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) a What percentage of bachelor’s degrees in math is now awarded to women (in U.S.)? b Same for Ph.D degrees? 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? What kinds of cognitive differences have been found by scientific studies? In particular, how different are spatial abilities? 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 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 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 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 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 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 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 Math is one of least sex-specific majors 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 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) • “Views [on women and mathematics] are hard to change Actual facts have little influence on those stereotypes.” • “It is clear that many people 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 [...]... 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... 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 progesteron
e and estrogen, in a monthly cycle Biochemical pathways for hormones, from The... "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... 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... 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... 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... 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? ... 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... 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... “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