There is a lot of evidence that stereotype threat can affect intellectual performance. Steele's early work on the topic looked at the affect of racial stereotypes on the intellectual performance of African Americans. However, he's found that even the performance of white males can be affected by stereotype threat if task-related stereotypes are active. Specifically, when the stereotype that Asian males have better math skills than white males is active, white men perform worse on standardized math tests than when the stereotype is not activated2. More recently, researchers (at Harvard, even) have shown that female undergrads in male-dominated majors (math, science, and engineering majors) experience high levels of stereotype threat compared to women in majors that are not male-dominated, to the extent that they are much more likely than males to consider changing majors3. If women experience stereotype threat in the context of math education, and given that stereotype threat has been shown to affect intellectual performance, it would not be surprising to find that stereotype threat affects women's performance on standardized math tests, and thus plays a role in the much-discussed gender differences in math ability.
The only study on the role of stereotype threat in gender differences in math ability that I remember seeing cited during the debate over the Summers remarks was one by Jason Osborne. Using data from more than 15,000 individuals drawn from a national study of high school seniors, Osborne found that anxiety (not necessarily stereotype-related anxiety) mediated the gender differences in scores on standardized math tests, though the effect of anxiety was fairly small. In other words, anxiety played a role in the gender differences Osborne observed in math performance, but the role was a small one. This studies strength is that it used an extremely large and diverse sample. It's weakness, however, is that it did not look at the role of stereotypes specifically, and that its only measure of anxiety was post-test self-report.
Other studies, which as far as I can tell have been neglected in the discussion of Summers' remarks, have looked at the role of stereotype threat more directly. Spencer et al., for example, found that for a sample of men and women who were highly and equally qualified, gender differences in mathematical performance could be eliminated by reducing stereotype threat4. After showing that their math test produced the frequently observed gender differences, they had participants perform the same test after being told either that the test does not produce gender differences, or that it does produce gender differences. Women who were told that it does not produce gender differences performed as well as men, while women who were told that it does produce them performed significantly worse than men.
Brown and Josephs conducted a similar study, with similar results5. In their first experiment, they either told participants that the math test they were about to take would show whether they were weak in math, or whether they were strong in math. Consistent with the hypothesis that stereotype threat would affect women's performance, female participants who had been told that the test would determine whether they were weak at math (the stereotype-consistent test description) performed worse than female participants who had been told that it twould test whether they were strong in math. Men showed the opposite pattern. They performed better when they were told that the test measured math strength than when they were told that it measured math weakeness. This indicates that the effects of gender-related math stereotypes can be positive or negative. If you are a member of a group that is negatively stereotyped, then stereotype threat will hurt your performance, whereas the performance of members of the group that is positively stereotyped will perform better when the stereotype is active.
Past research (see the paper for citations) has shown that the presence of an "external handicap," i.e., some external factor that may hurt performance, can alleviate stereotype threat. In experiments 2 and 3, Brown and Josephs allowed participants to practice math problems prior to completing the math test. However, for some participants, they produced an external handicap by having the computer crash at the beginning of the practice session. If stereotype threat is hurting women's performance on math tests, then alleviating that threat by providing an external handicap should reduce the effect of the stereotype, and increase performance. Consistent with this prediction, they found that emale participants who experienced the external handicap and were told that the test measured math weakness performed significantly better than participants in the "weakness" condition than women who did not experience the external handicap. Thus, experiments two and three provide another piece of evidence that gender-related math stereotypes are affecting women's math performance.
Another factor that influences the effect of stereotypes on performance is group identification. Individuals who highly identify with a stereotyped group will be more susceptible to the negative effects of that group's stereotypes. Thus, we would expect that women who place more importance on their gender identity will perform worse on math tests when math-related gender stereotypes are activated than women who place less importance on their gender identity. To test this, Schmader conducted a study using participants with either high or low gender identification, and found that women for whom their gender identity was important performed worse on a math test when they were told that the test produced gender differences than men, while women who placed little importance on their gender identity performed as well as men on the same test6.
In another set of studies, Josephs et al. looked at the relationship between stereotype threat and social status7. They hypothesized that for individuals who view math ability as important, high levels of social status concern will increase the efffects of stereotype threat. Josephs and others (see paper for citations) have shown that for both men and women, high levels of testosterone (high-T) are correlated with high levels of status concern. Thus, they predicted that high-T women (women with high levels of testosterone compared to other women),would be more affected by the stereotype, and thus their performance would suffer more than women who had low levels of testosterone (low-T). To test this prediction, they first took saliva samples from participants who rated math ability as important, to measure their current testosterone levels, and then had them complete a short questionaire. Half of the participants completed a questionaire that had previously been shown to prime math-related gender stereotypes, while the other half completed a control questionaire. The participants then completed 20 questions from the quantiative section of the GRE. In their fist study, they found that high-T women performed worse when the stereotype was activated (when they had completed the stereotype-activating questionaire) than when it was not, whereas low-T women performed equally well in both conditions. In fact, high-T women in the stereotype-prime condition performed worse than low-T women in both the stereotype-prime and control conditions, indicating that the effect of the stereotype was quite large for high-T women. Interestingly, in their second experiment, they showed that, consistent with the findings of Brown and Josephs, the effects of testosterone on men are reversed. High-T men actually performed better when gender stereotypes were activated than when they weren't, and better than low-T men in either condition, while low-T men's performance did not differ in the two conditions. High-T men who have had the gender stereotype primed apparently view the test as a way to show off their mathematical abilities, and thus increase their social status.
Finally, researchers have begun to look at the ways in which stereotype threat might affect women's performance on math tests. In one study, Johannes Keller used methods similar to those of Steele et al. (2002), in which participants complete a math test either after having the gender stereotype primed or without having it primed8. Consistent with the other research, he found that females (he used high school students) performed worse than men when the stereotype was active, but as well as men when it was not. He also found that the decrease in performance was largely due to self-handicapping, which is common in the face of stereotype threat. Self-handicapping involves things like decreased effort and attention, procrastination, and similar performance-reducing behaviors. In Keller's study, female participants form who the stereotype was primed were much more likely to perform self-handicapping behaviors.
In another study, Quinn and Spencer primed math-related gender stereotypes, and again showed that women in the primed condition performed worse than women for whom the stereotypes were not active, and that for the latter group, performance was equal to that of men9. In addition to completing the math test, participants in their study also described their problem-solving strategies. Quinn and Spencer then coded these strategies, and found that women in the stereotype-primed condition, women produced fewer and less effective problem-solving strategies. This indicates that stereotype-threat made it more difficult for women to produce problem-solving strategies, and that this reduced their performance on the test. Another interesting result from their study that is not directly related to the role of stereotype threat was that in their first experiment, in which stereotypes were not activated, women performed as well as men on numerical problems, but worse on word problems.
The point of all of this is that several studies have shown that stereotype threat influences women's performance on math tests, and thus is likely responsible for at least part of the observed gender differences in math ability. In fact, given that in most of the studies, gender differences were eliminated when stereotype-threat was absent or reduced, either through indicating that the test does not produce gender differences or producing an external handicap, or in participants for whom stereotypes are not as relevant due to the low importance of gender identity or low levels of social status concern, the role of stereotype-threat in gender differences may be quite large. The fact that Osborne found only a small, though statistically significant effect of anxiety is interesting, but it doesn't speak directly to the role of stereotype-threat, and is overshadowed by the long list of studies that directly demonstrated large effects of stereotype-threat. It would be difficult for innate factors, even those relating to the influence of spatial reasoning ability, to account for much of the data on gender differences in math ability. As of yet, no one has a theory explaining how innate differences account for the fact that gender differences disappear in untimed tests, in numerical problems vs. word problems, and when stereotype threat is alleviated. This doesn't mean that there aren't innate differences, but it does mean that for now, the best evidence we have indicates that social factors play a strong role in gender differences in math, and it would be a mistake to overlook them, particularly in the search for innate differences that cannot explain the data.
1 See e.g., Steele, C. M. (1997). A threat in the air: How stereotypes shape intellectual identity and Performance. American Psychologist, 52, 613-629, or Steele, C.M. (1999, August). Thin ice: “Stereotype threat” and Black college students. Atlantic Monthly, 44-54.
2 Aronson, J., Lustina, M., Good, C., Keough, K., Steele, C., & Brown, J. (1999). When white men can't do math: Necessary factors in stereotype threat. Journal of Experimental Social Psychology, 35, 29-46.
3 Steele, J., James, J.B., & Barnett, R.C. (2002). Learning in a man’s world: Examining the perceptions of undergraduate women in male-dominated academic areas. Psychology of Women Quarterly, 26, 46-50.
4 Spencer, S.J., Steele, C.M., & Quinn, D.M. (1999). Stereotype threat and women's math performance. Journal of Experimental Social Psychology, 35(1), 4-28. See also Walsh, M.,
5 Brown, R.B., & Josephs, R.A. (1999). A burden of proof: Stereotype relevance and gender differences in math performance. Journal of Personality and Social Psychology, 76(2), 246-257.
6 Schmader, T. (2002). Gender identification moderates stereotype threat effects on women's math performance. Journal of Experimental Social Psychology. 38(2), 194-201.
7 Josephs, R.A., Newman, M.L, Brown, R.P., & Beer, J.M. (2003). Status, testosterone, and human intellectual performance: Stereotype threat as status concern. Psychological Science, 14, 158-163.
8 Keller, J. (2002). Blatant stereotype threat and women's math performance: Self-handicapping as a strategic means to cope with obtrusive negative performance expectations. Sex Roles, 47(3-4), 193-198.
9 Quinn, D.M., & Spencer, S.J. (2001). The interference of stereotype threat with women's generation of mathematical problem-solving strategies. Journal of Social Issues, 57(1), 55-71.