D. J. Lewis is chair of the department of mathematics at the University of Michigan.
About two years ago, partly in response to urging from Uri Treisman of the University of California at Berkeley, our department decided to get involved in a summer program for undergraduate women. We were motivated to do so because of our concern for the small number of Americans earning doctorates in mathematics. While the number of Bachelors degrees in mathematics awarded by U.S. institutions plummeted from nearly 25,000 per year in the 1970s to 10,078 in 1980-1981, they had slowly risen and stabilized near the 16,000 mark in the late 1980s, with women approaching nearly half that number (about 7,500). On the other hand, the number of women earning doctorates at U.S. institutions seemed stuck near 125. (In the last two years, there have been 156 and 158 doctorates awarded to women, still less than 20% of the total--861 and 892, respectively. The percentage of women among U.S. citizens earning the doctorate is above the 20% mark and is climbing as the number of men doing so continues to decline). Clearly, a likely place to recruit additional doctorates who were U.S. citizens was from amongst women.
That men and women were completing the bachelor's degree in near equal numbers was striking to us, since considerably fewer women than men arrive at college with four years of secondary mathematics, far fewer take advance placement exams (though convergence in numbers may be possible in the near future), and a far larger percentage discontinue the study of mathematics after a year (this is partially explained by the fact that large numbers of women interested in science enter college planning to study biology or medicine, which have low mathematics requirements). We recognized the near parity in numbers stemmed in part from the failure of men to return to mathematics as quickly as women. Still, however you cut the cake, among the women there was a sizable pool of individuals who were persisting to a Bachelor's degree and, under the right circumstances, might go on to the doctorate.
We were also motivated by the fact that, during the 1980s, only five Michigan alumnae received the Ph.D., while in the sixties we regularly sent that many women to graduate school each year. (Other universities had not done much better, only four reached double that number: Berkeley with 14, MIT and Chicago with 12, and Texas with 11.) An added inducement was the discovery that mathematics and physics doctorates are quite likely to have done their undergraduate studies at a research university (40% of the mathematics, 49% of the physics doctorates in the 1980s did so; the figures for women are 32% and 41%). The doctorates in other scientific fields, the humanities, and the social sciences came from a more dispersed set of undergraduate institutions. Clearly we had a responsibility and a challenge.
We realized the social context within which mathematics is now studied and done is quite different from that of the 1960s. In those days, morale was high. Science and mathematics were universally held in high esteem and were well supported. Classes were small and faculty could know their students and their capabilities. Men and women arrived equally prepared, with enthusiasm and willingness to work, and all, as they report, were treated as equals. Today, women find it much easier to gain admission to the old line professional schools of law, medicine, and business and have reached parity with men in enrollments in these schools. We compete with these professions for the same women. One could explain the drop in interest in mathematics at Michigan by our having students well tuned to societal norms. Still, it was a puzzle why a generation of women, raised and steered in the feminist movement, should have withdrawn from mathematics, as seemed the case at Michigan. We hoped we might change the situation.
When we sought funding, we met a cool reception from the agencies. Some funding agencies questioned if there was a need. Some wondered whether interventions and special programs were based on anything but hope and whether there was any evidence they had accomplished their stated goal. The discussions ended with a challenge by Sam Goldberg of the Sloan Foundation to survey the literature concerning undergraduate women in mathematics and physics to see if there were well based principles upon which to base a program for women. With the help of Professor Patricia Gurin of the psychology department, Pat Shure of mathematics, and Carol Hollenshead, director of the Center for the Education of Women, as well as several part-time postdoctorates from psychology, we set to work.
We found that most of the research on women in science and mathematics concerned elementary and secondary students; there is a paucity at the collegiate level. What there is concerning the collegiate level is some what marginal--often one-time snapshots of a local group of student's perceptions or anecdotal reports. Little can be said to be scientific. Except for a few National Science Foundation (NSF) statistical reports, there are no large scale or national studies, and there have been no longitudinal studies. There may well have been critical evaluations of some intervention programs, but they are not reported in the literature. Still, after surveying the literature, one arrives at a number of factors effecting undergraduate student behavior and decisions regarding mathematics and which probably impact more on women than on men. They suggest a number of hypotheses and actions which merit serious testing and which could suggest some modifications in the way mathematicians teach. In addition, we conducted three studies on Michigan students that tended to point to the same factors.
Self-confidence regarding mathematics appears to be the most distinguishing characteristic separating collegiate men and women. There are clear indications that at every level, from middle school to the doctorate, women generally are less confident in their mathematical abilities than men. Successful women report receiving encouragement and assurance of their abilities at several critical junctions from parents and instructors. Women peers rate women mathematicians as far more self-confident, self-reliant, persistent, risk-taking, and imaginative than other women. Yet, despite excellent performances, for many successful women in mathematics, there is always a doubt that they are as good as they are. Perhaps some of this self-doubt arises because the general public has come to view mathematics as masculine and early on women perceive themselves as being outsiders to the mathematical world. If we are to increase the number of women doctorates we will need to find methods to give them honest feedback and reassurance throughout the collegiate experience.
Surprising to me is the evidence that present day women studying mathematics are extremely job oriented and a large proportion at both the bachelor's and master's level chose programs that lead directly to employment, which they then take rather than pursue further education. In this regard, they respond as first generation college graduates, although women earning mathematics degrees are generally children of college graduates having professional mothers. This is a curious finding that surely merits study. Does it spring from lack of confidence? From counselling? From not being expected or encouraged to take the more challenging courses? We found that Michigan women thought the degree requirements too easy!
While it is difficult to obtain hard data, there is strong evidence that women constitute only about 30% of those pursuing a curriculum that leads directly to a doctoral program. Thus, the fact that women constitute about 25% of U.S. citizens earning a mathematics doctorate would indicate we are not losing many well qualified women at the doctoral level and that to increase the number of women doctorates requires getting them into appropriate undergraduate programs.
Women respond more negatively than men to what they perceive to be poor instruction. There is some evidence that quality of instruction is the principle factor in the decision of so many to discontinue the study of mathematics. As already noted, women need feedback on their accomplishments and not just at the end of term. They have a greater need to be recognized as individuals. Further, there is some evidence that women respond negatively to mathematics because of a perception it is a bag of rules and tricks to be applied quickly and mechanically qualities that may often characterize calculus instruction and examination. Women appear to prefer discussive, discovery modes of learning and to dislike the advocacy style of many mathematics lectures. As a rule, women decide their area of concentration much later than men: in mathematics, at the end of the second year or into the third. Their experience in the first two years directly effects their choice. When you examine what is being conveyed by these statements, probably the only way to provide ideal instruction for women (and men also) is via small classes where the instructor has considerable freedom and the size permits regular feedback and interaction between student and professor. Such was the case in the 1960s, and, if we could do so again, undoubtedly the number of women completing the doctorate would climb. Would it change the percentages? Probably not--I expect in that situation men would also respond positively and enthusiastically. We surely need to conduct some scientific studies to determine how to attract and retain the mathematically gifted. Perhaps with good documentation we could persuade deans and government agencies that investing in mathematics instruction would and probably is the only way to meet the nation's mathematical needs.
Two phrases that appeared frequently in the literature coupled with negative responses to mathematics by women were ``competitiveness'' and ``chilly environment.'' These phrases were rather ill-defined and usually were left to questionnaire respondents to define in their own way. In some instances ``competitiveness'' was equated with ``personal comparison,'' at other times as the antithesis to cooperative group learning and study, and still other times with stress associated with the first year or two of study. Whatever it is, the literature suggests that women find mathematics classes and programs infused with competitiveness and find it distasteful. No doubt we need to determine more clearly what is being disliked and whether we can eliminate it and still achieve our objectives. Concern about the competitive environment also shows up in studies of the first year of graduate school. It is not clear that women find the first years of graduate study anymore stressful than their male peers or their peers in law, medical, and business administration schools, where women enrollments are now on a par with that of men. Probably as much of the stress comes from the need to adjust to a new locale, give up old friends and make new ones, and to impress a new set of faculty, as comes from the move to another, tougher level of learning.
The term ``chilly environment'' seems to sum up the totality of micro-inequalities women experience. These are situations or experiences that are subtle, hard to measure, and often based on perceptions. Though each in itself may be minor, they can in totality create an unfriendly environment. There has been no significant study of the ``chilly environment,'' but many women assert its existence within mathematics. Perhaps with today's heightened social awareness, individuals are more apt to respond openly to unintended slights than in the past. The phrase ``chilly environment'' appears sufficiently often that it warrants systematic study. If it is turning off students, we had better investigate it and develop strategies to create ``warm environments.''
The learning environment affects all students, but women still in the process of deciding what to study and for what duration are more effected by the environment in which they will work. The literature indicates women seek good student-faculty interactions, a peer support system, and a sense of community. Faculty undoubtedly need to examine both the social and the physical environment within their departments and seek ways to provide an environment that attracts, supports, and encourages students.
In recent years, considerable emphasis has been put on the role of research internships in helping students form career commitments. The assessments of the Research Experiences for Undergraduates (REU) program of the NSF as well as smaller internship programs, suggest that some research experience can be a key factor in encouraging uncertain students to seek a research career. The NSF study indicated 80% of those in REU programs found the experience heightened their interest in research. At Michigan, for each of the last several years we have had twenty plus undergraduates participate in the REU program. In addition, about the same number took summer internships in industry. Almost all of the REU alumni enrolled in graduate school, and there is an excitement that carries through the following academic year. At least five publications by students have been submitted. Many women approach internships differently than men. They use them to test whether research is for them. It is especially gratifying to see their growth in confidence and in mathematical maturity in the course of a summer internship. By summers end, most know they can do research and that it is challenging and fun. We do not know all the dynamics occurring during the course of the internship. Some women observers have suggested that confidence and self-assurance stems from the support and individual intimacy that occurs in working together.
Thirty years ago, I did not believe undergraduates could assist in a research project. The computer has changed this forever. I have come to the conclusion that in the future the best academic mathematical research will be done by teams consisting of senior faculty, postdoctorates, graduate students and undergraduates working together on a related set of problems. The undergraduates can be very useful to the others in testing hypotheses, seeking patterns, crunching numbers. The postdoctorates can and should play a significant role, in a supportive way, in the education of the graduates and undergraduates. Such groupings flourish in the other sciences, and we will need to learn from them. If we solve the problem of making the first two years of college mathematics attractive, I believe that this group approach, when perfected, will remove the remaining obstacles that now seem to lie in the road to women's success in mathematics and to our attracting the American student to this most beautiful and challenging subject.