The president of the United States has created a National Mathematics Advisory Panel. According to the Executive Order, the Panel is to "foster greater knowledge of and improved performance in mathematics among American students." More information about the panel, its charge, and its members is available at: http://www.ed.gov/about/bdscomm/list/mathpanel/index.html.
The Vice-chair of the Panel is Camilla Benbow, who is best known for the hypothesis that there are intrinsic gender differences in favor of males at the highest level of mathematical performance. Please see below for evidence against this hypothesis and for criticisms of Dr. Benbow's work.
In 1980, Camilla Benbow and Julian Stanley published an article in Science reporting large gender differences in "mathematical reasoning ability."(1) Their evidence was scores on the SAT taken by seventh graders as part of a talent search for a program at Johns Hopkins University. In their conclusion Benbow and Stanley explicitly favored (their word) "the hypothesis that sex differences in achievement in and attitude towards mathematics result from superior male mathematical ability . . . [which] is probably an expression of a combination of both endogenous and exogenous variables."(1)
In 1983, Benbow and Stanley reported that the male to female ratio of Hopkins talent search participants with scores over 700 was 13 to 1.(2)
In 1988, Benbow reported, "the ratio is 12.9 to 1 for the 278 cases reported in Benbow and Stanley (1983b). When in November 1983 SMPY had temporarily completed its national search . . . the ratio remained around 12 to 1." On page 219, she states, "From 1980, the [talent search] samples, have indeed been selected by the same criteria. During this time period there is no evidence for a decrease [in sex difference], rather the opposite." She concluded, "it is clear after the testing of several hundred thousand intellectually talented 12- to 13-year-old students nationwide over a 15-year period that there are consistent [emphasis added] sex differences favoring males in mathematical reasoning ability (or more specifically in SAT-M scores). These differences are pronounced at the highest levels of that ability."(3)
The male to female ratio for students scoring over 700 during the 15-year period was not given explicitly. However, some have interpreted this article as stating that the ratio has remained unchanged for fifteen years.(4),(5)
Benbow’s 14-page article in Behavioral and Brain Sciences is followed by 34 pages of commentary, mainly from psychologists, that includes critiques of methodology.(6) Eccles and Jacobs discuss Benbow and Stanley’s assumptions about students’ formal mathematical experiences in light of empirical studies of SAT performance and course taking. (7) Ruskai notes also that the Hopkins Center practice of sending students brochures stating that boys outperform girls on the mathematics SAT could bias results.(8)
Researchers at the Hopkins Center reported that between 1984 and 1991 the average for this ratio was 5.7 to 1.(9) The Hopkins Center brochures for 1988 and 1989 reported ratios of 4 to 1 and 8 to 1 respectively.(4) In 1997, Julian Stanley wrote that the ratio was 4 to 1.(10) In 2005, the Chronicle of Higher Education reported this ratio was 2.8 to 1.(11)
The Duke University Talent Identification Program (TIP) is a talent search that follows the Hopkins model. TIP was established in 1980. Its regional talent search covers sixteen states in the southeastern, midwestern, and southwestern United States. TIP talent search ratios are shown in the table below. The TIP researchers wrote in 1994, "These findings clearly indicate that the gender gap in mathematical ability is markedly smaller than the data from Benbow’s recent articles would suggest."(12)
The TIP findings and those of the Hopkins talent search are summarized below.
The decline in talent search ratios is consistent with changes in other measures: 48% of the undergraduate mathematics degrees in the U.S. now go to women, up from 40% in the 1970s; (13) about one third of the PhDs in mathematics going to U.S. citizens go to women (this percentage has more than doubled since the 1970s); (14) women have even begun to make inroads into the rarified air of the prestigious Putman competition: for decades no woman placed in the top fifteen, but in 2004 there were four women in this exceptional group. (15)
In 1992, Lubinski and Benbow gave the 13 to 1 ratio. Part of an endnote says that "In American samples, these ratios have been fluctuating over the past decade at least partly as a function of increasing numbers of Asian students entering talent searches. For example, in Asian samples, the proportion of males/females with SAT-M = 700 is 4/1 (this ratio has also been observed in China); in Caucasian samples, the ratio is closer to 16/1."(16)
Psychologists and others have used the 13 to 1 ratio. In his 1998 book, Male, Female: The Evolution of Human Sex Differences, the psychologist David Geary wrote, "The consequences of the sex differences in intrasexual variability are more dramatic for mathematics than for reading and are most extreme in samples of highly gifted people" and gave the 13 to 1 ratio without discussion of any fluctuations. (18) (Geary is a member of the National Mathematics Advisory Panel.)
In 2002, psychologist Steven Pinker’s 2002 prize-winning book,(19) The Blank Slate, also gave the 13 to 1 ratio--again, without discussion of later changes.(20) Pinker wrote, "At the right tail, one finds that in a sample of talented students who score above 700 (out of 800) on the mathematics section of the Scholastic Assessment Test, boys outnumber girls by thirteen to one, even though the scores of boys and girls are similar within the bulk of the curve." Pinker cites Lubinski and Benbow’s 1992 article but apparently did not read the endnote that accompanied the 13 to 1 ratio.
Also in 2002, psychologist Doreen Kimura wrote in Scientific American, "Benbow and her colleagues have reported consistent [emphasis added] sex differences in mathematical reasoning ability that favor males. In mathematically talented youth, the differences were especially sharp at the upper end of the distribution, where males vastly outnumbered females. The same has been found for the Putnam competition, a very demanding mathematics examination. Benbow argues that these differences are not readily explained by socialization."(21) (Two years after Kimura’s article was published, as noted previously, four women were among the top fifteen Putnam competitors.)
In 2005, during discussion of the remarks of Lawrence Summers, the 13 to 1 ratio, as well as Benbow's subsequent work, were cited in the national media, e.g., U.S. News and World Report(22) and Commentary. (23) The Harvard Crimson said, "Summers said the evidence for his speculative hypothesis that biological differences may partially account for this gender gap comes instead from scholars cited in Johnstone Family Professor of Psychology Steven Pinker’s bestselling 2002 book The Blank Slate: The Modern Denial of Human Nature."(24)
1. C. P. Benbow and J. Stanley, "Sex Differences in Mathematical Ability: Fact or Artifact?," Science, 210, no. 12 (1980): 1262-1264, http://www.vanderbilt.edu/Peabody/SMPY/ScienceFactOrArtifact.pdf
2. C. P. Benbow and J. Stanley, "Sex Differences in Mathematical Reasoning Ability: More Facts, Science, 222 (1983): 1029-1031, http://www.vanderbilt.edu/Peabody/SMPY/ScienceMoreFacts.pdf
3. C. P. Benbow, "Sex Differences in Mathematical Reasoning Ability Intellectually Talented Preadolescents: Their Nature, Effects, and Possible Causes," Behavioral and Brain Sciences, 11 (1988): 169-232, http://www.vanderbilt.edu/Peabody/SMPY/BBSBenbow.pdf . See pp. 172, 182.
4. D. Halpern, J. Wai, and A. Saw, "A Psychobiosocial Model: Why Females Are Sometimes Greater Than and Sometimes Less Than Males in Math Achievement," in Gender Differences in Mathematics: An Integrative Psychological Approach, ed. A. M. Gallagher and J. C. Kaufman (Cambridge: Cambridge University Press), p. 66. Halpern et al. write that the ratio is 17:1, probably a typographical error and 13 is meant.
5. M. B. Ruskai, "Guest Comment: Are There Innate Cognitive Gender Differences? Some Comments on the Evidence in Response to a Letter from M. Levin," American Journal of Physics, 59, no. 1 (1991): 11-14, http://www.aps.org/educ/cswp/gender.pdf. See p. 11.
6. C. P. Benbow, "Sex Differences in Mathematical Reasoning Ability Intellectually Talented Preadolescents: Their Nature, Effects, and Possible Causes," Behavioral and Brain Sciences, 11 (1988): 169-232, http://www.vanderbilt.edu/Peabody/SMPY/BBSBenbow.pdf
7. J. Eccles and J. Jacobs, "Social Forces Shape Math Attitudes and Performance," Signs, 11, no. 2 (1986): 367-380.
8. M. B. Ruskai, "Guest Comment: Are There Innate Cognitive Gender Differences? Some Comments on the Evidence in Response to a Letter from M. Levin," American Journal of Physics, 59, no. 1 (1991): 11-14, http://www.aps.org/educ/cswp/gender.pdf.
9. L. E. Brody, L. B. Barnett, and C. J. Mills, "Gender Differences Among Talented Adolescents: Research Studies by SMPY and CTY at Johns Hopkins," in Competence and Responsibility: The Third European Conference of the European Council for High Ability, ed. K. A. Heller and E. A. Hany (Seattle: Hogrefe & Huber, 1994).
12. D. Goldstein and V. Stocking, "TIP Studies of Gender Differences in Talented Adolescents," in Competence and Responsibility: The Third European Conference of the European Council for High Ability, ed. K. A. Heller and E. A. Hany (Seattle: Hogrefe & Huber, 1994).
14. "Annual Survey of the Mathematical Sciences (AMS-ASA-IMS-MAA), Report On The 2004-2005 New Doctoral Recipients," Notices of the American Mathematical Society (2006), http://www.ams.org/employment/2005Survey-DG.pdf. See p. 236.
15. S. Olson, "Nurturing Mathematical Talent: Views from the Top Finishers in the William Lowell Putnam Mathematical Competition," http://www.msri.org/activities/pastprojects/jir/Summary_report.pdf. See p. 5.
16. Lubinski and Benbow, "Gender Differences in Abilities and Preferences Among the Gifted: Implications for the Math-Science Pipeline," Current Directions in Psychological Science, 1(1992): 61-66, http://www.vanderbilt.edu/Peabody/SMPY/CurrentDirections.pdf
17. C. P. Benbow, D. Lubinski, D. Shea, and H. Eftekhari-Sanjani, "Sex Differences in Mathematical Ability at Age 13: Their Status 20 Years Later," Psychological Scientist, 11, no. 6 (2000): 474-487, p. 474, http://www.vanderbilt.edu/Peabody/SMPY/SexDiffs.pdf
18. D. Geary, Male, Female: The Evolution of Human Sex Differences (Washington, DC: American Psychological Association), pp. 314-315 cites Benbow, 1988, Benbow & Stanley, 1980; Stanley, 1993.
19. See list of prizes at http://pinker.wjh.harvard.edu/books/tbs/prizes.html
20. S. Pinker, The Blank Slate: The Modern Denial of Human Nature (New York: Viking, 2002), pp. 344-345. The citations for this statement are: Hedges and Nowell, "Sex Differences in Mental Test Scores, Variability, and Numbers of High-scoring Individuals," Science, 269 (1995): 41-45; Lubinski and Benbow, "Gender Differences in Abilities and Preferences Among the Gifted: Implications for the Math-Science Pipeline," Current Directions in Psychological Science, 1(1992): 61-66, http://www.vanderbilt.edu/Peabody/SMPY/CurrentDirections.pdf.)
21. D. Kimura, "Sex Differences in the Brain," Scientific American, May 13, 2002, http://www.sciam.com/article.cfm?articleID=00018E9D-879D-1D06-8E49809EC588EEDF&pageNumber=3&catID=9 The article does not give a reference for this statement.
22. J. Leo, "What Larry Summers Meant to Say," U.S. News and World Report, February 14, 2005, http://www.usnews.com/usnews/opinion/articles/050214/14john.htm
23. C. Murray, "The Inequality Taboo," Commentary, September 2005, http://www.commentarymagazine.com/production/files/murray0905.html