Boys vs. Girls in Twelfth Grade Math

Remembering, Understanding & Applying Math Concepts

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.

	American girls remember math concepts better than boys on 9 of 68 TIMSS advanced math questions.
	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.
	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.
	Only 4.3% of American girls who took "physics" (0.4% of all American girls) demonstrated physics knowledge on all 39 released physics items.
	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.
	The ROI on the extra $7 trillion expenditure for education was zero.
	23% of all 12th grade boys and 58% of the boys in the highest scoring countries answered the 28 math questions correctly.
	Men are better math teachers than women.

Item K18. "Geometric proof of isosceles triangle" illustrates that more American 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.

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.

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

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.

American Boys Apply Math Concepts Better Than Girls

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

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?

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:

x = 1

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.

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.

C. (5! 4! 3!) � 3 =51 840

D. 5 � 4 � 3 � 3 = 180

E. 2 12 � 3 =12 288

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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