Men tend to score higher than women in math on the SAT and the GRE; to a large degree, the gap between men and women in STEM can be explained by their GRE and SAT scores. If you would like to see the argument, I recommend you read this Slate Star Codex post, which goes into far more detail.
In the United States, all students are required to take a math assessment each year. As it happens, this assessment shows no difference between men and women in math ability, including in eleventh grade. The SAT is typically taken in eleventh grade.
This is somewhat strange. While there are theories that suggest that women are just as good at math when they’re young and lose their abilities as they get older, it is a bit much to expect that women would lose their skills in a matter of weeks.
No Child Left Behind assessments are taken by every student. However, only students who are interested in attending college take the SAT.
There are two factors here. First, within the No Child Left Behind data, men have a higher variance than women do, although the difference is not large. If you have two groups with the same mean but one has a higher variance, and you throw out all the low-performers, the high variance one will look like it performs better: you’re keeping all the very very high scores, but not the very low ones which balance it out. However, this is not sufficient to explain the gender gap:
For whites, the ratios of boys:girls scoring above the 95th percentile and 99th percentile are 1.45 and 2.06, respectively, and are similar to predictions from theoretical models. For Asian Americans, ratios are 1.09 and 0.91, respectively. Even at the 99th percentile, the gender ratio favoring males is small for whites and is reversed for Asian Americans. If a particular specialty required mathematical skills at the 99th percentile, and the gender ratio is 2.0, we would expect 67% men in the occupation and 33% women. Yet today, for example, Ph.D. programs in engineering average only about 15% women (14).
Furthermore, the greater male variability hypothesis applies to both quantitative and verbal IQ, and yet we see no such gap in SAT critical reading scores.
There is a six-point gap between the number of men who take the SAT and the number of women. Therefore, one ought to expect that men who take the SAT are probably smarter than women who take the SAT. But, again, this ought to affect both math and critical reading.
So: the Great Filter. There are various factors which affect whether someone wants to go to college: for instance, people who take the SAT have higher family incomes, are much more likely to be Asian, and (according to this SAT-to-IQ translator) have higher IQ scores. However, there may very well be gender-specific filtering.
Specifically: for some reason, there is a strong selective pressure for men who are good at math to want to go to college.
Imagine that the Czar of College Admissions said “we will solely admit men based on math SAT score, but we will admit women based on composite SAT score”. One would expect math classes to be male-dominated, even if the school at a whole wasn’t. While the Czar of College Admissions doesn’t seem to exist, there may be some other factor acting like the Czar.
Conversely, one might assume that the difference is that six-point gap: people who are marginal at math take the SAT and go to college if they’re female, but not if they’re male. However, it seems puzzling that that would create male-dominated fields, as opposed to balanced fields and female-dominated fields. Perhaps for some reason a slight male dominance in one field ends up driving women away?
There are a lot of unexplained factors in the Great Filter Theory. But I present the problem in the hopes that someone else will find the solution.