3
THE PRESENT SYSTEM AND SUCCESSFUL PROGRAMS

The recent technological explosion has continued to broaden the horizons of the mathematical sciences. But even though much of the new work in applied mathematics, statistics, operations research, and scientific computing has close ties with industry, the bulk of the mathematical sciences community is still employed in academia. Chapter 2 described the European influences that helped shape this system so oriented toward educating research mathematicians for employment in academic research. It is still the case that the doctoral curriculum at many institutions is restricted to classical core mathematics and that traditional educational methods are used. As a result, many researchers lack the broad knowledge needed to address real-world problems, many junior faculty members lack the direction to carry on their research and the experience to acquire funding to support their research, and the system of education is more or less self-contained, with graduates teaching what they have been taught in the same manner that they have been taught. Restricted career opportunities for mathematicians go hand in hand with a system oriented toward educating mathematicians for employment only in academic research.

At present, a large majority of the doctoral and postdoctoral programs in the United States are “standard-model” programs that educate research mathematicians for employment in academia and give too little attention to training for teaching. The following brief description of a research university provides insight into the increasing need for research universities to prepare mathematical scientists who can also teach and who can work effectively in government laboratories, business, and industry.

A research university is a large, complex institution with a multiplicity of purposes. A large staff of researchers, postdoctoral fellows, and other professionals as well as faculty and students, both graduate and undergraduate, are involved in research, education, and service. The nation, the states, and local communities rely on research universities for most of the basic research that is done in the United States as well as for a large part of the applied research. Research universities educate a large proportion of the scholars, researchers, and teachers not only for schools, colleges, and universities but also for business and industry. With few exceptions, all doctoral degrees awarded in the United States are from research universities….

Research and graduate education are often seen as the primary mission of a research university, especially in engineering and the sciences. This emphasis often influences other priorities, although … undergraduate teaching is a growing concern. States and the nation look increasingly to



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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States 3 THE PRESENT SYSTEM AND SUCCESSFUL PROGRAMS The recent technological explosion has continued to broaden the horizons of the mathematical sciences. But even though much of the new work in applied mathematics, statistics, operations research, and scientific computing has close ties with industry, the bulk of the mathematical sciences community is still employed in academia. Chapter 2 described the European influences that helped shape this system so oriented toward educating research mathematicians for employment in academic research. It is still the case that the doctoral curriculum at many institutions is restricted to classical core mathematics and that traditional educational methods are used. As a result, many researchers lack the broad knowledge needed to address real-world problems, many junior faculty members lack the direction to carry on their research and the experience to acquire funding to support their research, and the system of education is more or less self-contained, with graduates teaching what they have been taught in the same manner that they have been taught. Restricted career opportunities for mathematicians go hand in hand with a system oriented toward educating mathematicians for employment only in academic research. At present, a large majority of the doctoral and postdoctoral programs in the United States are “standard-model” programs that educate research mathematicians for employment in academia and give too little attention to training for teaching. The following brief description of a research university provides insight into the increasing need for research universities to prepare mathematical scientists who can also teach and who can work effectively in government laboratories, business, and industry. A research university is a large, complex institution with a multiplicity of purposes. A large staff of researchers, postdoctoral fellows, and other professionals as well as faculty and students, both graduate and undergraduate, are involved in research, education, and service. The nation, the states, and local communities rely on research universities for most of the basic research that is done in the United States as well as for a large part of the applied research. Research universities educate a large proportion of the scholars, researchers, and teachers not only for schools, colleges, and universities but also for business and industry. With few exceptions, all doctoral degrees awarded in the United States are from research universities…. Research and graduate education are often seen as the primary mission of a research university, especially in engineering and the sciences. This emphasis often influences other priorities, although … undergraduate teaching is a growing concern. States and the nation look increasingly to

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States research universities for economic development and to maintain or regain economic competitiveness. Finally, society also looks to research universities for leadership in health care and social programs. Faced with this overwhelming set of institutional responsibilities, a department of mathematical sciences at a research university is pulled in many directions. It is called on to teach mathematics (often including statistics) at all levels to an increasing number of students; to maintain research excellence and help support such excellence in engineering and the sciences; to help support the renewal and invigoration of school mathematics; and to help recruit and attract American students to mathematics and areas depending on mathematics. (NRC, 1991b, p. 7) Due to increasing production, to a large influx of researchers from the Soviet Union, China, Eastern Europe, and elsewhere, and to an economic downturn in the United States, the 1990s have brought a tight employment market with few permanent academic research positions for new PhDs. The increasing production of PhDs (adjusted totals of 884 in 1988–1989, 929 in 1989–1990, and 1061 in 1990–1991 reported in McClure, 1991, p. 1093), normally a sign of health in the field, is currently a mixed blessing because of the following two facts: Although many students are educated for the few jobs in academic research, only a few students are well educated for the many jobs in teaching, government laboratories, business, and industry. Although there are more new PhDs, there are still too few new domestic PhDs, in particular, women and underrepresented minorities. Although the number of new U.S. citizen PhDs has risen recently—there were 411 in 1988–1989, 410 in 1989–1990, and 461 in 1990–1991—the percentage of U.S. citizens among all new PhDs has decreased, from 46% to 43% to 43% (for the same three years). The number of female U.S. citizen recipients of the PhD was 98 in 1988–1989, 89 in 1989–1990, and 112 in 1990–1991. These numbers represent 24%, 22%, and 24%, respectively, of the new domestic PhDs granted in those years. However, these modest figures have been achieved not so much because the number of women receiving PhDs has increased dramatically but because the number of men has decreased. By way of comparison, among the 634 new U.S. citizen PhDs in 1977–1978, 545 were men and 89 (14%) were women, whereas among the 461 new U.S. citizen PhDs in 1990–1991, there were 349 men and 112 (24%) women. The numbers of underrepresented minorities among the new U.S. citizen PhDs continue to be small: in 1990–1991, 10 African-Americans, 6 Hispanics, and 2 Native Americans received a PhD in the mathematical sciences. Although some have questioned whether there are now too many new PhDs for the current employment market, it is clear that both the number and the percentage of new domestic PhDs, especially of women and underrepresented minorities, is far too small.

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States If the profession in general misses the opportunity to work toward a broader vision of U.S. graduate education in the mathematical sciences and also reacts to the current tight employment situation by again looking inward, the result may be a further decrease in both the number and the quality of domestic students in graduate programs. Fortunately, however, some U.S. programs have already moved beyond accepting a limited employment market and limited human resources as facts of life, and seek instead to educate students and postdoctoral associates in ways that make them employable in a wider range of jobs and to attract larger numbers of domestic students, including women and underrepresented minorities, to studies in the mathematical sciences. This report provides information to departments about which methods are already producing success and which are detrimental to success in these two areas. CHARACTERISTICS OF SUCCESSFUL PROGRAMS In its site visits to 10 doctoral/postdoctoral programs, the Committee on Doctoral and Postdoctoral Study in the United States looked for features that were present in successful programs as well as for elements that were detrimental to quality education. The committee noted that successful programs possessed, in addition to the sine qua non of a quality faculty, the following three characteristics: A focused, realistic mission A positive learning environment Relevant professional development The committee also observed during the site visits that there were in some cases significant differences between groups in the same department. One group might be successful in attracting and educating doctoral students or in training postdoctoral fellows and advancing their careers, whereas another would be struggling at both. The degree of success of each part of the program correlated well with the presence of the three characteristics mentioned above. In Chapters 5, 6, and 7, these three characteristics are discussed in detail. First, however, human resource issues are discussed in Chapter 4.