Claiming any American is an acolyte of Hitler, who was responsible for the death or disappearance of 264 million fellow Christians around the world, is also absurd, not to mention an insult, not to mention inflammatory.


Wow.  I really didn't expect you to confirm DvF's assertions so readily and completely.


Title: Re: assuming too much math knowledge?
Post by: kiana on September 22, 2010, 09:47:15 PM
Wow.  I really didn't expect you to confirm DvF's assertions so readily and completely.

Really? DvF quoted his websites earlier in the thread -- what he says here is but a pallid imitation of what he says on his personal websites and elsewhere on the internet.

I think people attempting to reason are doing so not because they hope to convince John himself, but rather because of others who read and may say 'hmm, he is way overboard, but x could be a valid point'. JMO.


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 11:36:58 AM
I think your first two points fairly clearly support my assertion.

As to the third, by all means report me to the moderators.  I would love an excuse to direct them to your websites and blogs, where you freely refer to Jews as "k***s" and African-Americans as "N*****s" and (for example) refer to these two groups as "animals at best, or beasts".  - DvF


You whine like a little girl.

Then again, I would never permit my little girl to whine like this.


Title: Re: assuming too much math knowledge?
Post by: tinyzombie on September 23, 2010, 11:38:44 AM
You have a child?

Dear G-d.


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 11:45:26 AM
And if you think The Bell Curve was politically correct, then you are far over on the racist side.
He likes the part of the Bell Curve that says that blacks are genetically inferior, but not the part which says that Jews are superior.  Adolf faced much the same predicament in Mein Kampf (his arguments for why Jewish intelligence is not 'real' intelligence are very tortured), and the predicament has plagued all his acolytes, down to and including Benami. - DvF


Absolutely FALSE on every point.

There was NOTHING in The Bell Curve that said anything new about blacks.  Every single point they made about blacks was published thousands of times before they wrote this book.

What REALLY discredits this book was for them to claim that the *average* IQ of Jews was 117.  NO race has an AVERAGE IQ almost two standard deviations higher than East Asians, and you know it.  This is a ridiculous and impossible claim.

Claiming any American is an acolyte of Hitler, who was responsible for the death or disappearance of 264 million fellow Christians around the world, is also absurd, not to mention an insult, not to mention inflammatory.


Oh for pity's sake.  You say "the blacks" (charming, by the way, to put "black" in lower case and "White" in upper case--you are telegraphing your attitudes big time) as though this is an isolated grouping in the US.  Wrong, wrong, wrong.  The history of slavery tells us that African-Americans are not that isolated gene pool that you, and your little friends, keep claiming that it is.  That's why Murray and Hernnstein's initial hypothesis was completely flawed from the outset.  You just don't understand the nuance.  

Let's do a thought experiment.  Would you agree, in your own...er....unique way that the Irish are "white" in the same way that the English are "white"?  I'm going to assume that you will say yes.  How, then, do you explain that the Irish score 15 points lower on IQ tests when newly immigrated to England than the English do?  This is exactly the same IQ point difference that Hernnstein and Murray say is so significant between African-Americans and European-Americans, and what they say is "racial."  The argument is, of course, complete bullsh!t.  It has to do with class, discrimination, and SES far more than their very inaccurate assumptions (and, thus, yours) about "race" as a real category rather than acknowledging the very real fact that the "one-drop" rule means that people whose ancestors are largely European-Americans are still identified by people like you as "black" belong in more complex categories.  President Obama is a good example as someone who is European-American as much as he is African-American, but in this country, he has to be pigeonholed, quite inaccurately, as "Black."

By the way, unlike you, I did not call YOU racist.  I called your ideas and your posts "racist."  Personal name-calling is against the rules in these fora, though of course ideas can and should be attacked.  You have called me a racist, so I will be reporting you to the moderators.  Mainly, though, you have no idea what you're talking about and you clearly are in way over your head.  

Had you bothered to look up the OED definition of racist, you would have understood that it's not a personal attack to call you a racist.  And while you intended it to be a personal attack to call my ideas (but not me) a racist, I will stick by the OED definition and consider it a compliment.

In ten years of living in and growing up in and being educated in Asia, I never met a single Korean, or Japanese, or Chinese, or Vietnamese, who might agree with you that their race is a mere social construct.  The five thousand + year old Korean history is that Koreans, and nobody else, are descendant of Dangun whose pyramid and burial place in North Korea is currently being excavated.  If you tried to convince Koreans they're not a race, they'd throw you in the looney bin.

The Korean word for race happens to match one of OUR (the real and current English word) following two definitions:

1. [L. radix and radius having the same original. This word coincides in origin with rod, ray, radiate, &c.]

2. The lineage of a family, or continued series of descendants from a parent who is called the stock. [It] is the series of descendants indefinitely.


Which do you believe is correct?  Both?

Which of these do you believe is the current correct concept of race?

Is there any difference between the two?  Are they identical?  Or is there an important difference between the two?  Do you have a definition of race which even implies social construct, or disputes the Korean concept of race?

By this definition, aren't both the English and Irish different races?


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 11:57:43 AM

2.  Take an introductory statistics course so that you understand the BASICS of experimental design. The fact that you don't understand anything about it indicates that you don't live in STEMLand or even in SocialScienceLand, while I know that Polly does live in STEMLand with several others of us.



So you agree with Polly that there is a study which *proves* that there is no correlation between psych ward admissions and full moons?

But you also agree with Polly that this putative study is also *proof* that there is NO correlation between, say, SAT scores and incomes?

AND you agree with Polly that there IS a correlation between SAT scores socionomic status?

Is that your position?  Do you think that is the position of this entire forum?  Do you think nobody on this forum disagrees with this position?


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 23, 2010, 12:16:22 PM

2.  Take an introductory statistics course so that you understand the BASICS of experimental design. The fact that you don't understand anything about it indicates that you don't live in STEMLand or even in SocialScienceLand, while I know that Polly does live in STEMLand with several others of us.



So you agree with Polly that there is a study which *proves* that there is no correlation between psych ward admissions and full moons?

But you also agree with Polly that this putative study is also *proof* that there is NO correlation between, say, SAT scores and incomes?

AND you agree with Polly that there IS a correlation between SAT scores socionomic status?

Is that your position?  Do you think that is the position of this entire forum?  Do you think nobody on this forum disagrees with this position?

The problem you are having is that you are assuming that correlation means causation. The fact is that, even if there are such correlations (I'll use the mathematically correct definition here), that correlation means nothing. Full moons do not "cause" psych ward admissions, and SAT scores do not "cause" incomes to rise. Someone (I forget who it was) tried to show this with the ice cream example. The studies have been done to show a correlation between ice cream sales and deaths by drowning. Would you conclude that drowning is "caused" by ice cream sales? I wouldn't, and neither would anyone else who truly understood statistics. Unfortunately, that doesn't seem to include you.


Title: Re: assuming too much math knowledge?
Post by: duchess_of_malfi on September 23, 2010, 01:13:26 PM
Since we are here and don't seem to be getting anywhere, does anyone have additional correlation vs. causation examples to use in class?

I use the ice-cream example but with shark attacks.  Drowning would be a better variable.  (This is from p. 18 of this thread.  I'm still curious to know the field of "Benami" but don't want to guess for fear of giving offense.)


Following your logic, we would expect these interpretations: 

France has a high crime rate and high math scores.  Therefore, math causes crime...

Let's not forget some of the classics:
Living together before marriage will increase the likelihood that you'll get divorced!
Eating ice cream causes shark attacks!
An individual's height increasing causes his or her vocabulary to increase!
My dog's barking scares away the intruder who puts things in my mailbox.  She has a 100% success rate!

Tell me, do you teach at the college level?  What topic?


Title: Re: assuming too much math knowledge?
Post by: slinger on September 23, 2010, 01:19:35 PM
Other than the ice cream/drowning I know of several-

Nightlights & Myopia
Some parents use nightlights in their kids bedrooms.  These kids grow up to have myopia (nearsightedness).

Soap operas & anorexia
Teenage girls who watch soap operas regularly are more likely to develop anorexia

Shoes & Headaches
College students who sleep with their shoes on get more headaches.

And of course, the old favorite of pirates and global warming.

I use these regularly as examples in my course; I don't remember where I got them from anymore.  It's fun getting the students to come up with reasonable explanations for these phenomena, and then develop an experimental design.


All that said, you're not going to win this argument. 


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 01:23:08 PM

2.  Take an introductory statistics course so that you understand the BASICS of experimental design. The fact that you don't understand anything about it indicates that you don't live in STEMLand or even in SocialScienceLand, while I know that Polly does live in STEMLand with several others of us.



So you agree with Polly that there is a study which *proves* that there is no correlation between psych ward admissions and full moons?

But you also agree with Polly that this putative study is also *proof* that there is NO correlation between, say, SAT scores and incomes?

AND you agree with Polly that there IS a correlation between SAT scores socionomic status?

Is that your position?  Do you think that is the position of this entire forum?  Do you think nobody on this forum disagrees with this position?

The problem you are having is that you are assuming that correlation means causation. The fact is that, even if there are such correlations (I'll use the mathematically correct definition here), that correlation means nothing. Full moons do not "cause" psych ward admissions, and SAT scores do not "cause" incomes to rise. Someone (I forget who it was) tried to show this with the ice cream example. The studies have been done to show a correlation between ice cream sales and deaths by drowning. Would you conclude that drowning is "caused" by ice cream sales? I wouldn't, and neither would anyone else who truly understood statistics. Unfortunately, that doesn't seem to include you.

So let's make your position clear.

If there IS a strong correlation between SAT math score data and income data by major, this has nothing to do with the CAUSE for why some incomes are higher than others?

In other words, even if each $110 increase in annual incomes follows a one point increase in SAT math scores, the increase in scores is completely independent from and has nothing to do with the average math skills of each college major?

Here's the data I'm referring to.  It has a Pearson Coefficient of 0.9.

Do you agree with Polly that this says nothing about causation?



Major   SAT Math   Annual Income
Math   607   $62,000
Physics   574   $50,000
Engineering   553   $49,800
Biology   480   $36,300
Computer & Info Tech   479   $46,300
Humanities/writers   478   $44,000
Sociology   464   $35,000
Education   446   $37,900




Title: Re: assuming too much math knowledge?
Post by: conjugate on September 23, 2010, 01:25:09 PM
The problem you are having is that you are assuming that correlation means causation. The fact is that, even if there are such correlations (I'll use the mathematically correct definition here), that correlation means nothing. Full moons do not "cause" psych ward admissions, and SAT scores do not "cause" incomes to rise. Someone (I forget who it was) tried to show this with the ice cream example. The studies have been done to show a correlation between ice cream sales and deaths by drowning. Would you conclude that drowning is "caused" by ice cream sales? I wouldn't, and neither would anyone else who truly understood statistics. Unfortunately, that doesn't seem to include you.

That "someone" was me.  I pointed Benami to a couple of web pages to explain the difference.  Unfortunately, he responded with an ad hominem dismissal of Wikipedia rather than address the argument.  However, while we're on the subject:

Does such a high degree of correlation imply causation?  Of course.  There's no question about it.


A correlation, no matter how high, does not imply causation.  That you misunderstand this basic fact shows that you have no business trying to pretend to understand the issues you're talking about.  Consider the very strong correlation between ice cream sales and drowning deaths.  Better yet, read the Wikipedia article (http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation) and perhaps this other page (http://stats.org/in_depth/faq/causation_correlation.htm) from Stats.org to get a fair idea of the difference.

Finally, I still don't know what you think we could do about it in any case.  I mean, you spew statistics at us, chide us because we aren't making as many suggestions as the other "forums" (your word), and still haven't said what we should do about any of it.  You didn't give a coherent answer in your other ID either, so I suspect the sock puppet you're now using will be similarly unresponsive.

If these other forums are giving you so many possibilities, why don't you go bother them some more and leave us alone?



I'll re-emphasize the underlined portions to point out that (1) my prediction of unresponsiveness to "what can we do about it" is fulfilled, and (2) why doesn't Benami go elsewhere?

On preview: Hi, Duchess.  I think the Stats.com site I referenced above has a few others.  Perhaps something like this:  Owning big-screen TVs is negatively correlated with rates of malnutrition.  Therefore, should we buy big-screen TVs for poor people so as to prevent malnutrition?  That's the best I can come up with off the top of my head, and I don't know how strong the correlation might be.

A colleague has pointed me to this site:

Purdue University Spurious Correlation Contest. (http://www.morris.umn.edu/~sungurea/introstat/public/instruction/causation.html)

Modified to add: Apparently that takes you to the 1998 contest; I don't know why.  Try this page (http://junkfoodscience.blogspot.com/2008/08/lice-and-good-health-and-other-spurious.html) as well.


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 01:34:41 PM
Other than the ice cream/drowning I know of several-

Nightlights & Myopia
Some parents use nightlights in their kids bedrooms.  These kids grow up to have myopia (nearsightedness).

Soap operas & anorexia
Teenage girls who watch soap operas regularly are more likely to develop anorexia

Shoes & Headaches
College students who sleep with their shoes on get more headaches.

And of course, the old favorite of pirates and global warming.

I use these regularly as examples in my course; I don't remember where I got them from anymore.  It's fun getting the students to come up with reasonable explanations for these phenomena, and then develop an experimental design.


All that said, you're not going to win this argument. 

Here's another one for you to use in the classroom.

Education spending per pupil and education outcome.

And another one:

Classroom size and test scores (which actually have a strong inverse correlation).




Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 23, 2010, 01:43:23 PM

2.  Take an introductory statistics course so that you understand the BASICS of experimental design. The fact that you don't understand anything about it indicates that you don't live in STEMLand or even in SocialScienceLand, while I know that Polly does live in STEMLand with several others of us.



So you agree with Polly that there is a study which *proves* that there is no correlation between psych ward admissions and full moons?

But you also agree with Polly that this putative study is also *proof* that there is NO correlation between, say, SAT scores and incomes?

AND you agree with Polly that there IS a correlation between SAT scores socionomic status?

Is that your position?  Do you think that is the position of this entire forum?  Do you think nobody on this forum disagrees with this position?

The problem you are having is that you are assuming that correlation means causation. The fact is that, even if there are such correlations (I'll use the mathematically correct definition here), that correlation means nothing. Full moons do not "cause" psych ward admissions, and SAT scores do not "cause" incomes to rise. Someone (I forget who it was) tried to show this with the ice cream example. The studies have been done to show a correlation between ice cream sales and deaths by drowning. Would you conclude that drowning is "caused" by ice cream sales? I wouldn't, and neither would anyone else who truly understood statistics. Unfortunately, that doesn't seem to include you.

So let's make your position clear.

If there IS a strong correlation between SAT math score data and income data by major, this has nothing to do with the CAUSE for why some incomes are higher than others?

In other words, even if each $110 increase in annual incomes follows a one point increase in SAT math scores, the increase in scores is completely independent from and has nothing to do with the average math skills of each college major?

Here's the data I'm referring to.  It has a Pearson Coefficient of 0.9.

Do you agree with Polly that this says nothing about causation?



Major   SAT Math   Annual Income
Math   607   $62,000
Physics   574   $50,000
Engineering   553   $49,800
Biology   480   $36,300
Computer & Info Tech   479   $46,300
Humanities/writers   478   $44,000
Sociology   464   $35,000
Education   446   $37,900



The point is that the increase in SAT score does not cause the increase in income. While the SAT math score is supposed to reflect the math skills of the person taking the test (they don't always, by the way), businesses do not pay people based on their SAT scores (I wish they did, though).

Several variables affect income, including the supply (number of people with the relevant degrees, training, etc.) of labor, the demand (how many of each type of person with the relevant degrees, training, etc. are needed) for that labor, the willingness of the business to pay that cost, and any scales set by union negotiations. In a free labor market, a high-supply, high-demand profession will have a lower average income than a low-supply, high-demand profession, while having a higher average income than a high-supply, low-demand profession.

By the way, the categories used in the data you want to use for conclusions are so broad as to be useless.

Oh, and I'm sorry I didn't remember that it was you, Conjy. My apologies.


Title: Re: assuming too much math knowledge?
Post by: duchess_of_malfi on September 23, 2010, 03:56:48 PM

Slinger and Conjugate, thank you very much for those examples, the stats.org and junkfoodscience links, and the fantastic contest.



Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 04:04:11 PM

2.  Take an introductory statistics course so that you understand the BASICS of experimental design. The fact that you don't understand anything about it indicates that you don't live in STEMLand or even in SocialScienceLand, while I know that Polly does live in STEMLand with several others of us.



So you agree with Polly that there is a study which *proves* that there is no correlation between psych ward admissions and full moons?

But you also agree with Polly that this putative study is also *proof* that there is NO correlation between, say, SAT scores and incomes?

AND you agree with Polly that there IS a correlation between SAT scores socionomic status?

Is that your position?  Do you think that is the position of this entire forum?  Do you think nobody on this forum disagrees with this position?

The problem you are having is that you are assuming that correlation means causation. The fact is that, even if there are such correlations (I'll use the mathematically correct definition here), that correlation means nothing. Full moons do not "cause" psych ward admissions, and SAT scores do not "cause" incomes to rise. Someone (I forget who it was) tried to show this with the ice cream example. The studies have been done to show a correlation between ice cream sales and deaths by drowning. Would you conclude that drowning is "caused" by ice cream sales? I wouldn't, and neither would anyone else who truly understood statistics. Unfortunately, that doesn't seem to include you.

So let's make your position clear.

If there IS a strong correlation between SAT math score data and income data by major, this has nothing to do with the CAUSE for why some incomes are higher than others?

In other words, even if each $110 increase in annual incomes follows a one point increase in SAT math scores, the increase in scores is completely independent from and has nothing to do with the average math skills of each college major?

Here's the data I'm referring to.  It has a Pearson Coefficient of 0.9.

Do you agree with Polly that this says nothing about causation?



Major   SAT Math   Annual Income
Math   607   $62,000
Physics   574   $50,000
Engineering   553   $49,800
Biology   480   $36,300
Computer & Info Tech   479   $46,300
Humanities/writers   478   $44,000
Sociology   464   $35,000
Education   446   $37,900



The point is that the increase in SAT score does not cause the increase in income. While the SAT math score is supposed to reflect the math skills of the person taking the test (they don't always, by the way), businesses do not pay people based on their SAT scores (I wish they did, though).

Several variables affect income, including the supply (number of people with the relevant degrees, training, etc.) of labor, the demand (how many of each type of person with the relevant degrees, training, etc. are needed) for that labor, the willingness of the business to pay that cost, and any scales set by union negotiations. In a free labor market, a high-supply, high-demand profession will have a lower average income than a low-supply, high-demand profession, while having a higher average income than a high-supply, low-demand profession.

By the way, the categories used in the data you want to use for conclusions are so broad as to be useless.

Oh, and I'm sorry I didn't remember that it was you, Conjy. My apologies.

Certainly it's true that "Several variables affect income, including the supply (number of people with the relevant degrees, training, etc.) of labor, the demand (how many of each type of person with the relevant degrees, training, etc. are needed) for that labor, the willingness of the business to pay that cost, and any scales set by union negotiations. In a free labor market, a high-supply, high [read: low]-demand profession will have a lower average income than a low-supply, high-demand profession, [STRIKE while having a higher average income than a high-supply, low-demand profession]", but the simple fact that the Pearson Coefficient is so high is all the proof you need that those other variables are relatively insignificant by comparison to proven math skills as demonstrated by high SAT math scores.

As you undoubtedly suspect, there was an outlier removed in order to reach that correlation.  And that outlier was economics majors whose low SAT math scores suggest that either they're overpaid by about 42% or everyone else is underpaid by about 42%.

And that's where your above [corrected] factors come into play, with the most likely being that they are a low supply, high-demand profession.  Why the low supply?  For the same reason we have such a low supply of American engineering and physics and chemistry graduates that we need to import them from China and India?


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 04:09:34 PM
Since we are here and don't seem to be getting anywhere, does anyone have additional correlation vs. causation examples to use in class?

I use the ice-cream example but with shark attacks.  Drowning would be a better variable.  (This is from p. 18 of this thread.  I'm still curious to know the field of "Benami" but don't want to guess for fear of giving offense.)


Following your logic, we would expect these interpretations: 

France has a high crime rate and high math scores.  Therefore, math causes crime...

Let's not forget some of the classics:
Living together before marriage will increase the likelihood that you'll get divorced!
Eating ice cream causes shark attacks!
An individual's height increasing causes his or her vocabulary to increase!
My dog's barking scares away the intruder who puts things in my mailbox.  She has a 100% success rate!

Tell me, do you teach at the college level?  What topic?

Would you agree that the close correlation between GRE scores and income by major (Pearson Coefficient of 0.96) has something to do with causation?



Major   GRE Score   Annual Income in Dollars
Math   720   62000
Physics   645   50000
Engineering   622   49800
Computer Science   622   46300
Education   467   37900
Sociology   434   35000


Do you believe it's at all possible that each $93 increase in average annual incomes per major has a causal relationship to a 1 point increase in GRE quantitative scores?


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 23, 2010, 04:50:33 PM
You whine like a little girl.

Oh grow up.  You're pushing 70, but you taunt like an 11-year-old.

Are you too thick to see the irony of someone who spends his day running websites and blogs which basically shout "I am a victim!" accusing someone else of being a whiner?  - DvF


Title: Re: assuming too much math knowledge?
Post by: legalgibbon on September 23, 2010, 05:04:04 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".






Some of us, because we have a full understanding of what Anthroid explained, listed our race as "human." 


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 05:47:07 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".






Some of us, because we have a full understanding of what Anthroid explained, listed our race as "human." 


Looking!  Looking!  Looking!

AH, here it is.

1,078,872 said "Korean"
another 1,122,528 said "Vietnamese"
and 1,850,31 said "Filipino"
1,678,998 said "Asian Indian"
2,432,585 said "Chinese"
796,700 said "Japanese"
140,652 said "Hawaiian"
91,029 said "Samoan"
6,826,228 said "two or more races", that's 2.4% of the total
36,419,434 said "black" to distinguish themselves from the above category
20,640,711 said "Mexican"
3,406,178 said "Puerto Rican"
1,241,685 said "Cuban"
where's that "human" category?
oh, here it is.
WAIT!
16,907,852 said "Hispanic white"
that's not it.
Do you mean the 194,552,774 who said "non-Hispanic White" are the only humans?  Is THAT what you mean?

You're not the first person to make that claim, are you?  I disagree, but it sure makes more sense than to claim that Koreans are only a social construct, doesn't' it?


Title: Re: assuming too much math knowledge?
Post by: legalgibbon on September 23, 2010, 06:18:31 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".






Some of us, because we have a full understanding of what Anthroid explained, listed our race as "human." 


Looking!  Looking!  Looking!

AH, here it is.

1,078,872 said "Korean"
another 1,122,528 said "Vietnamese"
and 1,850,31 said "Filipino"
1,678,998 said "Asian Indian"
2,432,585 said "Chinese"
796,700 said "Japanese"
140,652 said "Hawaiian"
91,029 said "Samoan"
6,826,228 said "two or more races", that's 2.4% of the total
36,419,434 said "black" to distinguish themselves from the above category
20,640,711 said "Mexican"
3,406,178 said "Puerto Rican"
1,241,685 said "Cuban"
where's that "human" category?
oh, here it is.
WAIT!
16,907,852 said "Hispanic white"
that's not it.
Do you mean the 194,552,774 who said "non-Hispanic White" are the only humans?  Is THAT what you mean?

You're not the first person to make that claim, are you?  I disagree, but it sure makes more sense than to claim that Koreans are only a social construct, doesn't' it?

What I mean is that I know of at least two people (including myself) who filled in the blank with the word "human". 


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 06:20:54 PM
The point is that the increase in SAT score does not cause the increase in income. While the SAT math score is supposed to reflect the math skills of the person taking the test (they don't always, by the way), businesses do not pay people based on their SAT scores (I wish they did, though).


IN fact businesses do pay employees based on their SAT math scores and this correlation is proof positive that they do.  There are a number of ways to measure critical thinking which businesses also pay dearly for.  Here's a summary of what these critical thinking tests have found:
 

 Standardized tests like SAT Math, SAT Verbal, GRE, GMAT, and ACT show a high degree of correlation with critical thinking skills.
 SAT Math shows a higher correlation than SAT Verbal--about 0.48 to 0.66.
 SAT total shows higher correlation than either SAT Math or SAT Verbal, at 0.68.
 GRE and GMAT show a slightly higher correlation than SAT Math, up to 0.69.
 MCAT had the lowest correlation in quantitative skills than all the standardized tests, at 0.40.
 Critical thinking skills don't improve with age, at 0.006.
 College GPA is virtually uncorrelated with critical thinking skills, as low as 0.20.
 The Major GPA is just slightly more correlated with critical thinking skills, up to 0.33.
 Amount of reading is even less correlated than college GPA, at 0.14.
 Graduate units are only slightly correlated to critical thinking skills, at 0.34 to 0.41.
 One study found that critical thinking skills did not improve after taking critical thinking course.
 College versus non-college had a relatively low correlation, at 0.40.
 "coursework not strong predictor of critical thinking scores (Banta & Pike, 1989)"


Title: Re: assuming too much math knowledge?
Post by: benami on September 23, 2010, 06:26:30 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".






Some of us, because we have a full understanding of what Anthroid explained, listed our race as "human." 


Looking!  Looking!  Looking!

AH, here it is.

1,078,872 said "Korean"
another 1,122,528 said "Vietnamese"
and 1,850,31 said "Filipino"
1,678,998 said "Asian Indian"
2,432,585 said "Chinese"
796,700 said "Japanese"
140,652 said "Hawaiian"
91,029 said "Samoan"
6,826,228 said "two or more races", that's 2.4% of the total
36,419,434 said "black" to distinguish themselves from the above category
20,640,711 said "Mexican"
3,406,178 said "Puerto Rican"
1,241,685 said "Cuban"
where's that "human" category?
oh, here it is.
WAIT!
16,907,852 said "Hispanic white"
that's not it.
Do you mean the 194,552,774 who said "non-Hispanic White" are the only humans?  Is THAT what you mean?

You're not the first person to make that claim, are you?  I disagree, but it sure makes more sense than to claim that Koreans are only a social construct, doesn't' it?

What I mean is that I know of at least two people (including myself) who filled in the blank with the word "human". 

Oh, I thought you meant when you said "a lot" that you were talking about all six of you?

I was referring to the other 99.99999800% of us.


Title: Re: assuming too much math knowledge?
Post by: conjugate on September 23, 2010, 08:39:18 PM
16,907,852 said "Hispanic white"
that's not it.
Do you mean the 194,552,774 who said "non-Hispanic White" are the only humans?  Is THAT what you mean?

You're not the first person to make that claim, are you?  I disagree, but it sure makes more sense than to claim that Koreans are only a social construct, doesn't' it?

What I mean is that I know of at least two people (including myself) who filled in the blank with the word "human". 

Oh, I thought you meant when you said "a lot" that you were talking about all six of you?

I was referring to the other 99.99999800% of us.

Okay, first of all, LegalGibbon didn't say "a lot."  You put those words into his/her mouth.  Next, yes, the notion of "race", including Korean, is a social construct.  Of course it's a social construct that the Koreans take seriously.  The willingness of people to fill out a form with "race" has nothing to do with its being a social construct.

The point is that there is no biological basis for race; the things people put on census forms are not a biological basis, they're a tick-mark on a piece of paper.  You can tell the difference; see, the census form is a piece of paper, and you check off a box.  A biological basis is a significantly large stretch of DNA.  The census bureau doesn't ask you to check off a stretch of DNA.  It asks you to check off a box. 

You and I and all the Asians and Jews and African-Americans and Native Americans and Europeans share 99% of our DNA.  In fact, we share a great deal of our DNA with the chimpanzee.  Now, just to make my point again, let me add:


Finally, I still don't know what you think we could do about it in any case.  I mean, you spew statistics at us, chide us because we aren't making as many suggestions as the other "forums" (your word), and still haven't said what we should do about any of it.  You didn't give a coherent answer in your other ID either, so I suspect the sock puppet you're now using will be similarly unresponsive.

If these other forums are giving you so many possibilities, why don't you go bother them some more and leave us alone?



I'll re-emphasize the underlined portions to point out that (1) my prediction of unresponsiveness to "what can we do about it" is fulfilled, and (2) why doesn't Benami go elsewhere?


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 23, 2010, 08:51:14 PM
Benami/John/Adolph/whoever:

You keep referring to "race" as though it is somehow meaningful.  Your implication is that it is a discrete biological category (though of course your reference to "Hispanic" is pretty silly even within the universe of silly things you imply).  It is not.  Anthropologists have argued for the last century that there is no such biological thing as "race," and the arguments have been significantly more nuanced in the last 20 years.  Certainly the colonialist constructions of "race" have serious social consequences across cultures (though those consequences are not commensurate across cultures), but that isn't at all what you're saying with your random number generator.

It is up to you to demonstrate that you are referring to actual, important categories, particularly given what appear to be profoundly racist posts based in no verifiable information.  I defy you to do that.  You are trying to prove the entirely discredited Bell Curve argument 15 years later.  You're going to fail despite all the numbers you think are significant.  You cannot build a logical argument, as you're starting out with demonstrably incorrect categories given the biological reality of American ethnicities.

What anthropologists and biologists argue about "American ethnicities" has no consequence to me and mine, nor to the 281,421,906 Americans who managed to tell the US Census Bureau precisely what race they are, including Hispanics and "White Hispanics".






Some of us, because we have a full understanding of what Anthroid explained, listed our race as "human." 


Looking!  Looking!  Looking!

AH, here it is.

1,078,872 said "Korean"
another 1,122,528 said "Vietnamese"
and 1,850,31 said "Filipino"
1,678,998 said "Asian Indian"
2,432,585 said "Chinese"
796,700 said "Japanese"
140,652 said "Hawaiian"
91,029 said "Samoan"
6,826,228 said "two or more races", that's 2.4% of the total
36,419,434 said "black" to distinguish themselves from the above category
20,640,711 said "Mexican"
3,406,178 said "Puerto Rican"
1,241,685 said "Cuban"
where's that "human" category?
oh, here it is.
WAIT!
16,907,852 said "Hispanic white"
that's not it.
Do you mean the 194,552,774 who said "non-Hispanic White" are the only humans?  Is THAT what you mean?

You're not the first person to make that claim, are you?  I disagree, but it sure makes more sense than to claim that Koreans are only a social construct, doesn't' it?

What I mean is that I know of at least two people (including myself) who filled in the blank with the word "human". 

Oh, I thought you meant when you said "a lot" that you were talking about all six of you?

I was referring to the other 99.99999800% of us.

Epic fail.

Alan


Title: Re: assuming too much math knowledge?
Post by: zharkov on September 24, 2010, 07:13:02 AM

The problem you are having is that you are assuming that correlation means causation.


Bingo!

I've said this, in different ways, a couple or three times, as have others.  Despite the title of the thread, it is not (now) about math at all, but about dealing with someone whose entire line of argument is based on a logical fallacy.



Title: Re: assuming too much math knowledge?
Post by: wet_blanket on September 24, 2010, 09:30:55 AM
Benami, if SAT scores CAUSE differing rates of pay, then can you explain:
1. Why no HR department includes SAT scores in their formulae for determining pay scales?
2. Why people move to different salaries at different points in their careers?
3. Why no employer has ever asked me for my SAT scores?


Title: Re: assuming too much math knowledge?
Post by: cgfunmathguy on September 24, 2010, 11:23:18 AM
Benami, if SAT scores CAUSE differing rates of pay, then can you explain:
1. Why no HR department includes SAT scores in their formulae for determining pay scales?
2. Why people move to different salaries at different points in their careers?
3. Why no employer has ever asked me for my SAT scores?
Thanks, W_B. I was just getting ready to ask this. In fact, I can imagine that applying for a job and listing SAT scores "so they would know how much to pay me" might, in fact, cause howls of laughter before the company in question deep-sixed my application.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 24, 2010, 11:29:12 AM
Benami, if SAT scores CAUSE differing rates of pay, then can you explain:
1. Why no HR department includes SAT scores in their formulae for determining pay scales?
2. Why people move to different salaries at different points in their careers?
3. Why no employer has ever asked me for my SAT scores?
Thanks, W_B. I was just getting ready to ask this. In fact, I can imagine that applying for a job and listing SAT scores "so they would know how much to pay me" might, in fact, cause howls of laughter before the company in question deep-sixed my application.

Better not ask me... I didn't take either the SAT or the ACT. I'd hate to see how that would affect my salary!

Alan


Title: Re: assuming too much math knowledge?
Post by: benami on September 24, 2010, 12:56:31 PM
Benami, if SAT scores CAUSE differing rates of pay, then can you explain:
1. Why no HR department includes SAT scores in their formulae for determining pay scales?
2. Why people move to different salaries at different points in their careers?
3. Why no employer has ever asked me for my SAT scores?
Thanks, W_B. I was just getting ready to ask this. In fact, I can imagine that applying for a job and listing SAT scores "so they would know how much to pay me" might, in fact, cause howls of laughter before the company in question deep-sixed my application.


If salaries weren't subject to all the OTHER factors you aptly cited above (plus one you did not bring up, which is the huge differences in education outcome as illustrated by the 220 SAT point difference between Rhode Island and North Dakota), and if salaries were dependent ONLY on math skills, do you think we would expect to see a linear relationship between math skills and salaries?  Would that give us a Pearson Coefficient of 1.0?

Well, you're right.

It turns out that to achieve that, annual salaries don't need to be adjusted by very much at all for most professions, with only a few exceptions.  To achieve linearity, salaries for engineers would need to be increased by a mere $1,200, for physicists $5,500, for biologists $700, and not adjusted at all for mathematicians as they fall right straight on the curve [read: line].  Conversely, salaries for computer scientists would need to be DECREASED by $9,700, for sociologists by $1,000, for writers by $7,000, and for educators by $7,100.  As pointed out above, the major adjustment is for economists whose salaries would have to be decreased by $25,000.

It's not "so they would know how much to pay me".  It's that over millions of employees in a free enterprise economy, those who produce get paid more and those who don't produce get paid less.

Kinda basic, eh?



Title: Re: assuming too much math knowledge?
Post by: benami on September 24, 2010, 01:03:22 PM

The problem you are having is that you are assuming that correlation means causation.


Bingo!

I've said this, in different ways, a couple or three times, as have others.  Despite the title of the thread, it is not (now) about math at all, but about dealing with someone whose entire line of argument is based on a logical fallacy.



So you also agree with Polly that there is a study which *proves* that there is no correlation between psych ward admissions and full moons?

But you also agree with Polly that this putative study is also *proof* that there is NO correlation between SAT scores and incomes?

AND you agree with Polly that there IS a correlation between SAT scores and socionomic status?

Is that your position? 




Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 24, 2010, 01:06:36 PM

<much snippage>

Would that give us a Pearson Coefficient of 1.0?

OMG. I think I'm going to request that the mods filter "Pearson Coefficient".

You are so not-Dude.

Alan


Title: Re: assuming too much math knowledge?
Post by: benami on September 24, 2010, 01:09:10 PM


You and I and all the Asians and Jews and African-Americans and Native Americans and Europeans share 99% of our DNA.  In fact, we share a great deal of our DNA with the chimpanzee. 



That means chimpanzees are just a social construct.


Title: Re: assuming too much math knowledge?
Post by: benami on September 24, 2010, 01:12:21 PM

<much snippage>

Would that give us a Pearson Coefficient of 1.0?

OMG. I think I'm going to request that the mods filter "Pearson Coefficient".

You are so not-Dude.

Alan

I think they ought to filter out people who lecture others on quotation errors in posts with quotation errors.

I'll surely miss you, Alan.


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 24, 2010, 01:23:25 PM

<much snippage>

Would that give us a Pearson Coefficient of 1.0?

OMG. I think I'm going to request that the mods filter "Pearson Coefficient".

You are so not-Dude.

Alan

I think they ought to filter out people who lecture others on quotation errors in posts with quotation errors.

I'll surely miss you, Alan.

Not-dude... c'mere... I'll tell you a secret...

<whispers>

I did it on purpose since I thought it was funnier that way. If you notice, it looked just like your mistakes. See?

I'm actually  trying to be amusing. I don't often hit it but I'm at least doing it on purpose. What annoys me is that you are trying to be serious but you come off as pretty d@mn funny.

Alan


Title: Re: assuming too much math knowledge?
Post by: benami on September 24, 2010, 01:49:58 PM
Benami, if SAT scores CAUSE differing rates of pay, then can you explain:
1. Why no HR department includes SAT scores in their formulae for determining pay scales?
2. Why people move to different salaries at different points in their careers?
3. Why no employer has ever asked me for my SAT scores?

GRE scores actually show a bit of a closer correlation to salaries for most professions than SAT math scores.  In order to achieve linearity (or a Pearson Coefficient of 1.0, for Alan), mathematicians' salaries would have to be reduced only $500 and economists only $8,000.  Most other salaries would need to be increased: $4,500 for physicists, $5,700 for computer scientists, $2,200 for engineers, and $15,200 for biologists.  Salaries for both educators and sociologists fall right straight on the curve and would not have to be adjusted at all.

So the only question, wet blanket, is whether SAT math scores are a better predictor of employee productivity than GRE quantitative scores (which are taken by far fewer test takers).


Title: Re: assuming too much math knowledge?
Post by: wet_blanket on September 24, 2010, 02:08:04 PM
Benami, if SAT scores CAUSE differing rates of pay, then can you explain:
1. Why no HR department includes SAT scores in their formulae for determining pay scales?
2. Why people move to different salaries at different points in their careers?
3. Why no employer has ever asked me for my SAT scores?

GRE scores actually show a bit of a closer correlation to salaries for most professions than SAT math scores.  In order to achieve linearity (or a Pearson Coefficient of 1.0, for Alan), mathematicians' salaries would have to be reduced only $500 and economists only $8,000.  Most other salaries would need to be increased: $4,500 for physicists, $5,700 for computer scientists, $2,200 for engineers, and $15,200 for biologists.  Salaries for both educators and sociologists fall right straight on the curve and would not have to be adjusted at all.

So the only question, wet blanket, is whether SAT math scores are a better predictor of employee productivity than GRE quantitative scores (which are taken by far fewer test takers).

 

The only question?
 
You have inspired me on a new career path: I'm going to go work for ETS.  They probably won't pay me a very good salary (though my GRE quant is >95%ile, so maybe they would, after all), but since everyone knows -- or soon will -- that pay is determined by SAT/GRE score, I'm gonna be making some excellent money under the table for adjusting scores.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 24, 2010, 02:10:52 PM
The moral of the story?  THE top student in one of America's (once) top physics and engineering colleges didn't even know calculus.

Your alma mater, while a decent school, was never one of America's "top" physics and engineering colleges.  To use one of your favorite metrics, the Math SATs of its students are roughly 200 points below those at MIT, and even below those at my own middling large state university.  (Moreover, the numerical selectivity of its student body improved once it started admitting women.)

However, I'd like to go on record with some of the others in this thread that I wish salary was determined by Math SATs or GREs. - DvF


Title: Re: assuming too much math knowledge?
Post by: cc_alan on September 24, 2010, 02:44:09 PM
However, I'd like to go on record with some of the others in this thread that I wish salary was determined by Math SATs or GREs. - DvF

Cut it out! You have no idea what you're doing to my salary.

Alan


Title: Re: assuming too much math knowledge?
Post by: benami on September 24, 2010, 06:44:42 PM
The moral of the story?  THE top student in one of America's (once) top physics and engineering colleges didn't even know calculus.

Your alma mater, while a decent school, was never one of America's "top" physics and engineering colleges.  To use one of your favorite metrics, the Math SATs of its students are roughly 200 points below those at MIT, and even below those at my own middling large state university.  (Moreover, the numerical selectivity of its student body improved once it started admitting women.)

However, I'd like to go on record with some of the others in this thread that I wish salary was determined by Math SATs or GREs. - DvF

Well, since you want to diverge from the main point to pursue this irrelevant topic, the main problem I have (which all of my fellow classmates agree with) is that they had changed their focus from an engineering school to a liberal arts school.  While the faculty was all impressed about how several surveys placed us first in liberal arts for years in a row, until last year when two other formerly famous engineering schools also mysteriously converted to liberal arts schools, we were depressed about it.

Even my fellow alumni who majored in humanities agreed that bragging about being a good liberal arts school in this day and age of the computer and semiconductor revolution feels about like wearing a raincoat in the shower, or rearranging the deck chairs on the Titanic.

Did you miss Economics 101 at your large state university?  Or do they just not understand how free enterprise works?  The point is not that salaries are determined by test scores--it's that SAT is a reasonable predictor of both math skills in college as well as in the workforce, just as it was designed to be.



Title: Re: assuming too much math knowledge?
Post by: benami on September 24, 2010, 06:59:51 PM
Benami, if SAT scores CAUSE differing rates of pay, then can you explain:
1. Why no HR department includes SAT scores in their formulae for determining pay scales?
2. Why people move to different salaries at different points in their careers?
3. Why no employer has ever asked me for my SAT scores?

GRE scores actually show a bit of a closer correlation to salaries for most professions than SAT math scores.  In order to achieve linearity (or a Pearson Coefficient of 1.0, for Alan), mathematicians' salaries would have to be reduced only $500 and economists only $8,000.  Most other salaries would need to be increased: $4,500 for physicists, $5,700 for computer scientists, $2,200 for engineers, and $15,200 for biologists.  Salaries for both educators and sociologists fall right straight on the curve and would not have to be adjusted at all.

So the only question, wet blanket, is whether SAT math scores are a better predictor of employee productivity than GRE quantitative scores (which are taken by far fewer test takers).

 

The only question?
 
You have inspired me on a new career path: I'm going to go work for ETS.  They probably won't pay me a very good salary (though my GRE quant is >95%ile, so maybe they would, after all), but since everyone knows -- or soon will -- that pay is determined by SAT/GRE score, I'm gonna be making some excellent money under the table for adjusting scores.

When you say that "that pay is determined by SAT/GRE score, I'm gonna be making some excellent money under the table for adjusting scores", you too indicate that you must have slept through Economics 101 (or that your economics teacher slept through Economics 101).

Here's how it actually works.  We have 100 million people in a large pseudo-free-enterprise economy who would be paid exactly as much as they deserve, based on their skills and productivity.  The only things that throw that off are those things cgfunmathguy pointed out, plus government largess like affirmative action and the equal pay act, plus the obviously huge disparity in education outcome as illustrated by the 220 SAT point gap between Rhode Island and North Dakota, plus our outrageously huge tax bite which redistributes massive amounts of wealth from the producers to the, er, useless eaters.  Without all those things, there would be a linear relationship between math skills and income.  And if SAT is a valid measure of math skills (and I'm actually not arguing that it is, as it now appears that TIMSS is a much more powerful and accurate tool) then why should we not expect an exact linear relationship between SAT math scores and personal income?

What kind of a relationship do you think we should expect with SAT verbal scores?  None?


Title: Re: assuming too much math knowledge?
Post by: mystictechgal on September 24, 2010, 07:04:34 PM
Not-Dude, you "diverged from the main point to pursue [an] irrelevant topic" in the first post you made in the thread, under your first pseudonym. You haven't quit posting irrelevancies, yet, under either pseudonym. Begone.


Title: Re: assuming too much math knowledge?
Post by: kraken on September 24, 2010, 08:23:09 PM

<much snippage>

Would that give us a Pearson Coefficient of 1.0?

OMG. I think I'm going to request that the mods filter "Pearson Coefficient".

You are so not-Dude.

Alan

I think they ought to filter out people who lecture others on quotation errors in posts with quotation errors.

I'll surely miss you, Alan.

I think they should filter out people with a demonstrated willful ignorance of their topic of choice.  You don't get the difference between correlation and causation, apparently.  I'd say it was like bringing a knife to a gun fight, but it's more like you brought a limp noodle.


Title: Re: assuming too much math knowledge?
Post by: daniel_von_flanagan on September 25, 2010, 12:29:24 AM
Well, since you want to diverge from the main point to pursue this irrelevant topic, the main problem I have (which all of my fellow classmates agree with) is that they had changed their focus from an engineering school to a liberal arts school.  While the faculty was all impressed about how several surveys placed us first in liberal arts for years in a row, until last year when two other formerly famous engineering schools also mysteriously converted to liberal arts schools, we were depressed about it.

Neither of those two other schools were or are famous for their engineering programs either, and the "first" ranking was technically first among a fairly odd cohort that only includes fewer than 30 institutions. 

Your alma mater has had a liberal arts major available since 1912.

The reason I brought this all up is that when pressed for your credentials to discuss higher education you have hinted connections to a top tech school like MIT, when I believe that your credential is a bachelors from a specialty undergraduate institution which is quite good for what it is but by no means a tech powerhouse.  At that, your firsthand understanding of what happens in higher education appears to be nearly half a century out of date, and it shows.  (Among other things, in the period since you graduated your school was dragged kicking and screaming into the 19th century, finally admitting women and people of color.  Had you been in classes with these students, you might have had to confront firsthand the reality that they are every bit as capable as students as you are, and perhaps had an opportunity to overcome your fearborne irrationality.) 

The discussion of SATs catalyzed my decision to say something. It is possible to have 50 or even 200 points lower math SATs than the best students and still be credible as an engineer.  That must be true, or else your own school would have no enginering program. - DvF


Title: Re: assuming too much math knowledge?
Post by: benami on September 25, 2010, 12:56:29 PM

<much snippage>

Would that give us a Pearson Coefficient of 1.0?

OMG. I think I'm going to request that the mods filter "Pearson Coefficient".

You are so not-Dude.

Alan

I think they ought to filter out people who lecture others on quotation errors in posts with quotation errors.

I'll surely miss you, Alan.

I think they should filter out people with a demonstrated willful ignorance of their topic of choice.  You don't get the difference between correlation and causation, apparently.  I'd say it was like bringing a knife to a gun fight, but it's more like you brought a limp noodle.

So even after seeing the high correlation between SAT math scores and incomes by profession (with a Pearson Coefficient of 0.9), you you still believe that there should NOT be any correlation between the two?

Why do you believe that?  Because you think it's unfair?  Because you hate the way the free enterprise system works?  Because you are on the outer edge of both and you don't like the idea that you can do nothing about it?  Do you have a better idea for how to establish salaries and wages than this? 

Does this mean you prefer communism over free enterprise?


Title: Re: assuming too much math knowledge?
Post by: benami on September 25, 2010, 12:58:25 PM
Well, since you want to diverge from the main point to pursue this irrelevant topic, the main problem I have (which all of my fellow classmates agree with) is that they had changed their focus from an engineering school to a liberal arts school.  While the faculty was all impressed about how several surveys placed us first in liberal arts for years in a row, until last year when two other formerly famous engineering schools also mysteriously converted to liberal arts schools, we were depressed about it.

Neither of those two other schools were or are famous for their engineering programs either, and the "first" ranking was technically first among a fairly odd cohort that only includes fewer than 30 institutions. 

Your alma mater has had a liberal arts major available since 1912.

The reason I brought this all up is that when pressed for your credentials to discuss higher education you have hinted connections to a top tech school like MIT, when I believe that your credential is a bachelors from a specialty undergraduate institution which is quite good for what it is but by no means a tech powerhouse.  At that, your firsthand understanding of what happens in higher education appears to be nearly half a century out of date, and it shows.  (Among other things, in the period since you graduated your school was dragged kicking and screaming into the 19th century, finally admitting women and people of color.  Had you been in classes with these students, you might have had to confront firsthand the reality that they are every bit as capable as students as you are, and perhaps had an opportunity to overcome your fearborne irrationality.) 

The discussion of SATs catalyzed my decision to say something. It is possible to have 50 or even 200 points lower math SATs than the best students and still be credible as an engineer.  That must be true, or else your own school would have no enginering program. - DvF

Isn't it interesting that the powerhouse institution MIT which you seem to be so proud of is located right in the squak dead center of the sinkhole of SAT scores, Massachusetts?  Could it be that there are no more people in Massachusetts qualified to go to MIT, and all the admissions now are Asians?


Title: Re: assuming too much math knowledge?
Post by: benami on September 25, 2010, 01:06:03 PM

Oh for pity's sake.  You say "the blacks" (charming, by the way, to put "black" in lower case and "White" in upper case--you are telegraphing your attitudes big time) as though this is an isolated grouping in the US.  Wrong, wrong, wrong.  The history of slavery tells us that African-Americans are not that isolated gene pool that you, and your little friends, keep claiming that it is.  That's why Murray and Hernnstein's initial hypothesis was completely flawed from the outset.  You just don't understand the nuance.  

Let's do a thought experiment.  Would you agree, in your own...er....unique way that the Irish are "white" in the same way that the English are "white"?  I'm going to assume that you will say yes.  How, then, do you explain that the Irish score 15 points lower on IQ tests when newly immigrated to England than the English do?  This is exactly the same IQ point difference that Hernnstein and Murray say is so significant between African-Americans and European-Americans, and what they say is "racial."  The argument is, of course, complete bullsh!t.  It has to do with class, discrimination, and SES far more than their very inaccurate assumptions (and, thus, yours) about "race" as a real category rather than acknowledging the very real fact that the "one-drop" rule means that people whose ancestors are largely European-Americans are still identified by people like you as "black" belong in more complex categories.  President Obama is a good example as someone who is European-American as much as he is African-American, but in this country, he has to be pigeonholed, quite inaccurately, as "Black."


Do you ever see the irony of claiming that there are no races in the same breath you claim there ARE racists?  If there are no races, there are no racists.  If the only thing that correlates with SAT scores is socioeconomic status, then you need to change your racist slur, and I recommend socioeconomic statusist.

I never considered before that I might hate someone just because they're at the lower end of the socioeconomic scale, but your posts are making me begin to believe that's entirely possible.


Title: Re: assuming too much math knowledge?
Post by: duchess_of_malfi on September 25, 2010, 01:42:48 PM
Time out to contemplate today's special number: 9/8 (http://www.youtube.com/watch?v=kc34Uj8wlmE).


Title: Re: assuming too much math knowledge?
Post by: legalgibbon on September 25, 2010, 02:56:56 PM



Do you ever see the irony of claiming that there are no races in the same breath you claim there ARE racists?  If there are no races, there are no racists.  If the only thing that correlates with SAT scores is socioeconomic status, then you need to change your racist slur, and I recommend socioeconomic statusist.

I never considered before that I might hate someone