Evidence for gender-based math ability differences?

Question

What evidence and counter-evidence is there for mathematical ability for being correlated with gender? If there is a difference, how significant is it (mean vs. variance) and when does it start to become visible? Actual causes for this difference are secondary and outside the scope of this question (although still very valid paths of research and investigation). Also, to further narrow the scope of the question, let's focus on evidence based on Western cultures (Europe, USA, Canada).

The evidence I have so far is this blog post, which finds a correlation between gender and math scores on the GRE and SATs. I also seem to recall finding somewhere evidence that gender-based math differences start as early as first grade, but I can't find the link at this point.

I'm not expecting a conclusive answer, more of a quick summary of the state of the field.

Answer 1

It is generally understood that girls develop a small to moderate deficit in math abilities, compared to boys, over the course of schooling, as measured by mean school grades or test scores (Hyde & Linn, 2006 give a number of .08 standard deviations in favor of men for mathematical problem solving on average, a larger effect favoring elementary school girls, and no difference for high school math; on the maths section of the SAT, girls score ~.3 SD below boys). Similarly, particularly math-heavy academic disciplines (such as physics, maths, computer science) feature a smaller proportion of women than other disciplines, although this effect is attenuated for some surprising cases, such as statistics, and present for some math-light degrees, such as philosophy. This effect is the stronger, the further advanced the position is (e.g., the ratio of female maths BAs is much higher than the ratio of female math PhDs).
All in all, across these various measures, women tend to score slightly worse than men, although not across the board, and extreme differences are only observable in comparatively rare and extreme contexts (e.g., math PhDs).

The variance ratio (that is, how much more men vary compared to women) is somewhere around 1.1 as given by Hyde, indicating that men show a bit, but not much more variance.

These findings concern data from the United States. Janet Hyde has published multiple cross-national meta-analyses on this topic, including:

Cross-National Patterns of Gender Differences in Mathematics: A Meta-Analysis

Gender, culture, and mathematics performance

Gender Similarities in Mathematics and Science

Her primary finding is the culture dependence of this gender gap. For example, she observes the gap not only varies with countries, but also interacts with, for example, gender equality (although see Fryer & Levitt, 2009). It is different for various ethnic groups within countries (e.g., amongst US Asians, women are somewhat more frequently top scorers). Furthermore, the effects are highly variable in time; for example, the ratio of female math PhDs hit an all-time low of 5% in the 1950s, was higher in the pre-war time, and has been on a steady upwards trend ever since.

Combining all of this evidence, it seems to me fair to say that there is currently, in Western countries in this time, somewhat stronger math performance by boys, but that there is no convincing evidence that this pattern is necessarily generalizable.

Answer 2

There is evidence much deeper than simply looking at grades. It should come as no surprise that male and female brains are different(for one the female weights 100 g less or so). Some key differences are that in general - 1.Women learn to speak language earlier than boys , speak more than boys in general, have less speech problems and use both sides of the brain for language 2.Men exceed in visual spatial task, 3d cube folding, labyrinth path finding(solving rubic cube blindfolded or playing chess blindfold for example should come very difficult for women ).

NONE OF THESE makes great difference in math and in math based sciences.

It's a behavioral difference due to testosterone. The old experiment goes(on 6 weeks of age) - give a baby a screen and some kind of rope. When the rope is pulled by the baby colorful images on the screen are changed(stimulus). On random the rope is made to stop working. 1.Typical boy behavior - gets angry, starts pulling with both hands, helping with the foot sometimes and eventually gives up and cry . 2.Typical girl behavior- immediately gives up and starts crying.

On average girl's don't like clinging onto a problem too much time. They just give up.

Furthermore the median should be looked for it is known that boys have greater variability in almost every physical and behavioral characteristic - that is girl's scores are more clustered and boy's are more dispersed. So i would expect that even in area's where women should have natural advantage - the top of the field guys to be men.-