(Background: this post)
1) Are the NCLB scores surprising?
I don’t think so; I think the difference between NCLB and SAT can be entirely explained by greater male variability and selection effects. The male:female ratio at the 99th percentile of NCLB data is 2.06. If around the top half of high schoolers take the SAT, that corresponds to 98th percentile on the SAT, which has a gender ratio of around 1.9. Similarly the 90th percentile of SAT scores has a gender ratio around 1.5, corresponding the 95th percentile of NCLB with a ratio of 1.45.
(based on this website)
(As I look back at the blog post I notice that these numbers are for whites. I have no idea what to make of the numbers on Asians. I guess I would say anecdotally that Asian girls are more overrepresented relative to white girls in math contests than Asian guys relative to white guys.)
I think that PhD programs in engineering probably require higher than 99th percentile math ability, so it shouldn’t seem that weird that they’re only 15% women. The gender ratio is like 4 for people scoring >100 on the AMC I think, and it only shoots up from there.
2) If it’s all variability, why don’t we see the same results on the verbal SAT as on the math?
I’m not really up on the intelligence research; I read a bunch of Wikipedia while writing this post and came away with the impression “people disagree with each other.” My model of the world is generally “men and women have the same average general intelligence, women have higher verbal intelligence, men higher mathematical, and men have higher variability” and this model rarely leads to my being too confused by the world around me. We know men are better than women at mental rotation, but I don’t know how well this correlates with what we think of as “being good at math.”
Why are the average scores on NCLB math tests the same if men are better at math? Idk. One thing is that NCLB tests, unlike the SAT, don’t actually count for anything and thus students have no incentive to try to do well on them. And in my experience they have a lot of stupid questions that ask you to, like, write a paragraph on the steps you took to add 12 and 15. I always tried to do a good job on those questions, I guess because I’m a girl. But anyway these tests aren’t just testing math ability, they’re also testing ability to explain your work and caring enough to do a good job, neither of which boys are that great at. (Source: interactions with teenage boys. Also, girls do better on the writing SAT than guys despite doing worse on the other two sections.)