When I was in primary school, my math teacher used to be very lenient on girls who struggled with their math assignments, because - as I realize in hindsight - he was of the impression that girls were simply not as capable of doing math as he thought boys to be. Likewise, my German teacher wouldn't fuss as much about sloppy handwriting with the boys as she would for the girls, since boys - in her opinion - were naturally not as good at writing neatly between the lines. Neither of my primary school teachers, were "sexist" (as far as I was able to tell as a then 8 year-old), and most likely they were simply drawing on their past experiences as teachers, regarding the distribution of "natural inclinations" and "abilities" which they had observed.
I don't think you can really blame them for making such inferences, although there is an obvious problem with such behavior: It is a problem of self-perpetuating stereotypes in which teachers think girls are worse at math, girls get away with lesser effort in their math classes, which reduces average math scores for girls, which makes teachers think that girls are worse in math, and so on...
Sometimes, poor science, or even pseudo-scientific data add to the anecdotal observations, such as when George Roman announced in 1887
"that mental abilities were secondary sex characteristics attributable to brain size"
(not quite the statistician, he seemed to have neglected the fact that brain size correlates with women's average smaller body size and lesser weight...), or when Eleanor Maccoby concluded in 1974 that
"gender differences in mathematics performance were scientifically well established"
when she showed data that
"boys and girls acquire early number concepts similarly in the preschool years, [...] and that their performance throughout elementary school was similar"
, (thus apparently indicating similar early math socialization) but that then
"boys' skills in mathematics increased faster than girls' beginning around 12 or 13 years of age, creating a significant gender gap in performance by high school".
Sadly, the study failed to take into account that by age 12 or 13 many more boys than girls enroll in elective math, chemistry and physics classes and that this choice of curricular significantly influences subsequent performance on standardized mathematical tests.
However, even when the analysis is done correctly, and the statistics are solid, it remains that scientists are stuck with having to perform their analysis on indicators of mathematical achievement rather than on mathematical ability (for which no real objective measure exists), and that on most indicators of mathematical achievements women trail men by significant margins.( E.g. there are more male math professors than female professors, and no female has ever won the Fields medal.)
Given this data situation (which is not uncommon in the social sciences in general, and certainly not in economics), one possibility for analyzing the origin of sex differences in math performance exists in looking at changes in the data over time, and in correlating math achievements with indicators of gender equality in order to see if changes in women's role in society have been followed by improved achievements in mathematics.
Last year ago, a study in the Proceedings of the National Academy of Science takes just this approach and in doing so focuses on the following four questions:
- Do gender differences in mathematics performance exist in the general population?
- Do gender differences exist among the highly mathematically talented?
- Do females exist who possess profound mathematical talent?
- How do sociocultural factors correlate with gender differences observed in measured mathematical performance?
Drawing on meatanalysis of the literature and new data gathered as a result of "No Child Left Behind" the researchers find that
"gender differences in performance were close to zero in all grades, including high school. [...] Thus, girls have now reached parity with boys in mathematics performance in the U.S., even in high school where a gap existed in earlier decades."
A question, that is not addressed by the study, but which I am curious about is how much of the narrowing of the gender gap is girls catching up vs how much is boys falling behind; especially as numeracy is one of my pet peeves.
Focusing on the mathematically talented, i.e. the professors and award winning mathematicians, the researchers also find the gap to be closing. This is interesting, since one popular hypothesis regarding sex differences in mathematical (and other cognitive) abilities used to state that possibly men's and women's ability was spread around the same mean, but that men displayed greater variance. This would explain why men dominate the lowest and the highest percentiles for many cognitive ability scores.
However, the researchers not only find the score to be narrowing, but also cite data that shows no difference in variance for math performance in a number of countries. Given that most people will not be willing to extend an hypothesis in which sex differences are the reason for differential math performance in some countries but not in others (which does seem quite absurd), this also seems to indicate that the "greater variance hypothesis", as I shall term it loosely, needs to be discarded.
Question three is quickly answered by a long list of female mathematicians who have contributed significantly to the discipline. Although the reported list is rather long, I must admit that it reads to me like the who-is-who of Big-Brother contestants...I've not heard of any single one on that list.
Getting to the final part of the study, the lead researchers Janet Hyde and Janet Mertz manage to show a significant correlation between the percentage of girls on a country's International Mathematical Olympiad Team, and that country's World Development Indicator Gender Gap Index. The emerging pattern is quite clear: The greater the gender parity in a country, the more girls go to the Math Olympiad; thus indicating a significant role - who could have doubted it - of social equality in girl's performance on this (and other) indicators of mathematical achievement.
Besides actually making me aware of a useful application of No Child Left Behind (who would have thought!?), I like the study in that it makes the point very clearly that, yes, there are differences between boys and girls (e.g. girls have ovaries and monthly cycles; boys do not), but, no, mathematical ability is not one of them. Also, the study gives a nice pep talk on what the U.S. should be doing to improve national math performance, which notably includes doing
"a better job of identifying and nurturing its mathematically talented youth, regardless of their gender, race, or national origin. Doing so is vital to the future of the U.S. economy."
As an economist, a math fan, and a constant advocate for improving numeracy, I can only agree.
Main References:
Hyde, J. S. (2009-06-02) Gender, culture, and mathematics performance. Proceedings of the National Academy of Sciences, 64(4627), 16-8807. DOI: 10.1073/pnas.0901265106 
