So a few days ago, I posted a comment on Möbius Stripper's blog (which is very good, by the way--be sure to check out her precalculus bingo board). The comment was a little too long for a comment (sorry MS), and really should have been my own post. So I'm going to crib from it and put it up here.

It's about that pesky gender problem that keeps coming up in discussions of teaching math. In some years, I find the boys in my classes more talented, and in some years it's the girls. It's odd how it's one or the other, but that's my experience. It is definitely *not* my experience, however, that girls just can't do math as well as boys. But on the other hand, of the four truly outstanding math students that have come through our school since I've been there, none are girls. Of the 16 students last year who did well enough on the AMC exam to qualify for the AIME exam (explanation), only one was a girl, and that's typical. Of the 6 members of the 2nd place American Team at the International Math Olympiad (congratulations!), only one is a girl, and that's also typical. And your internal image of a typical math geek is almost surely a boy.

So my theory of all this is as follows:

- Boys and girls indeed approach math somewhat differently if left to their own devices, but
- both approaches can lead to equally competent math students, and each can learn the others’ approach.
- The major differences in achievement past adolescence (like more boys
taking more advanced classes) come not from inherent ability, but from
the timing of adolescent behavior that really
*is*different for boys and girls. for example: - Boys have been demonstrated to be more interested in rules and data than girl when they’re younger. Think of how many boys learn minute details of baseball statistics ("Dude, I'll bet you don't know this one: What happened on the first pitch of the eighth inning of the third game of the 1971 World Series? Foul ball, dude!"), and that’s socially acceptable.
- Girls are (whether through biology or society, for better or for worse) more interested in learning and maintaining the structure of social relationships at that age. Think of how strict girls’ social cliques are compared to boys’. And think of how oblivious most of the boys are.
- This all happens at just about the age (12-15) that kids of both sexes develop the neurons capable of the higher-level abstract thought necessary for real math work. So,
- At just the right time, boys steep themselves in algorithms and numbers, and girls don’t (by which I mean, of course, they engage in those behaviors disproportionately).

The result is that more boys end up interested in more advanced math than girls. Not because girls don't have inherent talent. They do, and in the same proportion as boys--I've seen it. But because social differences (that probably *are* caused by some brain differences, or at least by *extremely* strong socialization pressures) give boys an advantage at just exactly the time when they need it. The observed differences in participation and (to some extent) achievement are an artifact of something completely different.

This means that, in my theory, boys and girls can be taught at the same levels of abstraction, and ought be capable of equal mathematical interest and achievement. But whether they actually *attain* that equality depends to some degree on social conditions at their school.

Okay, that's my theory. I fully admit that it is based on anecdotal evidence (=my classroom experience), and I'd love feedback about my ideas, even if (especially if) you have some expertise in this subject and you're telling me I'm waaaaaay off base.

I've heard that the average math ability of boys and girls is the same, but that boys span a wider range; That is, more boys are very talented and more are complete idiots. I don't know if there's anything to it. Any thoughts?

Posted by: Tom Harrison | August 10, 2005 at 09:11 AM

That is actually what Larry Sanders (Harvard) said in his infamous talk. I remember trying to explain what this meant on a pollitical blog and being decried as sexist (and racist as well for some reason) for explaining what this meant. I pointed out that there were studies that showed this effect, but also indicated I'd not done enough research to evaluate the validity of the studies or determine if their results had been replicated.

Posted by: Vito Prosciutto | August 10, 2005 at 11:51 AM

Thanks for the comments, Tom and Vito. I went and looked up the controversial speech in question, and indeed, Larry Summers (Sanders is the TV show, heh) did cite evidence that men had a higher variability in innate math skill, and then went on to argue that since their standard deviation was higher, you'd expect proportially more men to make it to the very highest ranks of math and science fields. This would simply be because the level of intelligence required would be, say 4 standard deviations off the mean for women, but maybe only 3 for men.

I will admit that Summer's speech appeared to me to be much less sexist than it was portrayed, but I will also admit that the conclusions he reached could easily be rephrased in a very sexist way. He did indeed argue that inherent statistical differences in math ability in the sexes caused more men to be able to do math/science/engineering jobs. A sexist-sounding conclusion from a non-sexist argument.

Very relevant to my post, although I think it neither supports nor refutes my hypothisis. Thanks for your thought!

Posted by: Polymath | August 10, 2005 at 02:41 PM

Interesting post. One comment and one idea:

Comment: I have heard that boys under 10 typically have far less control of fine motor body skills (eg, hand and finger movements) than do girls. Hence, their school work is not as neat as girls' generally is. This may be why girls seem to do better at math (and at school generally) than boys in pre-adolescence.

Idea: If your thoughts are correct, how about a redesign of the high school maths curriculum to emphasize math that is closer to girls' ways of thinking (eg, category theory, visual computer programming) than what is taught now.

Posted by: Peter | October 16, 2005 at 05:29 AM