Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States (1992)

As a rule, the professional development provided by current doctoral and postdoctoral programs is appropriate for positions at research universities. However, only a small fraction of new PhDs and postdoctoral associates spend their careers at research universities. Most pursue careers in environments quite different from that of a mathematical sciences research department. The majority of new PhDs devote much of their professional lives to teaching undergraduates. An increasing number take positions in government laboratories, business, and industry. Some become involved in pre-college mathematics.

Currently, new PhDs are typically not provided with the professional skills they need for teaching or for work in government R&D, business, or industry. However, in some programs, particularly in many specialized programs, professional development relevant to such positions is provided to the students.

A large percentage of new PhDs, including those from the strongest programs, take positions in which teaching is their principal professional responsibility. However, little time is spent teaching them how to teach.

A surprising number of students (well over half) who were asked about their interests said they were interested in “teaching,” “teaching in a four-year college,” or “curriculum development” in secondary schools. There is no formal notice taken of these interests.

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Because most programs currently support most of their students by making them teaching assistants, these students do have some teaching experience. However, using graduate students as teaching assistants and giving them experience as teachers in a classroom are not the same as training them to be teachers. It was the committee's observation that more structured guidance is needed on how to teach.

During the long years of work toward the doctoral degree, the candidate is rarely, if ever, introduced to any of the ingredients that make up the art, the science, and the special responsibilities of teaching. Yet, the major career option for most holders of the PhD degree is full-time teaching in a college or university. (AAC, 1990, p. 35)

Few universities recognize explicitly in the design of their graduate mathematics programs that the future careers of most of their doctoral students will be devoted primarily to undergraduate teaching. Few if any mathematics graduate programs attempt to familiarize graduate students with important curricular and policy issues of undergraduate education. Few graduate assistants undergo systematic training to prepare them for their lifelong role as teachers. (NRC, 1991b, p. 27)

It is important that all students, especially future educators, have the opportunity to receive instruction on how to teach and to have supervised experience in teaching.

The Department … will develop a seminar for third and fourth year PhD students on [what is involved in] becoming a college professor.

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Departments and programs should assure that their graduate students receive instruction in teaching methods, with assessment and feedback on teaching performance and, if possible, with a progression of increasingly advanced teaching experiences including significant in-class teaching. (AAU, 1990, p. 4)

Professional mathematicians also need communication skills for non-classroom settings, skills such as how to conduct seminars, give professional talks, interact with people working in other sciences and in engineering, and communicate mathematical ideas and results to others in applied/industrial teams. Having students conduct their own seminars is a useful tool for helping them learn how to give professional talks.

One feature of the department's offerings is a course fondly termed the “torture chamber.” This experience, required of every student, is designed to prepare the student to give polished professional talks in her/his field. Faculty provide criticism (considered constructive by the students) and encouragement, and students talked about it with a mixture of dread and admiration.

Committee Site Visit Report

Not everyone is gifted with natural communication skills, but practice and work can lead to improved skills. As much or more than colleagues working in academia, mathematical scientists working in industry need to know how to communicate their knowledge and discoveries.

I have often heard, “My student can't lecture so he/she should consider an industrial job.” This is perhaps the biggest misconception about a non-academic career. Communication skills are even more important outside of classrooms. An industrial researcher interacts with a wide variety of people including engineers, computer scientists, physicists, chemists and business people. The effectiveness of one's work depends on the ability to convey the power and impact of mathematics as well as its beauty and elegance. It is quite possible to explain mathematics in general terms to non-experts. Even a good colloquium talk involves several different levels of depth. Successful communication not only transfers knowledge and insight helpful to others but also brings up good problems, new directions and interesting ideas. (Chung, 1991, p. 560)

Of the full-time mathematical sciences graduate students in 1987, 57% were supported by teaching assistantships, whereas in the physical and biological sciences and in engineering, only 24% of the graduate students were dependent on teaching assistantships for support (NRC, 1990c). This imbalance is due to the lower level of research funding for the mathematical sciences vs. that for the other sciences and engineering, as well as to the service role that has been imposed on mathematical sciences departments. Nevertheless, since teaching is the main professional activity of most students who receive the PhD, better use could be made of teaching assistantships to teach students how to teach.

Graduate students teach too much but are not sufficiently assisted in becoming effective teachers; we find this both ironic and unacceptable. (AAU, 1990, p. 3)

Although most universities normally limit the duties of teaching assistants to 20 hours or fewer per week, some departments still have unrealistic expectations, often neglecting to take into account all duties, including preparing for class, holding office hours, writing, giving and grading exams, and attending instructor meetings.

Students felt that their teaching assistantship duties were consuming more than the nominal 20 hours a week. TAs are asked to teach their own courses and, in addition, grade one of the faculty's classes or participate in research. The time pressures are such that students are reluctant to register for more than two courses per semester. This stretches out their program and leads, in turn, to students running up against the limitation on how much time students are supported.

Committee Site Visit Report

Departments sometimes fill graduate teaching assistantships to meet the teaching needs of the department, often with students who have little hope of getting a master's degree, let alone a PhD. This practice is not only wasteful for the students involved but also detrimental to program morale.

Students should be given responsibilities that reinforce their studies and promote progress toward their degrees. The total number of hours of teaching duties should be limited to 20 or fewer per week so that teaching does not interfere with academic progress. The department should make it clear that the study of mathematics is the primary activity and should design its program to accord with the philosophy that

[t]he primary reason why graduate students should teach is to prepare them to be effective teachers. (AAU, 1990, p. 3)

To prepare graduate students, postdoctoral associates, and temporary faculty for non-academic career paths, programs must provide greater breadth of mathematical experience, which often means including statistics, computational mathematics, or operations research. Students also need to learn and to speak the languages of the disciplines to which the mathematical sciences are applied. The committee visited programs that were very effective in fostering such an approach. Some of these programs had close ties to regional industry.

More mathematical scientists with the PhD should learn mathematics relevant to computations, applications, or interdisciplinary problems so as to fulfill needs for the mathematical sciences in the U.S. technology base.

From engineering design and research to management and organizational structures to the control of smart machines and robots, the computer is leading a revolution that vitally affects the competitiveness of industry and of our entire society. The mathematical sciences are at the basis of many of these changes, and they provide a crucial technology in effecting this revolution. (NRC, 1991a, p. 7)

Computational fluid dynamics, medical scanning technology, spatial statistics, remote sensing, and environmental monitoring are but a few of the areas of applications of the mathematical sciences. These and many other areas (NRC, 1990c, App. B; NRC, 1991a) provide growing opportunities for appropriately trained mathematical scientists. Industrial connections in these areas can lead to support for students, consulting for faculty, jobs for new PhDs, and solutions to problems of economic interest to business and industry. The

committee saw many successful examples of good working relationships between mathematical sciences programs and industry in its site visits.

The department has so many contacts with industry. . . .Industrial recruiters visit the campus and many students take industrial positions.

Committee Site Visit Report

The postdoctoral experience of every new PhD, whether as a postdoctoral associate or a young faculty member, should include time for research. Understanding research and its role in the mathematical sciences is important for anyone doing, applying, or teaching mathematics. Research experience after receiving the PhD is appropriate experience for all careers. Such experience is most appropriately gained in a postdoctoral fellowship at a research university but, due to limitations on funding, may be gained in a research instructorship or term position at a research university. The need for a continuing research apprenticeship in the postdoctoral period reflects the breadth and complexity of the mathematical sciences. Research during the postdoctoral period should be viewed as the logical next step after the doctorate. The committee observed that clustering of postdoctoral associates and junior faculty with senior faculty and graduate students as well as the continuing guidance of a mentor for each postdoctoral associate or junior faculty member are particularly effective in promoting professional growth in research.

The postdoctoral experience should include development in other areas also. Currently, nearly all postdoctoral fellowships are oriented toward doing research alone. Interdisciplinary but mathematics-based postdoctoral fellowships, only a few of which exist, are a way of broadening the fellow's scientific outlook. It would be appropriate to introduce professional development components—teaching or applications— into many more postdoctoral fellowships. Such fellowships could form a bridge to future careers in which teaching or applications are important. A postdoctoral fellowship should be considered to be one step in continuing, lifelong professional development.