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Education isn't supposed to improve IQ related skills. Test designers take great pains to make up questions that should be largely universal and almost entirely unaffected by amount of education.

Test designers take great pains to make up questions that should be largely universal and almost entirely unaffected by amount of education.

Test designers purport to do that, but it's a generally replicated research finding that increased exposure to schooling, cross-culturally and across different brands of IQ tests, improves IQ test scores. See

Ceci, Stephen J. (1991). How Much Does Schooling Influence General Intelligence and Its Cognitive Components? A Reassessment of the Evidence. Developmental Psychology 1991, Vol. 27, No. 5, 703-722

for one classic paper on this subject.

The fact that education has little or no effect on IQ happens to be true, but it's not guaranteed by definition or design. I.e., it's logically possible (and, in fact, popularly believed) that education makes your brain work better in general, and that learning French will improve your chess rating and your grades in calculus class. It was discovered that education doesn't help general intelligence much through tests designed on more fundamental principles like elimination of group factors and improving test-retest reliability.

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