Why are you talking about “shouldn’t” when simple studies shows that common prejudices (i.e. blanket judgements based on right or wrong statistics) *do* influence results?

My favourite study is a math test with Asian-American female students. Half of them were subtly reminded before the test that they were Asian (and thus good at math) and half of them were reminded before the test that they were female. The difference in results of the two groups was significant.

]]>First of all I’d just like to point out that there is no reason that anyone, especially mathematicians should care about the distribution of abilities/accomplishment by gender (or race or anything else) except maybe as a vague PR concern. Certainly they shouldn’t think it reflects on their ability in any fashion. I mean I’m a member of the set of all people who really suck at math + me but that doesn’t give me reason to believe I’m bad at math.

What presumably matters is how conditioning on one’s gender changes your expectation of your mathematical accomplishment. Now if one knew nothing except one’s gender finding out that there was some correlation between gender and mathematical accomplishment. However, anyone who has made it to math grad school (or even taken a test in elementary school) has so much information about their own ability I doubt conditioning on some vague weak correlation should ever substantially adjust that expectation. Moreover, **there is no reason to think that conditioning on gender has to go the same way for math grad students as it does for the population at large.** It’s totally possible that P( x has high math ‘ability’ | x is a woman ) P ( x has high math ‘ability’ | x is in math grad school). In fact so long as you think that women have less encouragement to do mathematics or tend to have fewer role models you should probably think that conditioning on being female increases the expectation of ‘ability’ given that one has made it to grad school regardless of what is true for the population at large.

It’s simply a mathematical fallacy to infer something about female grad students or other distinguished sub-population based on any statistical claim about women at large. Since any given person knows a great deal about their own ability by the time they pass third grade any general result really shouldn’t substantially affect any person’s self-judgment no matter what it says about gender and math.

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Second of all there isn’t even really a meaningful notion of ‘innate math ability.’ Certainly there may be some innate concept of intelligence/brightness but that is only very indirectly related to revealed math ability. There are many people who are quite smart, most are very bad at mathematics because they simply aren’t interested or don’t want to bother to do the work to learn mathematics.

Does being less interested in math count as having less math ability? If not then you can conclude almost nothing about ability from any test or survey of accomplishments. Math ability would become a notion even more ethereal than g (factor supposedly explaning correlations between IQ like tests) with no way to prove the concept even is well defined much less measure it. On the other hand if you want to say that being less interested in mathematics counts as having less mathematical ability the notion ceases to resemble our intuitive concept at all.

After all if I’m better at other subjects/pursuits I will be less interested in doing math. Taking the same person and making them a better artists would reduce their mathematical ability even if we changed nothing else about them. Hell, giving someone better social skills would increase the relative attractiveness of spending time with friends rather than hiding and reading your math book and thus would ‘reduce’ your math ability. On this definition not only is it unclear if having more/less mathematical ability is a good thing for a group (depends on the reasons) but person A might have more mathematical ability than person B even by dint of the fact that person A always does better than B at everything they have equal practice with (thus giving A more options that draw them away from math).

Moreover, this hints at the broader incoherence of most of the nature/nurture debate that assumes that there is a definite answer and that answer maps onto our intuitive idea of ability. Many possible explanations don’t even make sense in these terms. For instance, there are studies showing that girls tend to experience more peer pressure from their female classmates in their pre-college years both to do well in school and to please teachers while boys experience some pressure along the opposite lines (not to look like they are too studious or the teachers pet). Given the way math is taught in pre-college courses I wouldn’t be surprised if listening too much to the pre-college teachers isn’t a serious hinderance to entering real mathematics while kids who ignore the teacher and try to figure it out on their own have an advantage. Now suppose (totally hypothetically) that it turns out this greater social pressure to be studious has some biological basis. Does that mean girls are innately worse at math? The question doesn’t even really make sense on this explanation.

I don’t offer the above explanation because I think it’s particularly probable (one possibility amoung a multitude) but only to point out that there are many explanations on which the whole discussion simply doesn’t turn out to really make sense.

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Anyway I thought you might be interested in these points since you seem to be interested in acutally looking at this from a logical/fact based point of view. However, as I’ve discovered making these kind of logically based arguments doesn’t get through to even most mathematicians on the subject because people don’t parse these claims as factive claims that can be right or wrong. Rather most people parse statements about statistical differences the same way they would parse statistical statements comparing their sports team and it’s rival.

I mean if one was to say, “My team averages twice as many points as yours does each game,” people interpret that as a coded way of saying “my team rocks, yours sucks,” even though it’s totally compatible with my team just focusing on defense. That seems to be more or less how these claims and discussions are interpreted with people so talking about the literal meaning of the claims and what consequences those might have doesn’t really penetrate.

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