 TIMSS Probability & Statistics Item L10

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Question L10 on the 12th Grade TIMSS Math test given to 12th graders around the world in 1995 reveals an astounding difference in math skills between the sexes in all the countries who participated.  The average difference in all countries was 8.3%, with 31.9% of boys and 23.6% of girls answering correctly, but the difference in the US was 12.3% (14.9% of girls and 27.2% of boys).   In countries like Sweden where 59.8% of the boys answered correctly, guesses on the test would not have influenced the scores by that much, but where only 14.9% of American girls answered correctly, guesses must be taken into account.

Since this was a multiple choice question with five possible choices, the probability of getting the correct answer just by guessing is 20%.  In other words, for every five students who guessed, one of them would have gotten the correct answer by chance.  The maximum score would have been achieved had all the students who didn't understand the problem guessed at the answer, so where 14.9% of American girls answered the problem correctly, 20% of them would have gotten the correct answer if all of them had just guessed at the question.  It's not clear how they managed to score lower than if they had just guessed, but discovering why may go a long way towards understanding what has gone wrong with American "education".

27.2% of American boys got the correct answer, 22.75% by guessing, and 4.45% indicating that they understood the problem [x = total guesses, 0.2x = correct guesses, 0.8x = incorrect guesses = 72.8%, x = 91%, 0.2x = 18.2% guessed correctly, 27.2% got the correct answer - 18.2% guessed the correct answer = 9% understood the problem].  However, with an estimated error of plus or minus 3%, only 6% are known with certainty to have understood the problem.

Prior to adjustment for the 3% error, 59.8% of the boys in Sweden got the correct answer, 10.05% guessed correctly, 49.75% indicated that they understood the problem, and 40.2% guessed incorrectly [x = total guesses, 0.2x = correct guesses, 0.8x = incorrect guesses = 40.2%, x = 50.25%, 0.2x = 10.05% = correct guesses, and 59.8% correct answers - 10.05% correct guesses = 49.75% who understood the problem].  After adjustment for the 3% error, only 46.75% are known with certainty to have understood the problem.  Per capita, compared to American boys, 8 times as many boys in Sweden are known to have understood the problem, and compared to American girls, an infinite number are.  Even though American boys did poorly on this question, compared to American girls, an infinitely larger number of them are known to have understood the problem.

Is this adequate proof that our attempt to establish "gender equality" is a failure?  Yes.  To achieve that ephemeral goal, our "educators" began an unnecessary and destructive "gender war" of unprecedented proportions, more than doubled education spending as a percent of GDP, and out-spent by more than three times countries whose students far outperformed ours.  Japan, whose 8th graders scored 105 points higher than ours, spends half as much for education.  Korea, whose 8th graders scored 107 points higher than ours, spends even less per student than Japan.  