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11 Federal Support of Education In this chapter we survey federal support of higher education in the mathematical sciences, considering separately graduate educa- tion, postdoctoral research education, and the continuing education of college teachers. Under this last heading we also note briefly the National Science Foundation's support of certain other activities designed to improve undergraduate education, notably the valuable studies and conferences of the CUPM. As observed in the introduc- tory paragraphs of Part III, our report does not concern itself directly with the extensive activities in support of curriculum re- vision and continuing teacher training for the elementary and secondary school levels. GRADUATE EDUCATION Where graduate students are concerned, federal support of research merges directly into support of education. In fact, one form of graduate-student support, research assistantships, has already been noted above in our discussion of project grants. More important, the intellectual activities central to research and advanced graduate education are literally inseparable, a point that has also been emphasized in the preceding chapter. The CBMS survey found that in academic year 1965-1966 some 750 research assistants were supported on project grants in the mathematical sciences. We observe that, since some 900 senior mathematical scientists (associate and full professors) were on 179

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180 [eve! and Forms of Support federal research grants for the summer of 1966, this gives an average ratio of less than one research assistant to each senior research grantee. We feel that the research assistantship is a valuable form of graduate-student support, especially because of the local control and flexibility in the appointment of research assistants. As a goal for the immediate future, an average ratio of one research assistant to each senior research grantee would seem reasonable, with the ratio continuing to be highest in such mathematical sciences as computer science and statistics, as is the case now. Apart from research assistantships, federal support of graduate students assumes two principal forms: fellowships and traineeships. With the exception of fellowships awarded under the National Defense Education Act (NDEA), fellowships are awarded by the granting agencies directly to students. Traineeships and NDEA fellowships are awarded in blocks to institutions, which in turn award them to students. For fiscal 1966 the CBMS survey found that some 1,200 graduate students in the mathematical sciences were supported on federal fellowships and some 630 on federal trainee- ships. The total magnitude of this support was slightly over $10 million, as shown in Table 15. TABLE 1 5 Federal Fellowships and Traineeships in the Mathe- matical Sciences for Fiscal Year 1966 FORM OF SUPPORT $ MILLIONS NSF predoctoral fellowships NDEA graduate fellowships Other federal fellowships . . NSF trainees. llpS Other federal traineeships SF summer fellowships for teaching assistants TOTAL 3. 3.1 a.: To 1.6 0.2 0.2 Altogether, federal fellowships, traineeships, and research as- sistantships supported about 28 percent of the approximately 9,400 full-time mathematical-science graduate students in U.S. universities in academic year 1965-1966, as Table 16 shows in more detail. As noted in the preceding section, we feel that it is federal sup- port of graduate students together with federal project-grant sup

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Federal Support of Education 181 TABLE 16 Sources of Support of Graduate Students in the Mathe- matical Sciences in Academic Year 1965-1966 NUMBER SOURCE OF SUPPORT PERCENTAGE SUPPORTED SUPPORTED Federal fellowships1,203 13 Federal traineeships632 7 Federal research assistantships;~4 8 Private fellowships366 4 Teaching assistantships3,625 38 Self-supporting2,782 30 ~iOTALS9,362 100 port that has been decisive in the rise of the United States to a pos~- tion of world pre-eminence in the mathematical sciences, and that these forms of support will be decisive for the maintenance of this U.S. position in the future. Furthermore, in the face of the inten- sibed shortage of qualified college teachers of the mathematical sciences discussed in Chapter 7, we are especially concerned that federal fellowship and traineeship programs at least keep pace with, and support, the projected 10 percent per year growth in mathe- matical-science PhD production. Thus we would recommend that federal fellowships and traineeships combined continue to support, as Table 16 shows they did in academic year 1965-1966, about 20 percent of the expanding full-time graduate-student population in the mathematical sciences (see Chapter 2, Recommendation 11~. In accordance with recommendations of our Panel on Under- graduate Education, we also propose two special-purpose programs for support of graduate students in the mathematical sciences. Their aim is to broaden and improve opportunities for graduate study by women and by graduates of weaker or less well-known colleges. The first of these programs, for women, is designed to offset to some degree the dropout rate of women between receipt of the BA and PhD degrees, a rate which postwar figures suggest is perhaps six times as high as the rate for men. The program recognizes that a woman's graduate study may have to be part time or may have to involve retraining after several years' absence. The specific recom- mendation to federal funding agencies is for 100 special part-time graduate fellowships for women. Accompanying this is a recommen

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182 Level and Forms of Support cation to academic institutions to provide more opportunities for part-time employment of women and in particular to remove nepotism rules that prohibit or restrict teaching in the same insti- tution by husband and wife. The second of these programs, for graduates of weaker or less well-known colleges, is designed to afford such students the oppor- tunity to prove themselves in their early graduate years and to encourage them, if successful, to enter college teaching. The pro- gram recognizes that such students represent a "higher risk" and that they may require extra preparatory courses prior to full grad- uate work. The proposal calls for tuition scholarships, perhaps 200 a year, supplemented by "forgivable loans" to cover the initial years in graduate school, with a portion of the loan, perhaps 20 percent, to be forgiven for each year the student subsequently spends in college teaching. More details concerning these two special proposals and the problems they are designed to meet are given in the Report of our Panel on Undergraduate Education, Chapters 1 and 5. POSTDOCTORAL RESEARCH EDUCATION A limited number of research mathematical scientists are supported under various federal postdoctoral fellowship programs. The CAMS survey found that during academic year 1965-1966 approximately 100 U.S. mathematical scientists were in residence at U.S. univer- sities under postdoctoral fellowships and research instructorships. About one third of these were holding awards under the National Science Foundation's regular and senior postdoctoral fellowship programs. Such awards have remained fairly steady in number over recent years, as Table 17 shows. We feel that, especially for the young research investigator, more such support is needed. In all sciences, and certainly in the mathe- matical ones, the immediate postdoctoral years are crucial for firmly launching young PhD's on research careers. At the same # Added in proof: Owing to lack of funds, the National Science Foundation has entirely suspended for academic year 1968-1969 its program of senior postdoctoral fellowships. See Fellowships and Research O pportunities in the Mathematical Sciences, Division of Mathematical Sciences, National Research Council, Septem- ber 1968, p. 3.

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Federal Support of Education ~3 TABLE 17 National Science Foundation Regular and Senior Post- doctoral Fellowships in the Mathematical Sciences REGULAR SENIOR FISCAL YEAR POSTDOCTORALS POSTDOCTORALS 1962 17 ~ 1963 29 5 1964 26 7 1965 21 8 1966 27 7 time many feel that capable young PhD's at academic institutions should be doing some teaching as well as research during these years and should be encouraged to seek teaching positions in a broader range of colleges and universities. Research instructorships and postdoctoral fellowships are pres- ently available for no more than 100 young mathematicians each year; but we feel that by 1969, which is as early as new programs could be implemented, such opportunities could profitably be offered to 200 or 300. This would be about 20 to 30 percent of the 1,000 PhD degrees that we may reasonably anticipate will be awarded in the mathematical sciences in 1969. (Young's PhD study in the CBMS Survey Report16 suggests that in recent years only approximately 15 percent of the PhD's in the mathematical sci- ences have become consistently productive research mathematicians; it is this percentage that we believe can be improved.) For this situation we would like to recommend to federal funding agencies two new programs of teaching fellowships for the immediate post- doctoral years. The first proposal, coming from our Panel on Undergraduate Education, calls for approximately 50 two-year teaching fellowship awards for young PhD's who would carry out research activities at a major mathematical center while teaching a course or two at a nearby smaller college. The purpose is the dual one of helping to launch young PhD's on academic careers of research and teaching while encouraging the distribution of such research and teaching talent to a broader range of colleges. Another proposal deserving serious study would offer two-year teaching fellowships for postdoctoral training at regional centers

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184 Level and Forms of Support located at well-established mathematical centers around the country. Beyond the objective of further training in research and acquisition of teaching experience, there would be the hope that, after two years of working together, small groups of these trained PhD's might be willing to go together to form research nuclei in a uni- versity or in a geographical cluster of smaller colleges. CONTINUING EDUCATION FOR COLLEGE TEACHERS The report) of our Panel on Undergraduate Education and Chapter 9 of the present report have emphasized the importance of keeping college teachers of the mathematical sciences profes- sionally alive and knowledgeable about new developments. The principal academic-year program with this objective is the National Science Foundation Science Faculty Fellowship Program. Table 18 shows the numbers of mathematical awards under this program in recent years. TABLE 1 8 National Science Foundation Science Faculty Fellow- ships in the Mathematical Sciences FISCAL YEAR POSTDOCTORAL PREDOCTORAL FELLOWSHIPS FELLOWSHIPS 962 18 49 963 19 57 964 23 59 965 16 60 1966 16 73 The Science Faculty Fellowship Program offers an excellent way to upgrade and update college and university faculty in the mathe- matical sciences. In view of the continuing and seriously growing need for such upgrading and updating, this NSF program merits very considerable expansion. As a minimal objective, the Science Faculty Fellowship Program should be expanded gradually to provide for about 150 awards in the mathematical sciences by 1971, roughly double the number in recent years. Fiscally this would amount to

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Federal Support of Education 1LS5 an expansion from $1 million to perhaps $~.5 million by 1971. Our Panel on Undergraduate Education has estimated that a program of this expanded size would offer opportunity for awards to approxi- mately one quarter of the doctorate faculty and one half of the non- doctorate faculty at least once in their teaching careers. Only a very limited number of the more than 10,000 college teachers of the mathematical sciences can be on leave in any given academic year to take advantage of fellowship programs. The most favorable time for training activities for larger numbers of college teachers is during the summer. The NSF already sponsors limited programs of such summer activities for college teachers in the form of summer institutes, research-participation projects, and short courses, conferences, and seminars. For college mathematical-science teachers in the summer of 1966 the total magnitude of these pros grams was approximately $1.4 million, the major item being sum . . ~ . mer institutes ot various sorts. The Mathematical Association of America has urged a greatly exported program in this direction in a resolution addressed to the Congress of the United States and the officers of the NSF.4 In addi- tion, the Association's Committee on Institutes and the Panel on College Teacher Preparation of CUPM have issued a joint report on summer institutes5 which says, in part, ". . . a greatly expanded effort in the direction of summer institutes of all types is urgently needed . . . Even if summer institutes are to reach only 10 percent of all college mathematics teachers each summer, the number of institutes will need to be approximately tripled." The NSF also supports, at a modest level, certain other activities designed to improve undergraduate education in the mathematical sciences. Support of these activities encompassing course content improvement programs, curriculum conferences, acceleration of student development, instructional equipment, and visiting scien- tists amounted in 1966 to approximately $2.7 million. An espe- cially important item here has been support of the Committee on the Undergraduate Program in Mathematics. The published cur- riculum studies and recommendations of CUPM have formed valu- able guidelines for college curriculum development in the mathe- matical sciences; these have, in fact, been used extensively by our Panel on Undergraduate Education in writing its report. We feel that continued support of CUPM, as well as of the college visiting lecturer program and these other NsF-funded activities, is justified,

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186 ]:eve! and Forms of Support and we heartily endorse the resolution of the Mathematical Asso- ciation of America to this effects In concluding this section we invite attention to the reports of our Panel on Undergraduate Eduction, and particularly Chapters ~ and 6 of that report, in which the special problems and needs of the undergraduate teacher of the mathematical sciences are dis- cussed in detail.