This came to me recently and I thought all might be interested.


As you may know, 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.  The Association for Women in
Mathematics has urged the removal of Dr. Benbow from the Panel in order to
avoid actual or perceived bias against women and girls in the Panel's
recommendations. If you are interested in reading a rather lengthy paper
about this-here it is:

1980, 1983, 1988 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) 

Critiques of Methodology Used in 1980s Work
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) 

New Findings Since 1983: Changes in Talent Search Ratios and Other Measures
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 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) 

Recent Talent Search Ratios Not Cited By Benbow and Colleagues 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) 
In 2000, although Stanley had stated the ratio was 4 to 1 three years
earlier,(8) Benbow et al. cited the 1983 ratio of 13 to 1 without mention of
later changes.(17) 
Recent Talent Search Ratios Not Cited By Psychologists 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.)


Recent Talent Search Ratios Not Cited in National Media
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). 
10. J. Stanley, Letter to the editor, Johns Hopkins Magazine, September,
1997, http://www.jhu.edu/~jhumag/0997web/letters.html 
11. R. Monastersky, "Primed for Numbers?" Chronicle of Higher Education, 51,
no. 26 (2005): A1, http://chronicle.com/free/v51/i26/26a00102.htm 
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). 
13. National Science Board, Science and Engineering Indicators 2004 (Vol. 1,
NSB 04-1; Vol. 2, NSB 04-1A), (Arlington, VA: National Science Foundation).
http://www.nsf.gov/statistics/seind04/ 
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-1D06-8E49809EC588EE
DF&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 
24. http://www.thecrimson.com/article.aspx?ref=505363 
  


Judy Ward, Ed.D.
6886 Young Farm Avenue
Springdale, AR 72762
Phone: 479.361.2223
Fax: 479.361.2223
Email: j.e.ward at cox.net

Arkansas Adult Numeracy Campaign
Teaching Mathematics Effectively to Adult Learners