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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Jean E. Taylor
ΦΒΚ Visiting Scholar
Courant Institute of Math Sciences, NYU
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?
(at NYU last year)
A picture is worth a thousand words … but takes up 300 times the memory.
But 1972 large national study : 39% of males, 22% of females. (Little publicity!)
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.
“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.
Alice Chang women?
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!
`Ms. Benbow, a widely published scholar, said she stood completely by the research in the three articles…’ (Education Week 2006)
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
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.
(1985: Linn and Petersen meta-analysis on on available studies.
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)
(from Los Angeles Times article reprinted in Cape Cod Times, October 8, 2006)
(Davies & Spencer in Gender Differences in Mathematics)
Joshua Aronson, NYU: U.S. students produced no gender differences for Chinese and Japanese students.
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…
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.
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.”
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
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
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).
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
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.
(in series Conceptual advances in brain research)
(in series Conceptual advances in brain research)