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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States 8 TOWARD MORE SUCCESSFUL PROGRAMS This country's emphasis on science and technology, coupled with generous federal funding, attracted some of the best students to the mathematical sciences during the 1960s and early 1970s. Standard programs worked well then. Today, the pedagogical and technological needs of U.S. society are larger, the available funding is less, and the competition for the human resource pool is more intense. But prudent, thoughtfully introduced changes in doctoral and postdoctoral programs can result in more of the best undergraduates again choosing careers in mathematics rather than in computer science, business, law, or medicine. The health of the mathematical sciences will always depend on having a number of standard programs that offer highly selective doctoral and postdoctoral programs. The observations and recommendations in this report apply to these programs as well as to other departments. However, many departments that do not have the human or financial resources to have a successful standard-model program nevertheless attempt to follow the standard-model. As a result, many capable graduate students do not get a PhD. Those who do are prepared for a career of research, yet only 1 out of 10 PhDs in the mathematical sciences makes a published contribution to mathematical research. (Additional contributions to research in other areas are made by mathematical scientists who have moved into substantive work on applications.) The many PhDs who become full-time teachers after receiving the PhD have often not been given instruction on how to teach effectively. The ones who work in government and industry are often ill prepared for work in applications and do not have well-developed communication skills. The goal of U.S. doctoral and postdoctoral programs in the mathematical sciences should be to provide the well-trained people necessary to meet the needs of all of the mathematical sciences—pure mathematics, applied mathematics, statistics, operations research, and scientific computing—for research, teaching, and work in government laboratories, business, and industry. Teaching involves the instruction of all students, mathematics majors and others, and includes partial responsibility for pre-college instruction and continuing education. A high-quality faculty is necessary for a successful program, but it is not enough. A focused and realistic mission, a positive learning environment, and relevant professional development are the ingredients that create success. The best undergraduate students with strong mathematical backgrounds can choose to continue their studies in the mathematical sciences, the physical sciences, engineering, law, medicine, or other areas. But a larger portion of the best domestic students can be induced to study the mathematical sciences if a program recruits aggressively and also provides a positive learning environment and relevant professional development.
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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States The department has been successful in attracting many domestic students because of its vigorous recruitment in small regional colleges, the warm atmosphere, the renown of the program, the availability of adequate financial aid, and a reputation for placing people in excellent positions on graduation. Committee Site Visit Report The current U.S. system of doctoral and postdoctoral education was created by the combined efforts of the faculty, departmental management, collegiate administrators, and the federal agencies with influence by students and, to some extent, by society. The efforts of these groups have been fundamental not only in creating standard-model programs but also in creating specialized programs. If changes are to occur, the ideas suggested in this report implemented, and new programs created to meet the needs of our technological society, all of these groups will need to cooperate, agree on goals and missions, and find the necessary resources. FACULTY AND DEPARTMENTS A key to all doctoral and postdoctoral programs is the faculty. No program can function without the support, cooperation, and whole-hearted backing of the faculty. Any attempt at assessment and change must involve the faculty from the start. The first step for a mathematical sciences program is an assessment of how well it is functioning. All universities collect data, and some of the necessary information will be available. Many universities conduct periodic reviews of departments and programs through outside teams, whose reports can contain valuable information. It is important to factor into the planning process realistic estimates of the human resources—students and new PhDs—available to the program. The questions about mission, learning environment, and professional development posed in Appendix A may prove useful. The assistance of faculty who are not currently involved in administering the program or department can provide an invaluable objective viewpoint. Involvement of the university administration in the process can have benefits during the implementing of decisions once they are made. Soliciting feedback from institutions that will employ the graduates of the program—colleges and universities, government, and industrial organizations—is useful. After the assessment is complete, the faculty and the department should decide whether the current mission for the program is appropriate or a new mission should be developed. Unless resources are sufficient to permit implementation of a standard mission/model with coverage of a broad range of areas, a more specialized mission should be devised that better fits the resources available. Determining the mission first is important, because many aspects of the learning environment and professional development depend upon the particular mission—for example, how the learning environment and professional
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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States development should be oriented will depend on whether the program is designed to emphasize teaching or industrial applications. Once the mission has been established and the structure set for the learning environment and professional development, recruiting procedures of the kind mentioned in Chapter 4 can be used. Systematic recruiting of undergraduates at colleges and other universities as well as at one's own university does not merely reapportion the pool of candidates. It increases the pool. PROFESSIONAL SOCIETIES Doctoral and postdoctoral education has been a topic at meetings of some committees of the mathematical sciences professional societies. However, no professional society currently has a standing committee devoted solely to this topic. A standing committee—or perhaps three: one in pure and applied mathematics, one in statistics, and one in operations research—with ongoing responsibility for doctoral and postdoctoral education should be established. One of the activities of this committee should be to collect and annually publish statistics on doctoral programs, including statistics on completion rate such as the two types mentioned above in the introduction: (1) the percentage of students who entered a program five years earlier and who have received their doctorates, and (2) the percentage of students who completed their second year of graduate study four years earlier and who have received their doctorates. These statistics would assist departments in assessing their own programs and students in choosing graduate programs. FEDERAL AGENCIES Research support from federal agencies has been one of the foundations of the success of the mathematical sciences in the United States. In the past, this research support has usually been given without an assessment of its effects on doctoral and postdoctoral education. The new practice at the NSF of requesting information on the impact of a grant on doctoral and postdoctoral training is a step in the right direction. This information needs to be taken seriously in evaluating proposals and this policy extended to all federal agencies. The GAANN grants recently instituted by the Department of Education have had the effect of increasing the recruiting activity of departments. Although some of this recruiting activity has resulted in merely reapportioning students to the universities that recruit actively, the long-term effect should be to increase the pool of students. The committee strongly urges continuing the GAANN Program at least until active recruiting becomes part of the community culture.
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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States Another way to support doctoral/postdoctoral education would be to fund grants to support the mathematical sciences infrastructure. Block grants could be awarded to groups that include doctoral students and postdoctoral associates with the stipulation that a major factor in renewal would be the number and quality of the domestic doctoral and postdoctoral students produced by the group. A program that combines the features of the NSF's Minority Predoctoral Fellowship Program and the Department of Education's Ronald E. McNair Post-Baccalaureate Achievement Program would be a powerful factor in increasing the number of women and minority undergraduate and graduate students in the mathematical sciences. Such a combined undergraduate scholarship/graduate fellowship program for women could work as follows. A grant equal (in dollars) to a graduate fellowship would be given to each woman selected and to her undergraduate department: the woman would receive a partial scholarship for her senior year valued at half of a graduate fellowship stipend, and her undergraduate department would receive a grant of equal value. Each woman would be obligated to major in the mathematical sciences. Each woman would receive, in addition, a two-year fellowship to pursue graduate studies in the mathematical sciences. Undergraduate departments would be motivated by this program to identify and encourage women undergraduates starting in their sophomore year, that is, at a time when many women are still in the mathematical sciences pipeline. A similar program could work for students from underrepresented minorities, but it would have to begin a year earlier. Few minority undergraduate students major in mathematics, but a substantial number do take calculus. Departments could identify the outstanding minority students in calculus classes and urge them to apply for such a scholarship/fellowship program in their sophomore year. Two years of undergraduate support of the same type as that for the senior year of the women's program would be needed. The federal support for postdoctoral fellowships in the mathematical sciences should be brought into balance with that for the physical sciences; that is, the number of postdoctoral fellowships should be significantly increased, but without decreasing the number of senior investigators. This could be accomplished by increasing the number of postdoctoral fellowships in larger grants, so as to encourage stronger ties between the postdoctoral associate and the mentor. The recent track record of the mentor in working with postdoctoral associates, not just the quality of the research of the mentor, should be considered in the review of the proposal. The proposed mentor's evaluation of the relevance of the research of the postdoctoral associate should also be considered. In order to provide a larger fraction of new PhDs with an opportunity for a postdoctoral fellowship, restrictions on new PhDs being supported for more than two years by postdoctoral fellowships, whether funded by federal agencies or universities, might be useful. The benefit that new PhDs receive from being postdoctoral associates at research universities is important enough that a larger fraction of new PhDs should have the experience. Postdoctoral fellowships should not be prizes for the few but should be, as
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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States in the physical sciences and in engineering, a next logical step for many qualified new PhDs. THE KEY TO ACTION Changing the American doctoral and postdoctoral system in the mathematical sciences so that it responds better to the needs of the profession, students, and the society is a task that requires the cooperative efforts of faculty, departments, professional societies, and federal agencies. The departments at research universities have a special responsibility to raise the level and increase the knowledge of talented but underprepared entering American doctoral students. Federal agencies should continue their programs and also increase their awareness of the impact of their programs on the doctoral and postdoctoral system. Professional societies should be involved in monitoring change in the universities, the agencies, and the community. But action, if it starts at all, will start from the faculty. The faculty should be aware that creating and maintaining a successful doctoral/postdoctoral program will require additional effort and time. The long-term benefits to the department, the students, and the society are clearly worth the effort.
Representative terms from entire chapter: