In my opinion, there is no way to administer a math test that will identify inborn ability. So people who think the greater presence of men in high-end math and science positions is a result of the distribution of inborn abilities generally rely on the observation of (a) big gender gaps, (b) long-standing gender gaps, or (c) widespread gender gaps, to make their case.
Big gaps (a) are only useful for creating a big impression. Long-standing gaps (b) are undermined by the scale of change in recent decades. And a new study does a very nice job weakening type-C support.
In "Debunking Myths about Gender and Mathematics Performance," in the Notices of the American Mathematical Society, Jonathan Kane and Janet Mert study variation both between and within countries to test a variety of hypotheses about the sources male math advantage. They look at the distribution and variance in scores, the association with single-gender schooling, religious context and, most importantly, broader patterns of gender inequality. The main message I get is that gender ability in math differs so much across social contexts that any conclusion about "natural" ability is untenable. Also, gender equality is good.
Here's my favorite figure from the paper, showing the distribution of eighth-grade scores for boys and girls in three countries.
In the Czech Republic there is no difference in either the means or the distributions for boys versus girls, and the average ability is high. Bahrain shows a much greater variance for boys versus girls - which is sometimes used to explain why to many top achievers are men - but women's average is higher. Finally, in Tunisia the girls have a higher variance but a lower mean. Where's the natural ability story?
An important consideration in all of these patterns is the role of selective dropouts. That is a potential problem with any school-based test, but also shows the problem with using any test of school-based knowledge to understand underlying "natural" ability (including SATs). Unless you can test populations with no schooling, or identical schooling experiences, you can't resolve this.
In the meantime, the great social variability shows us that context matters, and since that's something we can definitely address, there is no reason to get hung up on the biological stuff — at least as far as policy and practice are concerned.
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