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Topic: assuming too much math knowledge?  (Read 7467 times)

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daniel_von_flanagan

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Re: assuming too much math knowledge?

Reply #105 on: December 16, 2008, 04:07:15 PM �


Quote from: christianp on December 16, 2008, 03:17:20 PM

Quote from: daniel_von_flanagan on December 12, 2008, 04:00:59 AM

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

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Re: assuming too much math knowledge?

Reply #106 on: December 16, 2008, 04:10:44 PM �


Quote from: 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


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.


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Re: assuming too much math knowledge?

Reply #107 on: December 16, 2008, 04:18:36 PM �


Quote from: jacobisrael on December 16, 2008, 04:10:44 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

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Re: assuming too much math knowledge?

Reply #108 on: December 16, 2008, 04:31:35 PM �


Quote from: daniel_von_flanagan on December 16, 2008, 04:07:15 PM

Quote from: christianp on December 16, 2008, 03:17:20 PM

Quote from: daniel_von_flanagan on December 12, 2008, 04:00:59 AM

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.

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Re: assuming too much math knowledge?

Reply #109 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

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Re: assuming too much math knowledge?

Reply #110 on: December 16, 2008, 05:08:47 PM �


Quote from: daniel_von_flanagan on December 16, 2008, 04:18:36 PM

Quote from: jacobisrael on December 16, 2008, 04:10:44 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?

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Re: assuming too much math knowledge?

Reply #111 on: December 16, 2008, 05:34:22 PM �


Quote from: 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


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?

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Re: assuming too much math knowledge?

Reply #112 on: December 16, 2008, 09:13:49 PM �


Quote from: jacobisrael on December 16, 2008, 05:08:47 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

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Re: assuming too much math knowledge?

Reply #113 on: December 16, 2008, 09:19:07 PM �


Wow, Charles Murray reads the Chronicle fora. Who knew?

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Re: assuming too much math knowledge?

Reply #114 on: December 17, 2008, 12:41:28 PM �


Quote from: jacobisrael on December 16, 2008, 05:08:47 PM

Quote from: daniel_von_flanagan on December 16, 2008, 04:18:36 PM

Quote from: jacobisrael on December 16, 2008, 04:10:44 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.

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Re: assuming too much math knowledge?

Reply #115 on: December 18, 2008, 04:49:12 PM �


Quote from: cgfunmathguy on December 17, 2008, 12:41:28 PM

Quote from: jacobisrael on December 16, 2008, 05:08:47 PM

Quote from: daniel_von_flanagan on December 16, 2008, 04:18:36 PM

Quote from: jacobisrael on December 16, 2008, 04:10:44 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?

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Re: assuming too much math knowledge?

Reply #116 on: December 18, 2008, 08:38:07 PM �


Quote from: jacobisrael on December 18, 2008, 04:49:12 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.

Quote from: jacobisrael on December 18, 2008, 04:49:12 PM

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.

Quote from: jacobisrael on December 18, 2008, 04:49:12 PM

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.

Quote from: jacobisrael on December 18, 2008, 04:49:12 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.

Quote from: jacobisrael on December 18, 2008, 04:49:12 PM

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.

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Re: assuming too much math knowledge?

Reply #117 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*

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Re: assuming too much math knowledge?

Reply #118 on: December 18, 2008, 10:58:47 PM �


Quote from: cgfunmathguy on December 18, 2008, 08:38:07 PM

Quote from: jacobisrael on December 18, 2008, 04:49:12 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).

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Re: assuming too much math knowledge?

Reply #119 on: December 18, 2008, 11:07:22 PM �


Quote from: circularity on December 18, 2008, 10:58:47 PM

Quote from: cgfunmathguy on December 18, 2008, 08:38:07 PM

Quote from: jacobisrael on December 18, 2008, 04:49:12 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

 

 

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Re: assuming too much math knowledge?

Reply #135 on: December 19, 2008, 07:11:14 PM �

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Quote from: cgfunmathguy on December 19, 2008, 03:20:14 PM

Quote from: jacobisrael on December 19, 2008, 03:01:46 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.

cgfunmathguy
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?

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Re: assuming too much math knowledge?

Reply #136 on: December 19, 2008, 08:11:34 PM �

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Quote from: jacobisrael on December 19, 2008, 07:11:14 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).

Quote from: jacobisrael on December 19, 2008, 07:11:14 PM

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".

Quote from: jacobisrael on December 19, 2008, 07:11:14 PM

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.

Quote from: jacobisrael on December 19, 2008, 07:11:14 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.

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Re: assuming too much math knowledge?

Reply #137 on: December 19, 2008, 08:35:20 PM �

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Quote from: mystictechgal on December 19, 2008, 05:48:50 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

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Re: assuming too much math knowledge?

Reply #138 on: December 20, 2008, 01:25:08 AM �

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Quote from: daniel_von_flanagan on December 19, 2008, 08:35:20 PM

Quote from: mystictechgal on December 19, 2008, 05:48:50 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


How 'bout having the students build their own?

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Re: assuming too much math knowledge?

Reply #139 on: December 20, 2008, 02:56:26 AM �

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Quote from: cgfunmathguy on December 19, 2008, 08:11:34 PM

Quote from: jacobisrael on December 19, 2008, 07:11:14 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).

Quote from: jacobisrael on December 19, 2008, 07:11:14 PM

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".

Quote from: jacobisrael on December 19, 2008, 07:11:14 PM

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.

Quote from: jacobisrael on December 19, 2008, 07:11:14 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.


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.

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Re: assuming too much math knowledge?

Reply #140 on: December 20, 2008, 03:55:34 AM �

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Re: assuming too much math knowledge?

Reply #141 on: December 20, 2008, 11:34:39 AM �

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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

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Re: assuming too much math knowledge?

Reply #142 on: December 20, 2008, 11:41:24 AM �

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Quote from: 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


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?

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Re: assuming too much math knowledge?

Reply #143 on: December 20, 2008, 11:44:54 AM �

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I have recently come to the conclusion that yes, we are assuming too much math knowledge.

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Re: assuming too much math knowledge?

Reply #144 on: December 20, 2008, 01:07:03 PM �

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Quote from: cgfunmathguy on December 19, 2008, 08:11:34 PM

Quote from: jacobisrael on December 19, 2008, 07:11:14 PM

 

Quote from: jacobisrael on December 19, 2008, 07:11:14 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?

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Re: assuming too much math knowledge?

Reply #145 on: December 20, 2008, 01:17:54 PM �

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Quote from: 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.


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?

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Re: assuming too much math knowledge?

Reply #146 on: December 20, 2008, 02:18:23 PM �

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Quote from: jacobisrael on December 20, 2008, 11:41:24 AM


"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.

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Re: assuming too much math knowledge?

Reply #147 on: December 20, 2008, 02:30:06 PM �

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Are we allowed to rotate the books?

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Re: assuming too much math knowledge?

Reply #148 on: December 20, 2008, 02:32:00 PM �

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Quote from: darkmatter on December 20, 2008, 02:30:06 PM

Are we allowed to rotate the books?


I like the way you think. :-)

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Re: assuming too much math knowledge?

Reply #149 on: December 20, 2008, 03:10:51 PM �

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Quote from: jacobisrael on December 20, 2008, 01:17:54 PM

Quote from: 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.


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.

 

 

 

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Re: assuming too much math knowledge?

Reply #150 on: December 20, 2008, 03:21:06 PM �

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Quote from: jacobisrael on December 20, 2008, 11:41:24 AM

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

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Re: assuming too much math knowledge?

Reply #151 on: December 20, 2008, 06:56:45 PM �

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Quote from: daniel_von_flanagan on December 20, 2008, 03:21:06 PM

Quote from: jacobisrael on December 20, 2008, 11:41:24 AM

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)?

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Re: assuming too much math knowledge?

Reply #152 on: December 20, 2008, 09:24:34 PM �

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Quote from: jacobisrael on December 20, 2008, 06:56:45 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

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Re: assuming too much math knowledge?

Reply #153 on: December 21, 2008, 11:24:11 AM �

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Quote from: 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


*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

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Re: assuming too much math knowledge?

Reply #154 on: December 21, 2008, 11:36:07 AM �

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I am not sure that some of them even know that the concept of order of operations exists.

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Re: assuming too much math knowledge?

Reply #155 on: December 21, 2008, 02:00:07 PM �

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Quote from: daniel_von_flanagan on December 20, 2008, 09:24:34 PM

Quote from: jacobisrael on December 20, 2008, 06:56:45 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?

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Re: assuming too much math knowledge?

Reply #156 on: December 21, 2008, 07:01:20 PM �

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Quote from: jacobisrael on December 21, 2008, 02:00:07 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

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Re: assuming too much math knowledge?

Reply #157 on: December 22, 2008, 12:03:50 AM �

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Quote from: daniel_von_flanagan on December 21, 2008, 07:01:20 PM

Quote from: jacobisrael on December 21, 2008, 02:00:07 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


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?

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Re: assuming too much math knowledge?

Reply #158 on: December 22, 2008, 03:40:59 AM �

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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
S / n where S gives
=expressed as SESRS 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

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Re: assuming too much math knowledge?

Reply #159 on: December 22, 2008, 04:04:22 AM �

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Quote from: cgfunmathguy on December 19, 2008, 03:14:18 PM

Quote from: jacobisrael on December 19, 2008, 02:49:41 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.


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.

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Re: assuming too much math knowledge?

Reply #160 on: December 22, 2008, 04:16:25 AM �

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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

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Re: assuming too much math knowledge?

Reply #161 on: December 22, 2008, 01:58:51 PM �

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Quote from: 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


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?
 

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Re: assuming too much math knowledge?

Reply #162 on: December 22, 2008, 06:33:06 PM �

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Quote from: daniel_von_flanagan on December 20, 2008, 03:21:06 PM

Quote from: jacobisrael on December 20, 2008, 11:41:24 AM

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.

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Re: assuming too much math knowledge?

Reply #163 on: December 23, 2008, 11:12:17 AM �

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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).

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Re: assuming too much math knowledge?

Reply #164 on: December 23, 2008, 01:51:00 PM �

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Quote from: 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).


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.

 

 

 

 

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Re: assuming too much math knowledge?

Reply #165 on: December 23, 2008, 06:28:46 PM �

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Quote from: jacobisrael on December 23, 2008, 01:51:00 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

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Re: assuming too much math knowledge?

Reply #166 on: December 23, 2008, 08:36:08 PM �

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Quote from: wittgenstein on April 21, 2008, 02:39:18 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.


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

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Re: assuming too much math knowledge?

Reply #167 on: December 23, 2008, 08:39:37 PM �

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Quote from: daniel_von_flanagan on December 23, 2008, 06:28:46 PM

Quote from: jacobisrael on December 23, 2008, 01:51:00 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?

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Re: assuming too much math knowledge?

Reply #168 on: December 23, 2008, 09:52:48 PM �

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Quote from: jacobisrael on December 23, 2008, 08:39:37 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

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Re: assuming too much math knowledge?

Reply #169 on: December 23, 2008, 10:11:01 PM �

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[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.

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Re: assuming too much math knowledge?

Reply #170 on: December 24, 2008, 12:10:25 AM �

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Quote from: 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]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?




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Re: assuming too much math knowledge?

Reply #171 on: December 24, 2008, 12:43:15 AM �

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Quote from: conjugate on December 12, 2008, 01:47:20 AM

Quote from: jacobisrael on December 12, 2008, 01:42:01 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.

 

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Re: assuming too much math knowledge?

Reply #172 on: December 24, 2008, 01:30:49 AM �

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Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

Quote from: 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]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.

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

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.

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

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.

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

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.

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

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.

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

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. 

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

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.

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Quote from: jacobisrael on December 27, 2008, 01:14:58 PM

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Re: assuming too much math knowledge?

Reply #173 on: December 24, 2008, 06:54:34 AM �

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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.

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Re: assuming too much math knowledge?

Reply #174 on: December 24, 2008, 08:42:12 AM �

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Folks, why in the world are you feeding this troll?

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Re: assuming too much math knowledge?

Reply #175 on: December 24, 2008, 10:11:37 AM �

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Quote from: 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.


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

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Re: assuming too much math knowledge?

Reply #176 on: December 24, 2008, 10:19:58 AM �

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Wow.

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

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Re: assuming too much math knowledge?

Reply #177 on: December 24, 2008, 10:50:53 AM �

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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

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Re: assuming too much math knowledge?

Reply #178 on: December 24, 2008, 11:29:47 AM �

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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. 

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Re: assuming too much math knowledge?

Reply #179 on: December 24, 2008, 04:38:51 PM �

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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.

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Re: assuming too much math knowledge?

Reply #180 on: December 24, 2008, 05:00:23 PM �

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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

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Re: assuming too much math knowledge?

Reply #181 on: December 25, 2008, 09:46:44 AM �

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Quote from: 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


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.

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Re: assuming too much math knowledge?

Reply #182 on: December 25, 2008, 10:07:36 AM �

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Quote from: 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. 


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.

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Quote from: jacobisrael on December 27, 2008, 01:14:58 PM

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Re: assuming too much math knowledge?

Reply #183 on: December 25, 2008, 10:13:39 AM �

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Quote from: polly_mer on December 24, 2008, 01:30:49 AM

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

Quote from: 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]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%
 
 

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galactic_hedgehog

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Re: assuming too much math knowledge?

Reply #184 on: December 25, 2008, 10:58:41 AM �

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Quote from: jacobisrael on December 25, 2008, 10:13:39 AM

Quote from: polly_mer on December 24, 2008, 01:30:49 AM

Quote from: jacobisrael on December 24, 2008, 12:10:25 AM

Quote from: 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]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.)

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Conjugate's alternate self.  Or is that vice versa?

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Re: assuming too much math knowledge?

Reply #185 on: December 25, 2008, 11:05:39 AM �

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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


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