Women and Mathematics
Jean E. Taylor
ΦΒΚ Visiting Scholar
Courant Institute of Math Sciences, NYU
math.rutgers.edu/~taylor
Pop quiz (now, 20 & 40 yrs ago)
1. a. What percentage of bachelor’s degrees in
math is now awarded to women (in U.S.)?
b. Same for Ph.D. degrees?
2. In studies of “math talented youth” (e.g. at age
13, scoring over 700 on math SAT), what is the
ratio of boys to girls?
3. What kinds of cognitive differences have been
found by scientific studies? In particular, how
different are spatial abilities?
4. What percentage of tenured positions at
doctoral-degree-granting math departments (in
American universities) is held by women?
Some faces of women in math
Becca Thomases
(at NYU last year)
Cynthia Rudin
Jean Steiner
A picture is worth a thousand words … but takes up 300 times the memory.
4 years of math in high school?
• 1998: sex differences in high school
math participation (including calculus)
had disappeared. (Still differences in
“optional” courses like statistics, in 1990.)
• 1960: 33% of boys, 9% of girls
• Sells 1973 study of random sample of
freshmen entering UC Berkeley: 57% of
males, 8% of females. (Lots of publicity!)
But 1972 large national study : 39% of
males, 22% of females. (Little publicity!)
Percentage of bachelor’s degrees
in math now going to women?
• Answer: About 50%.
• Earlier data:
1949-50: 24% of all BA degrees to women, 23% of BA
degrees in math to women.
1976-77: 46% of BA degrees to women, 42% in math to
women.
• Grades of women in similar math courses are at
least as good as men’s.
• Big difference is in physics and engineering;
often lumped with math. More on that later…
But (NYTimes, 7/9/06),across all fields:
“The idea that girls could be ahead is so shocking that
they think it must be a crisis for boys,” Ms. Mead said.
“I’m troubled by this tone of crisis. Even if you control
for the field they’re in, boys right out of college make
more money than girls, so at the end of the day, is it
grades and honors that matter, or something else the
boys may be doing?”
Or something the hirers are doing? I’ll come back to
that later.
Ph.D.’s in math to women?
• Now: about 30%
• 1968 (e.g.,by my count, from published names) : 6%.
Ingrid Daubechies
Alice Chang
Tenured women in math at Princeton University (2 of 32)
NYAS symposium on The Nature and Nurture of Women in Science April 4,2005,
from summary of talk of Richard Haier, UC Irvine:
Bell curves of male and female IQ scores "essentially completely overlap," Haier said.
This overlap can be found in bell-curve graphs of measures of many cognitive
functions, including visual, spatial, and mathematical reasoning. "But the
controversy," he said, "is why there are so many more men out there on the extreme
than women.“…Test-score statistics, however, point to a considerable difference in
the numbers per gender of extremely able people in math reasoning—people who fill
the top ranks of scientists in certain fields. … Some studies have suggested that the
ratio of males to females with extreme math-ability is 10 to 1. Though that number
may not be completely accurate, Haier said, it suggests the scale of the difference.
BUT IT DOES NOT, and HIS GRAPHS (below) ARE NOT BASED ON ANY DATA!
“Math-talented youth”
• Benbow and Stanley (1980, 1983) (Johns
Hopkins data): male:female ratio among
13-year-olds scoring over 700 on math
SAT was 13:1. Huge publicity!
• Subsequent Johns Hopkins data, Duke
data have showed decreasing ratios; by
late 1990’s, down to under 3:1 (2.8:1)
(I don’t know of any more recent data). No sign that
not still falling.
• Furthermore B-S Methods did not ensure
representative sampling; other issues.
`Ms. Benbow, a widely published scholar, said
she stood completely by the research in the
three articles…’ (Education Week 2006)
• She doesn’t talk about the more recent data.
• She made her reputation on these studies;
she was recently appointed to National
Science Board by Pres. Bush and confirmed
by the Senate
• Newspapers and magazines, and even one
author in Gender Differences in Mathmatics,
still use only the 13:1 figure!
Cathleen Morawetz, Marsha Berger,
Margaret Wright – all at NYU, all
members of the National Academy of
Sciences. Morawetz got a National
Medal of Science + big Canadian prize
From the NYAS symposium:
• Linda Gottfredson, professor in the School of
Education and affiliated faculty in the University Honors
Program at the University of Delaware, however, argued
that innate gender differences are very clear—so clear,
in fact, that a goal of gender parity in all professions
seems unrealistic. Specifically, she said, male minds
show a bias toward interest in things, while female minds
are interested in people, creating what she called a
genetic "tilt" that affects the types of careers they
choose. In this light, supporting an idea of infinite human
malleability "ignores both women’s own preferences and
the huge challenges they face when committed to having
both children and careers."
I will show that “innate gender differences” are NOT at all
clear! And women DO prefer math as much as men! Issue
of children+careers is big, not just for scientists.
What kinds of cognitive differences
found by scientific studies?
• No difference between males and females on
measures like paper folding, embedded
figures, two-dimensional rotation where
required to reason about spatially present
information; large differences for tasks
requiring the rapid mental rotation of 3-D
objects presented as 2-D drawings.
(1985: Linn and Petersen meta-analysis on on available studies.
• Significant difference on math SAT (one-half a
standard deviation)
From Haier’s NYAS talk:
Major difference between men and women: men produce more testosterone,
all the time; women more progesterone and estrogen, in a monthly cycle.
Biochemical pathways for hormones, from The Female Brain
Research since the Linn-Peterson meta-analysis
indicates that differences with regard to mental
rotation have diminished and are amenable to
instruction.
“Longitudinal studies show that
spatial abilities are related to early experiences such
as the amount of time spent playing with blocks.
(from The Female Brain book)
Mental rotations of actual 3D objects, rather than 2D
pictures, show no gender difference (from Gender
Differences in Mathematics).
What does all this have to do with how
women do mathematics? There are very
rarely any strong relationships between
measures of spatial reasoning and
measures of mathematical achievement
when general ability is controlled; many
literature reviews have concluded there is
no relationship.
Also, there is more than one way to do
math.
(driving around Princeton anecdote)
• SAT items that produced the greatest
gender differences for U.S. students
produced no gender differences for
Chinese and Japanese students. (Byrnes,
(Japanese and Chinese elementary
school children tend to disagree with statements
like “The tests students take show how much or
how little natural ability they have.” U.S. children
tend to agree. (Stevenson, Stigler et al.,Learning Gap))
2004).
What makes some research much
better than other?
• Peer-reviewed (by experts chosen NOT by
the author but by an impartial authority
such as a journal editor) and published in
a journal or series known to have high
standards
• Replicable – other people can redo the
experiment, or the steps of the proof, etc.
• References are relevant to the case cited,
graphs based on real data, etc.
• Up-to-date, state-of-the-art
More myths unsupported by data
(from Los Angeles Times article reprinted in Cape Cod Times, October 8, 2006)
• “The sexes see and hear quite differently.” Fact: No
evidence from peer-reviewed studies
• “Women use both sides of brain more symmetrically
due to larger corpus callosum.” Fact: No statistically
significant differences in size or shape of corpus
callosum.
• “Boys biologically programmed to focus on objects,
girls on people.” Fact: This idea based on one study
of day-old babies, demolished by experts. (experiment
lacked critical controls, including fact that day-old infants can’t
hold up their heads independently, and were seated on
parents laps)
• “Boys deductive, girls inductive.” Fact (once it’s peerreviewed!): data on 1,000’s finds no difference.
“Stereotype Threat”
anxiety about confirming a negative stereotype
of one's gender or other social category
• The threat of being personally reduced to these
gender stereotypes can evoke a disruptive state
that undermines women’s math performance.
(Davies & Spencer in Gender Differences in Mathematics)
• Biological basis seems to be increase in cortisol
levels, which can be measured even when
subjects say they don’t feel anxious (Ben-Zeev et
al).
Joshua Aronson, NYU:
• Nature made us very cultural animals, and
cultural environment (like the stereotype that
girls don't like math) has an impact on
performance. In particular, it affects test
performance.
How to study stereotype threat?
• Tell students prior to test that this test in the
past has revealed no gender differences. (Don’t
tell control group that.) Then women in control
group underperformed men, but no such deficit
if told no gender difference (Spencer et al
1999).
• Tell students the test is not diagnostic of their
math abilities. Again, completely eliminated
deficit (Davies, et al 2002)
Different social identities
• Asian-American females: completed a
questionnaire prior to taking difficult math
test; questions were of type “how many
generations lived in America,” or “is your
dormitory coed or single sex?” or neither.
Those primed on Asian-American identity
did better than control group; those on
gender identity, worse.
•Another experiment: some subjects told math
problems were developed for SAT; control group
didn’t refer to SAT, and were told men and women
performed equally well on the test.
•Women in first group were less able to formulate
effective problem-solving strategies,
underperformed men; women in the other group
performed equally well as men. (Note the SAME
test problems were given.)
•Another experiment: 3 person groups. When all
women, women did best, did worse for each man
included in group.
• “Highly practiced or automated skills are
the ones that resist disruption by stressful
circumstances [so little effect of stereotype
threat on easy tests], consistent with the
gender differences in processing
reported..”
• “The negative consequences may be most
striking for ..highly invested and skilled”
The “priming” can be as simple as checking a
box indicating gender before or after taking the
AP Calculus test. Since women normally
experience stereotype threat, this is a very
conservative test. Yet women who indicated
gender before scored significantly lower than
those who did so after. (Stricker 1998). (There is
continuing debate over size of the effect, but it is statisitically
significant—Science 6/2/06, p.1310)
“The reality of stereotype threat is disconcerting” (BenZeev et al) – especially when it might be enhanced by
something as simple as checking a box.
NYTimes, 10/5/06 – Stereotype threat and aging:
The idea is to flash provocative words too quickly for people to be
aware they read them. .In her first study, Dr .Levy tested the memories of 90 healthy older people. Then
she flashed positive words like “guidance,” ”wise,” “alert,” “sage”
and “learned” and tested them again. Their memories were better
and they even walked faster. Next, she flashed negative words
like “dementia,” “decline,” senile,” “confused,” and “decrepit.” This
time her subjects memories were worse, and their walking paces
slowed…
In his [Thomas Hess] studies, older people did significantly worse on
memory tests if they were first told something that would bring to
mind aging stereotypes. It could be as simple as saying the study
was about how aging affects learning and memory. They did
better on memory test if Dr. Hess first told them something
positive, like saying that there was not much of a decline in
memory with age….
It turned out that the people who had more positive
views about aging were healthier over time. They lived
an average of 7.6 years longer than those of a similar
age who did not hold such views…
Tenured women in mathematics at Rutgers between 1973 and 2002:
Jane Scanlon
Tilla Klotz Milnor Weinstein
Not pictured: Helen Nickerson, Joanne Elliott, Katherine Hazard, Barbara
Osofsky, Amy Cohen, me. Ingrid Daubechies came briefly as tenured professor.
What percentage of tenured
positions in the doctoral math
departments held by women?
• 16 of 300 tenured faculty members are female at
the top 10 math departments (a little over 5%).
• Doctoral programs in general: tenured faculty
under 7% female
• In colleges in general, tenured mathematics
faculty are 17% female, tenure-eligible are 31%
female, and other full-time faculty are 47%
female
Reasons so few?
• Constant stereotype threat. Always feel
under suspicion.
• Death of a thousand cuts (Virgina Valian, Why so
few?)
• Women, if turned down on a grant
proposal, often do not submit again; men
do. Women don’t apply at many of the top
places in proportion to their numbers.
Maybe life is tough enough for women
math researchers; asking for possible
additional failure is something to avoid, in
order to preserve that important
confidence, keep cortisol levels down.
• Family issues – following husbands, prime
child-bearing years are same as grad
school, post-doc, and tenure-earning
years.
•
Yet most women mathematicians I know
are married and have had children at
various states in their careers; Tilla
Weinstein had kids while in grad school;
Joan Birman went to grad school after her
children were grown.
• Still, child care is a fundamental, central
issue.
A speculation from Gender Differences in .. :
Females may be “less likely to develop the intense,
almost obsessive involvement with mathematics that
may well be critical to truly outstanding
achievement…For men in the Terman study, the
breadth of interests was a negative predictor of
career success, and women ..[had] broader
interests. The culture of the U.S. places a high value
on being a well-rounded individual, and this
continues to be even more true for women than for
men.”
But again, many ways to do math.
From a friend: “This sort of thing reminds me of the time that I was walking across
campus thinking about math when someone (male, who I did not know)
interrupted my thoughts by telling me to smile. Sometimes I think intense
involvement with anything is incompatible with accepted behavior for women.”
• With respect to traditionally masculine domains
such as math and science, the parents and
teachers of equally gifted children underestimate
girls’ talent and overestimate boys’ talent (Yee and
Eccles, 1988)
• Societal expectation that women should “be
nice.” e.g. (NYT, 9/5/06) instant replay to challenge
line calls at US Open Tennis. Through 9/3, men
challenged 73 calls, women 28. Men were
successful 32% of the time and women 36% of
the time.
Women in political office (NYTimes Mag., 10/29/06):
To be sure, these candidates will not win or lose their races
on the basis of their sex alone. Talent on the stump, credentials and fund-raising
will be decisive. The fact that they have the opportunity to make their case, however, speaks to Western
states’ receptivity to women in public life.
That legacy dates back to the pioneer era
and was partly born of necessity. The agricultural model of the ranch — unlike, say, the Southern plantation — often demanded that the sexes work side by side.
Western states were the first to grant female suffrage, and allowing women access to the ballot was followed by electing them to high office: the first U.S.
congresswoman hailed from Montana, the first female state senator from Utah.
To this day, political parties in Western states tend to be more open to women than the networks that reign in parts of the East
Coast.
“The
process for getting on the ballot isn’t as transparent in states
with entrenched machines,” says Debbie Walsh, director of the Center for American Women and Politics at Rutgers University. She
New Jersey, where county chairmen — and they
are almost always men — often determine who will run. “In
points to her home state,
part because those decisions are generally made behind closed doors, it makes it harder for women to get involved,” Walsh says.
[NJ] and Massachusetts — two states with strong machines — have allmale Congressional delegations, despite their
progressive political leanings.
JUST LIKE MATH DEPTS THAT ARE ALL MALE!
Indeed,
• How to enable greater participation of
women in research in math, physics, and
other sciences is the subject of much ongoing study. See in particular
InterAcademy Council report Women for
Science.
p. 3, Women for Science, InterAcademy Council:
“It has been hypothesized … that the high-level aptitude that
characterizes top scientists and engineers might not be
commonly found in women (Summers, 2005). Yet although
there is a substantial body of psychological and brain
research that verifies some differences between
men’s and women’s mental processes, these differences
have not been linked conclusively to S&T aptitude (Hyde et
al., 1990; Leahey and Guo, 2001). That being the case, the
clearing of existing, well-documented hurdles appears to be a
more practical approach than speculating on women’s innate
aptitudes.”
Hyde, J., E. Fennema and S. Lamon. 1990. Gender differences in mathematics
performance: A meta-analysis. Psychological Bulletin,107(2): 139-155.
Leahey, E., and G. Guo. 2001. Gender differences in mathematical
trajectories. Social Forces 80: 713-732.
My favorite women in mathematics: my daughters!
What about physics, engineering,
computer science?
• Low number of female majors in those subjects
is an object of current study
• Math courses are often required; girls realize
that they can do math, so may keep doing it.
Physics is optional; girls may worry about male
advantage in physics (I sure did).
• Remember stereotype threat; females are less
confident about math (even when doing equally
well). Odds of becoming a science major 5 times
as great for math confident vs. anxious.
• Also (affecting both sexes) these subjects (and math!) usually give
lower grades (= have less grade inflation) than other subjects.
Barnard College 1986 study
• Mean QSAT of ALL Barnard students was higher
than mean of all U.S. males receiving bachelor’s
degrees IN PHYSICAL SCIENCES. So Barnard
students are capable of earning physical science
degree. Yet 45 degrees in physical sciences out of
1074, and 0 degrees in math. And more phys.sci.
majors from group initially uninterested in phys.sci.
than those initially interested!
• Strong influence of math confidence/anxiety,
independent of QSAT scores (some very high
performers had very low math confidence).
Yet small Mount Holyoke College (2000
undergrads) consistently produces more women
graduates per year who go on to get Ph.D.’s in
physical sciences than any other institutions except
MIT, U. of Michigan, U. of Calif. (Rutgers, with its
nearly 50,000 students, was proud to be about at
MHC level).
Self-selection of women who go to Barnard??
Joan Birman,
Barnard/Columbia
Summary
1. Math is one of least sex-specific majors.
2. Top SAT scores of 13-year-olds: boys still outnumber girls, by nearly 3:1, but since ratio still
decreasing, not clear where it will end up.
3. Some cognitive differences, at some points in
menstrual cycle. Spatial: Males better at mental
rotation (only!), but it can be taught. Scores on
math tests are strongly influenced by
“stereotype threat” (cortisol levels); “priming” for
tests can erase gender differences.
4. Tenured at top 10: About 5% female
5. Huge changes over 40 years! But publicity
lacking; sex differences are sexy; negative
results are not.
Some presidents of the Association for
Women in Mathematics (AWM
www.awm-math.org):
Mary Gray, Alice Schafer, Lenore Blum,
Judy Roitman, Linda Keen, Sylvia
Wiegand, Bhama Srinivasan, Barbara
Keyfitz, Carol Wood
Chipman article conclusions
(in Gender Differences in Mathematics)
• “Views [on women and mathematics] are hard to
change. Actual facts have little influence on
those stereotypes.”
• “It is clear that many people do not want to
believe that girls and women can be good at
mathematics…When observed, small mean
differences get mentally transformed into
dichotomized stereotypes.”
• “The topic of sex differences remains far too
sexy a topic.”
• “A case can be made that the primary women and
mathematics problem in the U.S. today is that people
keep talking about the women and mathematics
problem.”
Education is power!
Final words of Susan Chipman:
Education is power. Math is power.
And, it seems, power positions are still not
seen by many as appropriate for women.
Recommended Books
• Gender Differences in Mathematics, edited by Ann
Gallagher and James Kaufman, (Cambridge University
Press, 2005) review by Kessel and Linn to appear AWM Newsletter Sept 2006
• The Female Brain, by Cynthia Darlington, (Taylor and
Francis, 2002) – NOT the 2006 “popular” book of the
same title!
(in series Conceptual advances in brain research)
• Women for Mathematics, by InterAcademy Council,
2006
• Complexities, by Bettye Anne Case and Anne Leggett
(Princeton Univ Press 2005) (some stories about current women
mathematicians)
• Notable Women in Mathematics, by Charlene Morrow
and Perl
Books
• Gender Differences in Mathematics,
edited by Ann Gallagher and James
Kaufman, (Cambridge University Press,
2005) review by Kessel and Linn to appear AWM Newsletter Sept 2006
• The Female Brain, by Cynthia Darlington,
(Taylor and Francis, 2002) – NOT the 2006
“popular” book of the same title!
(in series Conceptual advances in brain research)
• Women for Mathematics, by
InterAcademy Council, 2006