I stumbled on this 2009 paper illustrating the gender gap in the AMC and other math competitions. It’s a long paper, but here are some highlights:
“…the gender gap widens dramatically at very high percentiles…the highest-achieving girls are concentrated in a very small set of elite schools.” (page 1)
“…the AMC contests…are much better than standard tests at distinguishing among high achieving students.” (page 1)
Regarding the most elite students participating in USAMO and IMO: “Whereas the boys come from a variety of backgrounds, the top-scoring girls are almost exclusively drawn from a remarkably small set of super-elite schools. … This suggests that almost all girls with extreme mathematical ability are not developing their talent to the degree necessary to do very well on Olympiad contests.” (page 3)
Compare typical questions from the AMC 12A (page 7) to questions on the NAEP (used by the US Dept. of Ed.), PISA and TIMSS (pp. 34-36)
4 million US students per year start high school. 1.5-1.8 million take the SAT. 50,000 high school seniors take the AMC 12. (page 9)
Girls who qualify for the China Girls Math Olympiad often attend the most elite schools in the country, including several Bay Area schools. (p. 23, bottom half)
“…even in the highest-level ‘honors’ courses, it is probably unusual to teach material at the level needed to bring students to the 99th percentiles. If girls are less likely to complain and get schools to make special accommodations, then we would expect them to be more underrepresented among students with skill levels that are farther beyond those developed in the classroom.” (page 28)
Math Problem Solving Skills 