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Boys vs. Girls in Twelfth Grade Math

Remembering, Understanding & Applying Math Concepts

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American girls demonstrated that they have been taught and can remember math and physics principles better than American boys.  Even though they remember the principles, they demonstrated that statistically zero percent of them were able to apply these principles to basic problem solving.  Main TIMSS page.

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American girls remember math concepts better than boys on 9 of 68 TIMSS advanced math questions.

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July 15, 1995 Hedrick Smith in "Rethinking America" points out 6% of US, vs. 40% of German and 94% of Japanese students in high school study calculus.

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Only 3% of American girls who took "advanced math" (0.3% of all American girls) demonstrated any math knowledge on 28 of 68 TIMSS questions.

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Only 4.3% of American girls who took "physics" (0.4% of all American girls) demonstrated physics knowledge on all 39 released physics items.

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With a standard error of plus or minus 3%, effectively zero percent of American 12th grade girls demonstrated the ability to apply math or physics principles to problem solving.

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The ROI on the extra $7 trillion expenditure for education was zero.

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23% of all 12th grade boys and 58% of the boys in the highest scoring countries answered the 28 math questions correctly.

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Men are better math teachers than women.

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Item K18. "Geometric proof of isosceles triangle" illustrates that more Isosceles TriangleAmerican girls (11.4%) than boys (8.2%) understood basic principles of geometry. Internationally, 24% more of both boys and girls demonstrated their understanding of geometry concepts.

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Item K1 illustrates that more American girls than boys understood the concepts of numbers, equations, and functions (68% vs. 66.4%), but that internationally 15% more girls and 21% more boys understood the concept: If xy = 1 and x is greater than 0, which of the following statements is true?

A. When x is greater than 1, y is negative.

B. When x is greater than 1, y is greater than 1.

C. When x is less than 1, y is less than 1.

D. As x increases, y increases.

E. As x increases, y decreases.

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Item L4 illustrates that an equal percent (36.3%) of American boys and girls understood the concept, but that internationally 7% more girls and 15% more boys did: An examination consists of 13 questions. A student must answer only one of the first two questions and only nine of the remaining ones. How many choices of questions does the student have?

A. 13 C 10 = 286

B. 11 C 8 = 165

C. 2 �11 C 9 = 110

D. 2 �11 P 2 = 220

E. some other number

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Item K1 illustrates that more American girls (68%) than boys (66.4%) understood a numbers, equations, and functions concept, but that internationally 15% more girls and 21% more boys understood the concept: If xy = 1 and x is greater than 0, which of the following statements is true?

A. When x is greater than 1, y is negative.

B. When x is greater than 1, y is greater than 1.

C. When x is less than 1, y is less than 1.

D. As x increases, y increases.

E. As x increases, y decreases.

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American Boys Apply Math Concepts Better Than Girls

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Item L10 illustrates that American girls didn't apply better than boys the concepts (which they learned better than boys) to probability and statistics questions. If all girls had guessed on this 5 choice multiple choice question, 20% of them would have guessed correctly, but only 15% answered correctly.  This could happen only if girls didn't answer the question at all. 27% of American boys answered correctly, so 20% of them might have guessed while only 7% of them might have understood how to correctly apply the concept.  It illustrates that zero percent of American girls were able to effectively apply the math concept which they were able to remember, and that their test taking strategy as a group was uniformly bad. 

It's not good news that only 7% of American boys understand probability and statistics well enough to answer the question.  But even 7% is infinitely higher than zero percent, and it's not much lower than the average percent of boys internationally (4% lower) who answered correctly: 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.

A. 0.995

B. 0.975

C. 0.95

D. 0.90

E. 0.855

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Item K13 shows that when principles are applied and computation is required to answer a non-multiple choice question, 11.7% more American boys (29.8%) than girls (18.1%) correctly applied the concepts which American girls demonstrated that they understood better than boys.  Internationally, 6% more girls and 4% more boys answered correctly: The number of bacteria in a colony was growing exponentially. At 1 pm yesterday the number of bacteria was 1000 and at 3 pm yesterday it was 4000. How many bacteria were there in the colony at 6 pm yesterday?

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Item L16 illustrates that only 6% of American girls were able to solve an equations and functions question, compared to an international average of 26.2% of boys: Find all real values of x which satisfy the following equation:

Show all your work.

x - 2

x = 1

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Of the 67 TIMSS questions, there were 32 questions of which an average of less than 5% of American girls demonstrated an ability to comprehend.  A smaller percentage of American girls answered 7 of the multiple choice questions correctly than would have answered correctly if students had just guessed.   For example, only 9% of American girls answered Item K10 (ANGLE INSCRIBED BY FIGURES INSIDE A SEMICIRCLE) correctly: AB is the diameter of a semicircle k, C is an arbitrary point on the semicircle (other than A or B), and S is the centre of the circle inscribed into D ABC. Then the measure of:

A. �ASB changes as C moves on k.

B. �ASB is the same for all positions of C but it cannot be determined without knowing the radius.

C. �ASB = 135� for all C.

D. �ASB = 150� for all C.

But 25% of students who just blindly guessed at the answers to this four question multiple choice problem would have gotten it correct, 16% more than who actually got it correct.

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Item K2 is another example of a 5 part multiple choice question which random guesses would have given 20% of the students correct answers, but which only 17% of American girls answered correctly: In how many ways can one arrange on a bookshelf 5 thick books, 4 medium sized books and 3 thin books so that the books of the same size remain to-gether?

A. 5! 4! 3! 3! = 103 680

B. 5! 4! 3! = 17 280

C. (5! 4! 3!) � 3 =51 840

D. 5 � 4 � 3 � 3 = 180

E. 2 12 � 3 =12 288

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Of the 20 multiple choice math questions which have been released by TIMSS to date, the percent of American 12th grade girls answering correctly on 7 of them was lower than if they had just guessed at the question.  An average of 20% of students would correctly answer a five answer multiple choice question if they just guessed at the answer.   Thus, when 20% answer such a question correctly, this is evidence of zero knowledge of the question by the test takers.

Conversely, if 100% of the test takers answer correctly, zero percent of them will have guessed at the answer.  To correct for guesses, each 1.25% of students above 20% who answer correctly adds 1% to the percent of students who understand the subject.   Similarly, 4 answer multiple choice questions add 1% to the percent of students who understand the subject for each 1.33% additional students above 25% who answer correctly.

After adjusting for guesses,  an average of only 2% of American girls demonstrated a knowledge of 20 multiple choice questions, versus an international average of 23% of all 12th grade boys participating in TIMSS, and 61% of the boys in the top scoring countries on each question.

NOTE: the countries whose 12th graders took TIMSS exclude countries like Japan, Korea, Singapore, Taiwan, Hong Kong, whose 8th graders scored more than 100 points higher than ours.  Had they participated, the percent answering these question correctly might have exceeded 50%.

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Item Number & Question

US Girls

Average Int'l Boy

Prob-ability of Multiple Choice Correct

US Girls Less Multiple Choice Guesses

Intl Boys Less Multiple Choice Guesses

Highest Scoring Countries

Scores of Boys in Highest Scoring Countries

I05 NEW MEAN AND STANDARD DEVIATION

26

41.4

20

8

27

Denmark

56.4

I06 USING CHAIN RULE

33

53.5

25

11

38

Australia

62.9

I09 INTEGER COORDINATES OF FUNCTION

29

66.3

25

5

55

Lithuania

86.9

J02 CUBING A TRIGONOMETRIC FUNCTION WITH IMAGINARY NUMBERS

22

40.1

20

3

25

Russia

63

J06 RADIUS OF CYLINDER WHILE MAXIMIZING VOLUME

25

39

25

0

19

Switzerland

52

J09 EQUATION REPRESENTING SET OF POINTS

18

28.1

20

-2

10

Australia

39.2

J10 VALUE OF VECTOR IN TRIANGLE

26

41.1

20

8

26

Cyprus

60.5

J13 OVERALL AVERAGE TEST SCORE

29

59.5

20

11

49

Switzerland

84.6

J16B TRIANGLE ABC/ ROTATION

27

30

20

9

13

Russia

50.8

J17 LIMIT OF PERIMETER OF POLYGON CONTAINED IN A CIRCLE

15

34.6

20

-5

18

France

51.9

J19 PROVE THAT E IS MIDPOINT OF QUADRILATERAL

19

37.6

20

-1

22

Israel

74

K02 PERMUTATIONS OF BOOKS ON A SHELF

17

30.5

20

-3

13

Australia

56.7

K04 LIMIT OF A FUNCTION

25

29.4

20

6

12

Greece

51.9

K08 CONIC REPRESENTED BY AN EQUATION

24

30.2

25

-1

7

France

82.1

K09 DISTANCE BETWEEN INTERCEPTS ON A PLANE

29

47.3

25

5

30

Australia

39.2

K10 ANGLE INSCRIBED BY FIGURES INSIDE A SEMICIRCLE

9

21.8

25

-16

0

Cyprus

60.5

L05 SUM OF INFINITE GEOMETRIC SERIES

22

50.6

20

3

38

Lithuania

69

L06 CRITICAL POINT OF VELOCITY EQUATION

24

34.1

20

5

18

Australia

69.2

L07 GRAPH OF y= f( x)

24

38.3

20

5

23

Sweden

53.5

L10 PROBABILITY OF AT LEAST ONE ALARM OPERATING

15

31.9

20

-5

15

Australia

48.1

J15B FUNCTION/ WHERE NOT DIFFERENTIABLE

8

11

0

8

11

Denmark

30.5

J18 STEPS FOR MATHEMATICAL INDUCTION

1

20.2

0

1

20.2

Greece

77

K14 LENGTH OF STRING AROUND ROD

1

13.7

0

1

13.7

Lithuania

27.9

K15 COMPLEX NUMBER SOLUTION OF EQUATION

1

20.6

0

1

20.6

Israel

50

K18 GEOMETRIC PROOF OF ISOSCELES TRIANGLE

11

34.8

0

11

34.8

France

49.5

L13 ANGLE BETWEEN TWO VECTORS

11

35.1

0

11

35.1

Greece

54.8

L16 SOLUTION OF REAL VALUES OF A QUADRATIC EQUATION

6

26.2

0

6

26.2

Lithuania

68.5

L17 EQUATION FOR CIRCLE

6

22.7

0

6

22.7

Greece

50.7

Average

3.2%

22.9%

57.9%

 

 

TIMSS Physics Questions from timssallitems.pdf shows that, once corrected for multiple choice guesses, only 4.3% of American 12th Grade girls demonstrated any knowledge of the entire TIMSS Physics exam.  With a standard error of plus or minus 3%,  the confidence level that there was ANY knowledge demonstrated is this is too close to ZERO to be a coincidence.

Percent of US 12th Grade Girls With Correct Answers

Correction for Multiple Choice Questions

Actual Percent of US 12th Grade Girls Demonstrating knowledge of the question

G01 PATH OF ELECTRONS TRAVELING THROUGH A MAGNETIC FIELD 26 2.5 27 3.4 25 2.7

25

25

0

G02 VOLUME OF STEAM 60 2.3 65 3.6 55 3.8

55

20

44

G03 PHYSICAL PROPERTIES OF TWO GASES AT THE SAME TEMPERATURE 49 2.5 48 3.7 51 3.7

51

25

33

G04 RELATIONSHIP BETWEEN INDUCED CURRENT AND VARYING MAGNETIC FIELD 26 2.6 31 3.8 22 2.7

22

25

-3

G05 DIRECTION REFRACTED RAY OF LIGHT 27 2.8 33 3.5 20 2.9

20

20

0

G06 PROCESS BY WHICH STARS RELEASE ENERGY 52 2.8 61 4.1 43 3.4

43

20

29

G07 ENERGY TRANSFORMATION AND COLLISION OF CARS 23 2.4 27 3.9 18 2.5

18

20

-2

G08 MECHANICAL ENERGY OF BLOCK AND SPRING SYSTEM 13 1.6 14 2.5 11 2.3

11

25

-14

G09 DIRECTION OF FORCES IN AMUSEMENT PARK RIDE 15 2.2 13 2.1 17 4.0

17

20

-3

G10 MINIMUM VOLTAGE NEEDED TO PRODUCE X- RAYS 23 2.6 25 3.5 20 4.2

20

20

0

G11 EFFECT OF ICE MELTING ON WATER LEVEL IN AQUARIUM 5 1.1 6 1.8 4 0.8

4

0

4

G12 CALCULATION OF MASS USING CONSERVATION OF MOMENTUM 14 2.0 19 3.4 8 1.4

8

0

8

G13 DOPPLER EFFECT AND MOVING CAR 12 1.7 16 3.0 7 1.9

7

0

7

G14 PATHS OF ALPHA, BETA, AND GAMMA RAYS THROUGH AN ELECTRIC FIELD 5 1.1 7 2.1 2 0.8

2

0

2

G15 DIRECTION OF ACCELERATION OF A BOUNCING BALL 6 1.2 10 2.1 2 1.1

2

0

2

G16 EFFECT OF PRESSURE ON WATER LEAKING FROM A BOTTLE 3 1.0 4 1.3 3 1.0

3

0

3

G17 DIRECTION OF FORCE DUE CURRENT 12 2.1 11 1.9 12 3.9

12

0

12

G18 ALPHA PARTICLES PASSING THROUGH GOLD 2 0.7 3 1.3 1 0.5

1

0

1

G19 LENZ’S LAW AND FALLING ALUMINUM RING 1 0.3 1 0.6 . .

0

0

0

H01 BOXES SLIDING DOWN INCLINED PLANES 40 2.5 38 2.9 42 4.1

42

25

21

H02 LIQUID EVAPORATION 39 2.5 39 2.8 39 3.5

39

25

18

H03 PHOTOELECTRIC EFFECT AND KINETIC ENERGY OF EMITTED ELECTRONS 24 2.4 26 2.7 23 3.1

23

25

-2

H04 TENSION OF STRING BETWEEN TWO FALLING OBJECTS 33 2.2 43 3.1 23 2.2

23

25

-2

H05 LENGTH OF SPACESHIP IN FLIGHT 34 2.3 33 3.4 35 3.1

35

25

13

H06 INDUCED emf IN ROTATING COIL 34 2.1 38 3.4 29 3.1

29

25

5

H07 RELATIONSHIP BETWEEN TEMPERATURE AND PRESSURE WITH CONSTANT VOLUME 15 2.0 20 3.1 9 1.8

9

25

-16

H08 PATH OF ELECTRONS IN ELECTRIC FIELD 12 1.6 13 2.5 10 1.9

10

20

-10

H09 REFRACTION AND VELOCITY OF BLUE LIGHT 19 2.1 23 3.2 15 2.3

15

20

-5

H10 VECTOR SUM OF ELECTRIC FORCES 15 1.5 18 2.1 11 1.7

11

25

-14

H12 PARTICLE MOVEMENT IN A TRANSVERSE WAVE 11 2.0 16 3.5 6 1.7

6

0

6

H13 INTERPRETATION OF A FORCE VERSUS DISTANCE GRAPH 7 1.7 10 2.2 3 1.5

3

0

3

H14 EFFECT OF DENSITY ON THE FREEZING OF WATER 2 0.6 3 0.9 1 0.8

1

25

-24

H15 DE BROGLIE WAVELGTH OF A MOBILE ELECTRON 7 1.4 7 1.5 7 1.9

7

0

7

H16 SPEED OF AN ELECTRON TRAVELING THROUGH PERPENDICULAR ELECTRIC AND MAGNETIC FIELD 2 0.6 1 0.7 2 1.1

2

0

2

H17 RESISTANCE OF A SERIES CIRCUIT COMPONENT 2 0.7 2 1.2 1 0.4

1

0

1

H18 TELEVISION AS PARTICLE ACCELERATOR 1 0.3 2 0.6 0 0.1

0

0

0

H19A SPEED OF SOUND EXPERIMENT/ OUTLINE 9 1.2 12 2.2 6 1.9

6

0

6

H19B SPEED OF SOUND EXPERIMENT/ REASON 37 2.6 40 3.7 34 2.9

34

0

34

AVERAGE

4.3%

 

12 grade American boys performed almost as badly in Mathematics Literacy as they did in Advanced Math and Physics, scoring 479, higher than only Cyprus and South Africa.   12th grade American girls scored another 17 points lower than that, demonstrating extremely poor math skills when only 17% correctly answered a multiple choice question which 25% would have answered correctly if they had merely guessed.Example 5: Brighto Soap powder is packed in cube-shaped cartons.  A carton measures 10 cm. on each side.  The company decides to increase the length of each edge of the carton by 10 per cent.  How much does the volume increase:
  1. 10 cm3
  2. 21 cm3
  3. 100 cm3
  4. 331 cm3
 

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