The president of Harvard, Lawrence H. Summers, has caused an uproar in the blogosophere, with comments about alleged differences between males and females in mathematics and science. Unsurprisingly, those on the liberal side of the blogosphere have been quite harsh in their criticism of Summers. Does he deserve the attacks? Short answer: yes. Long answer: hell yes.
The study of sex differences in cognitive abilities has been muddled, for decades, by political agendas on both sides, but there is a fairly clear picture beneath all the muck, and that clear picture is that there is no clear picture. For a long time, it was believed that the primary area in which robust cognitive differences between males and females existed was in spatial-reasoning1. Spatial reasoning, in turn, was thought to underlie what are sometimes called the "secondary" mathematical abilities, i.e. those that we use for the first time in high school math courses (especially geometry and calculus). Those who held these view were not surprised, then, when sex differences in secondary mathematical abilities were discovered. For instance, Casey et al.2 found that for "high-ability groups" (i.e. those who might someday want to make mathematics or math-intensive sciences their careers), superior performance on mental rotation tasks by males explained the bulk of the difference in performance on the math section of the SAT ("high ability" males perform better on the SAT-M than "high ability" females).
The view that there are differences between mathematical abilities in males and females, and that these abilities are due, in large part, to differences in spatial reasoning abilities (to the exclusion of social and affective explanations) is still prominent, and might even be called the received view3. To be fair, there is empirical support for this view (e.g., the Casey et al. study, and those listed in footnote 3). Yet, for decades, there has also been a substantial amount of research demonstrating a.) that spatial differences don't explain differences in math performance and b.) differences in both spatial and mathematical abilities vary greatly depending on the context and population studied. For example, Goldstein et al.4 demonstrated that the performance of females and males on a mental rotation task only differed in a timed version of the task, indicating that the speeded mental rotation task may not be testing absolute spatial ability, but the speed with which people are able to reason about spatial ability. Further, an extensive review of the literature from a 4 decade period showed no significant correlation between spatial and mathematical abilities, but did find a significant correlation between verbal and mathematical abilities5. This review also found that female college students performed better on math tests than males. Another problem is that there appears to be a high degree of intra-individual variability in performance on both math and spatial reasoning tests. Some have even found that females' performance differs depending on their hormone levels, and thus their menstrual cycle6.
This is by no means an exhaustive review of the literature. Such a review would have to be of book length. Still, this is enough to make my point: while it does appear that there may be some specific sex differences in both spatial and mathematical reasoning, exactly what these differences are, and what causes them, is still very unclear. There is, however, one thing about gender differences in acheivement in mathematics and math-intensive sciences that is undeniable: gender discrimination exists, and it does play a significant role. As research on stereotype-threat theory has shown, the existence and consciousness of stereotypes can significantly affect people's performance on stereotype-relevant tasks7. Specifically, female performance on math tests has been shown to be negatively affected by gender stereotypes8.Furthermore, these stereotypes will, consciously or unconsciously, affect the evaluation of female students and job/tenure candidates, a fact that research on implicit attitudes has demonstrated quite well.
This brings us to the real reason why Summers deserves the harsh criticism. He is probably right that there exist real sex differences, across the entire population, in math abilities, but we know too little about the sources of these differences to be speaking definitively about them in public forums. Furthermore, what he is horribly wrong about is the role of discrimination and stereotypes in the success of women in math and science careers, or even on their performance on math and science tests. As Andrew of Universal Acid aptly notes, the existence of innate differences does not necessarily explain all of the differences in acheivement, and since research has shown that stereoptypes and discrimination are responsible for some acheivement differences, Summers' attempt to discount these as factors can only serve to perpetuate those differences. The effects of stereotypes are mediated, in part, by the authority of their purveyors, and when someone in Summers' position reiterates pernicious stereotypes, their negative effects can only increase.
1 See Vandenberg, S. G. & Kuse, A. R. (1978) Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills 47: 599-604, for an old review of the mental rotation literature, on which most of the sex difference theories were and continue to be based.
2 Casey, M.B., Nuttall, R., Pezaris, E., and Benbow, C.P. (1995). The influence of spatial ability on gender differences in mathematics college entrance test scores across diverse samples. Developmental Psychology, 31, 697-705.
3 See e.g., Casey M.B. (1996). Understanding individual differences in spatial ability within females: A nature/nurture interactionist framework. Developmental Review, 16(3), 241-260; Geary, D.C., Saults, S.J., Liu, F., & Hoard, M.K. (2000). Sex differences in spatial cognition, computational fluency, and arithmetical reasoning. Journal of Experimental Child Psychology, 77, 337–353; Hyde, J.S., Fennema, E., & Lamon, S.J. (1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 2, 139-155; and Casey, M.B., Nuttall, R.L., Pezaris, E. (1997). Mediators of gender differences in mathematics college entrance test scores: a comparison of spatial skills with internalized beliefs and anxieties. Developmental Psychology, 33(4), 669-680.
4 Goldstein, D., Haldane, D., & Mitchell, C. (1990). Sex differences in visual-spatial ability: the role of performance factors. Memory and Cognition, 18(5), 546-550.
5 Friedman, L. (1995). The space factor in mathematics: Gender differences. Review of Educational Research, 65(1),22-50.
6 Silverman, I. & Phillips, K. (1993) Effects of estrogen changes during the menstrual cycle on spatial performance. Ethology and Sociobiology, 14, 257-270.
7 Steele, C. (1997). A threat in the air: How stereotypes shape intellectual identity and performance. American Psychologist, 52, 613–629.
8 Osborne, J.W. (2001). Testing stereotype threat: Does anxiety explain race and sex differences in achievement? Contemporary Educational Psychology, 26, 291-310.