TOO FEW WOMEN WIN AT MATHEMATICS Patricia Clark Kenschaft
The MAA Committee on Participation of Women urges all Americans to help change the cultural patterns that discourage girls and women from pursuing mathematics. In many cultures girls perform mathematically as well as or better than boys . We cannot believe that the biological effects of sex in other countries are different from those in ours.
The cultural conditions given below, although distinct, are not independent. The relationships among them are complex. The Committee has classified them into five preliminary categories (and has suggested other possible groupings at the end of the list):
To help readers identify leading causes, one of the most crucial is placed first within each category of the list (and another last). Many of the statements below might be placed in two or more of these categories. Other possible groupings follow the list.
Minority women are affected by all of these customs. However, some of them damage minority women even more than majority women. Among these are lower expectations of authority figures (#26), lack of role models and mentors (#34), and the effects of isolation (#35). Although most women have problems with departmental sporting activities, other types of social events often provide special disadvantages for minority women even if majority women feel comfortable with them (#38).
2. Society expects that males will be better than females at mathematics; this tends to be a self-fulfilling prophecy . Popular TV shows, movies, books, and computer games--from cartoons to drama--depict males as the scientists, inventors, and initiators. Women are too often valued only when they take off their glasses.
3. The American media give elaborate coverage to discussion of "why girls and minorities can't do mathematics" and ignore those who succeed. For example, the study of Stanley and Benbow claiming that tests of 12-year-olds "prove" innate differences in mathematical ability (presumably because there are no environmental influences on children before the age of 12) have been widely publicized . The impact of this publicity is apparent in the discovery that daughters of mothers who have heard of this study take fewer mathematics courses than daughters of mothers who haven't .
4. Misused statistics slant news coverage . People forget they apply only to populations, not to individuals. That no girl has yet been a member of an International Mathematical Olympiad Team is no reason to say or imply, "...so you won't be either." Also, the statistics women need are not provided. For example, when comparing scores on standardized tests too often a simple mean is used when a stratified sample would reflect more accurately the differing educational background of females.
5. Traditional games and pastimes for boys help to develop quantitative and geometric skills. Examples include computing averages in baseball. strategic computer or board war-games, and following step-by-step directions to build models. Such activities also foster both the cooperative and competitive social habits that are useful in the American mathematical community. In contrast, the traditional games and pastimes for girls encourage play in pairs and foster supportive, non-aggressive personality characteristics . Toys currently are marketed with boys viewed as creative and aggressive and girls as "princesses."
6. Little girl geniuses are more likely to be punished for being eccentric than little boy geniuses. Indeed deviance to any extent (and mathematical enthusiasm is seen as deviance) is often encouraged in males and discouraged in females .
7. The impression that mathematics is "not feminine" causes many adolescent girls to stop taking mathematics. Strong social pressures urge girls to pursue beauty and popularity, leaving less time and energy for individual interests than boys have. Furthermore, American adolescents (of either sex) who excel at mathematics are too often seen as nerds by their classmates, and are often depicted thus, for example, in TV sitcoms. Also, adult mathematicians are often portrayed as less attractive than people in other fields. To the extent that girls, more than boys, have been socialized to please others this affects them more.
8. Americans seem to believe that thoughtful planning is incompatible with caring about people. Thus they conclude that the deliberate planning associated with the precise, analytical, abstract patterns of thinking needed for mathematical analysis is inconsistent with "feminine" traits of nurturing and generosity, which are perceived as spontaneous and not requiring premeditation .
9. Some feminists assert that women in mathematics and related fields have abandoned feminist values .
10. Women before middle age tend to have less money than men. The mean salary for women with a college or postgraduate degree is less than that of men who never entered college . Thus women must work more hours while pursuing an undergraduate and graduate education and are less able to buy time for the study and research after earning a doctorate.
12. Preschool boys, more than girls, are given blocks and construction toys that develop spatial sense. Older boys receive more home training in tools, machines, electrical repairs, and car repairs that reinforces mathematics and introduces skills used in mathematics-based laboratory subjects.
13. In many families the father is regarded as better at mathematics than the mother, and he is the authority for high school mathematics homework .
14. Mothers often respond to a son's inadequate performance in mathematics with, "He must work harder," and a daughter's with, "Oh, I was never good at mathematics either."
15. Boys are more likely to have a home computer than girls .
16. Parents believe that their daughters have to work harder to learn math, and that it is less important for them . It seems likely, therefore, that they support daughters' decisions to drop mathematics more than sons'.
17. Families more often support, financially and emotionally, higher education for their sons more than for their daughters. More than twice as many women as men take jobs at minimum wage upon graduation from high school .
18. Women are expected to do most of the housework and child care, which decreases the time they can devote to research.
19. Doing mathematical research does not require a laboratory or large library, so it can be done practically anywhere. Time spent at home is, therefore, prime research time for many mathematicians (unlike researchers in most fields), but women are more likely to be interrupted at home.
20. A woman is expected to move in order to follow her husband's career. She may interrupt graduate work, separate herself from collaborators and co-authors, and make it harder to find an appropriate position for herself.
22. Teachers at all levels treat male students differently from females so that males have an advantage in mathematics. They tend to ask males higher-order questions  and to give them more encouragement . Favorable comments to boys tend to be about ability, but to girls about neatness . Teachers permit males more freedom to discover alternative solutions to problems, whereas they require females to follow rules more closely .
23. Teachers at all levels pay more attention to male students .
24. Many elementary school teachers themselves had a poor mathematical education , so do not teach it well. Whatever the teacher's preparation, the American mathematics curriculum is comparatively poor . Since girls learn less mathematics outside the classroom, this affects them more.
25. Computer use in most schools is dominated by boys, probably due to their greater experience and their general aggressiveness, which often results in their dominating computer use when only a few are available. Estimates of the ratios of boys to girls at computer camps ranges from 8:1 to 3:1 .
26. The lower expectations of teachers, counselors, and administrators who regard lower mathematics achievement as a sign of inferior ability result in less stimulation and challenge. Thus early mathematical disadvantages of girls are compounded. This pattern is especially severe for minority women .
27. Career counseling given to girls lacks crucial information about mathematics . Mathematics is important preparation for many careers (including social work and nursing), but girls are seldom told this. They therefore study less mathematics less seriously than they otherwise would . They rarely see women mathematicians except high school teachers . Also, too many guidance counselors discourage girls from taking it . Educators and counselors tend to pressure males with no firm career goals, more than females, to take courses that prepare them for potential careers .
28. Interest inventory tests often assume that a sociable person will not be interested in mathematical and scientific fields. Since girls are taught to be more sociable than boys, they are guided away from these fields .
29. Other mathematics-based fields (e.g., engineering and the physical sciences) share most of these 55 cultural patterns and are perceived as "male domains." Since many mathematicians (of both sexes) come to mathematics through these fields, the scarcity of females in such fields means there is a smaller pool from which to recruit women into mathematics than men in college . On December 6, 1989, fourteen women engineering students at the University of Montreal were killed because they were women studying engineering. The gunman passed by men and secretaries. His extremism reflects hostility that is still alarmingly common .
30. The subject matter of required courses in non-mathematical fields tends to emphasize white males. Since self-confidence and self-worth are essential for the continuing diligence required for mathematics, neglecting women and minorities in non-mathematical courses has a negative impact on their participation in mathematics-based fields .
31. Departmental power structures tend to judge men on their promise and women on their past achievements when hiring or tenuring. Despite good intentions discrimination still exists, although fear of lawsuits has moved much of it underground. Data collected by the American Association of University Professors indicates that less than half of the female faculty, 46%, have tenure compared with more than two thirds, 70%, of the male faculty. Furthermore, while the women's percentage has remained roughly constant for over a decade, that of men is climbing. Currently only 80% of full-time women faculty are "on tenure track" compared to 92% of the men, suggesting that this trend is fated to continue . In fields such as mathematics where the proportion of tenure track women is especially small, these effects compound.
32. While laws against sexual harassment have been passed in recent decades, it still exists. One incident can have a devastating effect on a woman. One uncurbed man can affect the careers of many women.
33. Departments where females are underrepresented may be reluctant to hire them on tenure track for fear that it would be hard to deny tenure down the road if the woman is not good enough .
34. The lack of women in college and university faculties deprives young women (and especially minority women) of role models and mentors as they make career decisions. Institutions of higher education are and should continue to be leading employers of women with advanced mathematical training, but a "glass ceiling" seems to prevent women from reaching top positions. Only 4.6% of the full-time women faculty nationally in all fields are full professors compared to 31.4% of the men .
36. The community of women in mathematics is still too sparse and weak to help young women much.
37. The ubiquity of phrases such as "Obviously," "We see at once," and "It is well known that" in mathematical discourse is especially demoralizing for people who have not been encouraged to develop the pioneering, competitive spirit needed to respond, "Would you please explain why that is obvious?" Women may also be more reluctant to write in a style that seems to embody conceit .
38. Departmental sports for bonding (such as student-faculty volley ball, basketball, or baseball games) often exclude women or make them feel unwelcome. In general, social events can be uncomfortable for minority women.
39. The educational system discourages acceptance of feelings of stupidity. High achievement in mathematics, especially mathematical research, requires great intellectual risk-taking; while taking intellectual risks. one feels stupid. "The discomfort of intellectual uncertainty is very difficult to tolerate, all the more if you are on the outside looking in" . Since females and underrepresented minorities are perceived as on the "outside" of the mathematical culture, their uncertainty is often perceived as evidence that they are inadequate, by their peer group, by authority figures, and by themselves.
40. Mathematics has had relatively little financial support for graduate students , a situation that has a greater impact on those who were disadvantaged previously. Also, 19% of the women enrolled in Ph.D. programs in mathematics are providing their own primary support, compared to 16% of the men . Thus the percentage of women supporting themselves is 18% more than the percentage of men.
41. Mathematics and mathematics-related courses are increasingly taught by foreign students who often were raised in cultures that circumscribe women's roles even more severely than ours. "Students complaining about such treatment often receive no support but are told instead to be 'understanding' because that person comes from another culture," reports Bernice Sandler, director of the Project on the Status and Education of Women of the Association of American Colleges .
42. Mathematics departments assign female graduate students to teach a disproportionate number of introductory non-majors' courses instead of the standard calculus sequence. These involve more work and less status and provide less reinforcement of the prerequisites for graduate study .
43. Because only 15% of the mathematics faculty on four-year college faculty (and 31% of those on two-year college faculty) are women , they tend to be overburdened with service on committees, counseling women students, teaching low-level courses where a kindly manner is needed, and other low-prestige (but valuable) activities that take time from the research on which tenure and promotion decisions will tend to be based.
44. A few male faculty members still believe women should not invade the male bastion of mathematics and say so openly, angrily and threateningly. Although not common, they have an impact far beyond their numbers.
45. The mathematical community's habits and expectations, like those of the rest of our society, favor men over women. Much of this behavior is unconscious; it should not be confused with that of the few faculty cited in the previous reason. There is no reason to believe men are more guilty than women, or that mathematicians are more guilty than others. This behavior has been called UWIB, Unconscious Well-Intended Behavior .
46. Some faculty members make overly gloomy predictions of their female students' career prospects.
47. The mathematics community's myth that research is a young person's activity is especially damaging to women because they have children when they are young, if at all . People do mathematics when they have undistracted time. Historically, men have had the most free time in their youth. Emmy Noether and Julia Robinson, however, did their revolutionary work later, after the expectation of childbearing was as over.
48. A tendency to invite the man on a male-female research team to give the speeches about the research, thereby diminishing women mathematicians' visibility and denying role models to younger women and girls. Male co-authors who have protested this pattern have been told they are "better known" than their female colleague--although they themselves have protested that this is due to the imbalance of such invitations! 
49. Cultural taboos against women working closely with men in an equal relationship not involving a sexual liaison are a special problem in a field where intense collaboration tends to be basic for success . The fact that most mathematicians are men is an extra hurdle. Since mathematical creativity usually involves close collaboration, these problems are more serious than in other male-dominated fields. Even when successful, too often the man gets the credit and/or the woman is accused of sexual hankypanky .
51. Women often credit their successes to luck and blame their failures on inability, while men exhibit the opposite pattern. Thus the normal problems of a competitive career can be more discouraging to women than men .
52. A reluctance to be competitive is imbued in women by a society and families preparing them to be compliant wives. This reluctance is a serious disadvantage in a subculture that thrives on openly aggressive behavior, as many mathematical classes and seminars do .
53. Even if their husbands cheerfully do a fair share of the domestic work many women feel guilty, and therefore less efficient, because their earlier brainwashing decrees tihey "should" be doing more .
54. Successful women often have developed excessively high standards for their own work, so they apparently submit for publication only articles that are better than average in their fields. They submit fewer articles to journals, but appear to have an acceptance rate at least as favorable as that of men .
55. It is a rare woman that possesses the combined requirements that she both enjoys men as close companions and has an unusually strong belief in women's capabilities. Without the former she won't develop the collaborators and coauthors so often needed for success in mathematics  and without the latter she may collapse under her own self-doubt.
The reasons listed above can be categorized many ways, with overlaps among the categories common. Misinformation perpetuating inequities is an issue in many contexts (# 1, 7, 8, 9, 16, 27, 28, and 47). The "vicious circle" of fewer females causing fewer females appears often (#2, 3, 7, 13, 14, 24, 26, 34, 35, 36, 38, 39, 43, 45, 49 and 50). Pressure for girls to develop personality characteristics that interfere with mathematical excellence is frequently mentioned (5, 6, 7, 11, 22, 30, and 52), as is the effect of self-fulfilling expectations ( #2, 7, 9, 14, 16, 18, 22, 26, 30, 41, 45, 46, 47, 48, 50, 51, 53, and 54). Fewer opportunities to develop associated skills is a repeating theme (5, 12, 15, 22, 25, 29, and 42). Lack of time (7, 18, and 19) and lack of money (10, 17, 40) are others. Reasons #4, 20, 21, 23, 31, 32, 33, 36, 37, 49, and 55 seem to fall outside these groups: these "miscellaneous" reasons include some of the most sinister. Some reasons cause others (as #1 begetting #26). Some could be interpreted as specific cases of others (as #12 being an especially damaging aspect of #5 or #36 being an extreme example of #34). Each reason above, however, provides a distinct opportunity to change a pattern that prevents women from winning, as much as they might, mathematically and otherwise. The list is certainly not complete. Let us know of reasons we omitted that you think are especially important.
2. Everybody Counts. A Report to the Nation on the Future of Mathematics Education by the Mathematical Sciences Education Board. Washington, DC: Nalional Academy Press, 1989, 9.
3. Ernest, John, Mathematics and Sex. Washington: MAA, April, 1976, 96.
4. Benbow, C.P. and Stanley, J.C., "Sex differences in rnathematical ability: Fact or artifact?" Science 210: 4475 (1980) 1262-1264.
5. Eccles, Jacquelynne and Janis E. Jacobs, "Social Forces Shape Math Attitudes." Signs: Journal of Women in Culture and Society 11: 2 (1986), 367-380.