Women and Mathematics

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Women and Mathematics

• Jean E. Taylor
• F?? Visiting Scholar
• Courant Institute of Math Sciences, NYU
• math.rutgers.edu/taylor

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Pop quiz (now, 20 40 yrs ago)

• 1. a. What percentage of bachelors 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?

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Some faces of women in math

• Becca Thomases

Cynthia Rudin
Jean Steiner
(at NYU last year)
A picture is worth a thousand words but takes
up 300 times the memory.
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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!)

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Percentage of bachelors 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 mens.
• Big difference is in physics and engineering
  often lumped with math. More on that later

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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. Im troubled by this tone of
crisis. Even if you control for the field theyre
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? Ill come back to that later.
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Ph.D.s in math to women?

• Now about 30
• 1968 (e.g.,by my count, from published names)
  6.

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Alice Chang
Ingrid Daubechies
Tenured women in math at Princeton University (2
of 32)
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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
reasoningpeople 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!
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Math-talented youth

• Benbow and Stanley (1980, 1983) (Johns Hopkins
  data) malefemale ratio among 13-year-olds
  scoring over 700 on math SAT was 131. Huge
  publicity!
• Subsequent Johns Hopkins data, Duke data have
  showed decreasing ratios by late 1990s, down to
  under 31 (2.81) (I dont know of any more
  recent data). No sign that not still falling.
• Furthermore B-S Methods did not ensure
  representative sampling other issues.

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• Ms. Benbow, a widely published scholar, said she
  stood completely by the research in the three
  articles (Education Week 2006)
• She doesnt 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 131 figure!

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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
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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 clearso 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 womens 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 childrencareers is big,
not just for scientists.
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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)

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From Haiers NYAS talk
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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
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Research since the Linn-Peterson meta-analysis
indicates that differences with regard to mental
rotation have diminished and are amenable to
instruction. (from The Female Brain book)
Longitudinal studies show that spatial abilities
are related to early experiences such as the
amount of time spent playing with blocks.
Mental rotations of actual 3D objects, rather
than 2D pictures, show no gender difference (from
Gender Differences in Mathematics).
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• 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)

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• SAT items that produced the greatest gender
  differences for U.S. students produced no gender
  differences for Chinese and Japanese students.
  (Byrnes, 2004). (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))

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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

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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 cant hold up
  their heads independently, and were seated on
  parents laps)
• Boys deductive, girls inductive. Fact (once
  its peer-reviewed!) data on 1,000s finds no
  difference.

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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 womens 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 dont feel anxious (Ben-Zeev et al).

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• 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.

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How to study stereotype threat?

• Tell students prior to test that this test in the
  past has revealed no gender differences. (Dont
  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)

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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.

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• Another experiment some subjects told math
  problems were developed for SAT control group
  didnt 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.

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• 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

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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 significantScience 6/2/06,
p.1310) The reality of stereotype threat is
disconcerting (Ben-Zeev et al) especially when
it might be enhanced by something as simple as
checking a box.
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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.
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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
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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.
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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

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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 dont 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.

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• 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.

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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 achievementFor 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.
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• 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.

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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 isnt as transparent in
states with entrenched machines, says Debbie
Walsh, director of the Center for American Women
and Politics at Rutgers University. She points to
her home state, New Jersey, where county chairmen
and they are almost always men often
determine who will run. In part because those
decisions are generally made behind closed doors,
it makes it harder for women to get involved,
Walsh says. Indeed, NJ and Massachusetts two
states with strong machines have all-male
Congressional delegations, despite their
progressive political leanings. JUST LIKE MATH
DEPTS THAT ARE ALL MALE!
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• How to enable greater participation of women in
  research in math, physics, and other sciences is
  the subject of much on-going study. See in
  particular InterAcademy Council report Women for
  Science.

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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 mens and womens mental processes, these
differences have not been linked conclusively to
ST 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
womens 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.
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My favorite women in mathematics my daughters!
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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.

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Barnard College 1986 study

• Mean QSAT of ALL Barnard students was higher than
  mean of all U.S. males receiving bachelors
  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).

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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??
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Joan Birman, Barnard/Columbia
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Summary

• Math is one of least sex-specific majors.
• Top SAT scores of 13-year-olds boys still
  out-number girls, by nearly 31, but since ratio
  still decreasing, not clear where it will end up.
• 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.
• Tenured at top 10 About 5 female
• Huge changes over 40 years! But publicity
  lacking sex differences are sexy negative
  results are not.

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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
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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
  mathematicsWhen 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.

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Education is power!
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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.
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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

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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

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