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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?

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Women and mathematics

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
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
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.


4 years of math in high school
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
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: women?

“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
Ph.D.’s in math to women? women?

  • Now: about 30%

  • 1968 (e.g.,by my count, from published names) : 6%.


Alice Chang women?

Ingrid Daubechies

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
“Math-talented youth” April 4,2005, from summary of talk of Richard Haier, UC Irvine:

  • 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
From the NYAS symposium NYU, all members of the National Academy of Sciences. Morawetz got a National Medal of Science + big Canadian prize:

  • 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
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)



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.

(from TheFemale 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).


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, 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))


What makes some research much better than other
What makes some research much better than other? U.S. students produced no gender differences for Chinese and Japanese students.

  • 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
More myths unsupported by data U.S. students produced no gender differences for Chinese and Japanese students.

(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 peer-reviewed!): data on 1,000’s finds no difference.


“Stereotype Threat” U.S. students produced no gender differences for Chinese and Japanese students.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: U.S. students produced no gender differences for Chinese and Japanese students.

  • 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
How to study stereotype threat? U.S. students produced no gender differences for Chinese and Japanese students.

  • 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
Different social identities U.S. students produced no gender differences for Chinese and Japanese students.

  • 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 beforeor 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” (Ben-Zeev et al) – especially when it might be enhanced by something as simple as checking a box.


NYTimes, 10/5/06 – Stereotype threat and aging: indicating gender

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
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
Reasons so few? departments held by women?

  • 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 years are same as grad school, post-doc, and tenure-earning years.Gender Differencesin .. :

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, women28. Men were successful 32% of the time and women 36% of the time.


Women in political office (NYTimes Mag., 10/29/06): and science, the parents and teachers of equally gifted children underestimate girls’ talent and overestimate boys’ talent

To be sure, these candidates will not win or lose their races on the basis of their sex alone. Talenton the stump, credentials and fund-raising will be decisive.The fact that they have the opportunity to make their case, however, speaks toWestern 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 transparentin 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, wherecounty 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!



p. 3, math, physics, and other sciences is the subject of much on-going study. See in particular InterAcademy Council report 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! math, physics, and other sciences is the subject of much on-going study. See in particular InterAcademy Council report


What about physics engineering computer science
What about physics, engineering, computer science? math, physics, and other sciences is the subject of much on-going study. See in particular InterAcademy Council report

  • 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
Barnard College 1986 study math, physics, and other sciences is the subject of much on-going study. See in particular InterAcademy Council report

  • 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, 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).

Barnard/Columbia


Summary
Summary 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).

  • Math is one of least sex-specific majors.

  • Top SAT scores of 13-year-olds: boys still out-number girls, by nearly 3:1, 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.


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
Chipman article conclusions (AWM www.awm-math.org):(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! (AWM www.awm-math.org):


Final words of Susan Chipman: (AWM www.awm-math.org):

Education is power. Math is power.

And, it seems, power positions are still not seen by many as appropriate for women.


Recommended books
Recommended Books (AWM www.awm-math.org):

  • 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
Books (AWM www.awm-math.org):

  • 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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