2
Background of the VIGRE Program
In the 1980s and 1990s, there was concern within the mathematical sciences community that postsecondary education in the mathematical sciences was in trouble. A series of challenges was identified in several important national reports, many of which provided the intellectual framework for the National Science Foundation’s (NSF’s) Grants for Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE) program. Prominent among these reports were the following:

Renewing U.S. Mathematics: Critical Resources for the Future, also known as the David Report after the chair of the committee, former Presidential Science Advisor Edward David (NRC, 1984);

Its successor report, prepared by a committee also chaired by Edward David (and hence sometimes referred to as David II), Renewing U.S. Mathematics: A Plan for the 1990s (NRC, 1990);

Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States, also known as the Douglas Report after committee chair Ronald Douglas (NRC, 1992);

A study, Graduate Education and Postdoctoral Training in the Mathematical and Physical Sciences, by a panel convened in June 1995 by the Mathematics and Physical Sciences Directorate of the National Science Foundation (NSF, 1996); and

The report of an international panel convened by NSF, Report of the Senior Assessment Panel for the International Assessment of the U.S. Mathematical Sciences, also known as the Odom Report after panel chair General William Odom, former head of the National Security Agency (NSF, 1998).
Together, these reports painted a picture for the mathematical sciences that focused on three major challenges: inadequate funding, insufficient numbers of students interested in mathematics, and shortcomings in the shape and direction of postsecondary mathematics education. This chapter reviews the state of education in the mathematical sciences in the 1980s and 1990s, as perceived by NSF, in order to understand the deficiencies that VIGRE was intended to ameliorate.
FUNDING FOR MATHEMATICAL SCIENCES IN THE 1980s AND 1990s
Federal support in the mathematical sciences is provided largely by NSF, and to a lesser extent by the Department of Defense (DOD) through the Office of Naval Research (ONR), the Army Research Office (ARO), and the Air Force Office of Scientific Research (AFOSR). Additionally, some funding is provided by the Department of Energy (DOE), the National Security Agency, and the National Institutes of Health (NIH), and minor amounts come from other federal agencies. In the 1990s, funding from NIH rose to match that provided by DOE. As the Odom Report noted and as is illustrated in Table 21: “The NSF provides the majority of support for mathematical research in U.S. universities and institutions” (NSF, 1998, p. 38).
The reports mentioned above raised three concerns about funding for the mathematical sciences: (1) federal funding was perceived as inadequate to sustain and grow the field, (2) funding was too heavily dependent on NSF, and (3) the modes of support and the targets of funding were imbalanced, with too much emphasis on investigators and not enough on graduate students and postdoctoral researchers, and with graduate support focused heavily on research assistantships with little allocated to fellowships and traineeships that would help professional development in other ways.^{1}
The David Report, which presented a “state of the field” in the early 1980s, cogently made the case for a higher level of funding for the mathematical sciences. In drawing its conclusions, the report focused on federal support for mathematical research in universities, federal support for students, and the budgets of federal agencies. Overall, the report found the following:

Federal support for the mathematical sciences research enterprise stood in 1982 at less than twothirds its 1968 level (in constant dollars);

the principal reduction occurred during the period 196873;

it was followed by nearly a decade of zero real growth in support;

these budgetary events occurred during the peak in growth of the field—growth in the range and depth of uses of mathematics, with a concomitant doubling of the number of mathematical scientists productively engaged in research (NRC, 1984, p. 36).
The followup to the David Report, released in 1990, indicated that there had been some improvement in the funding situation. David II noted: “NSF support of mathematical sciences research nearly doubled (almost 50% real growth compared to 29% for total NSF R&D) over the six years from FY 1983 to FY 1989” (NRC, 1990, p. 22). Likewise, “The Department of Energy (DOE) doubled its support for the mathematical sciences over the period from FY 1984 to FY 1988” (ibid., p. 26). The picture at DOD was more complex: although support had increased, much of it was “because two new mathematical sciences research programs were created, one at the Defense Advanced Research Projects Agency (DARPA) and the other at the National Security Agency (NSA)” (ibid., p. 24). While noting this progress, David II also pointed out that the increases were far from meeting the goals laid out in the David Report. The Odom Report noted that “students of these [mathematical sciences] programs are provided substantially less federal funding than are students of the other sciences” (NSF, 1998, p. 31). Figure 21 shows that total academic research and development (R&D) expenditures at universities in mathematics and statistics had been rising over the 1980s and 1990s, although the percentage coming from federal sources had been declining.
TABLE 21 Federal Obligations to U.S. Universities and Colleges for Research in Mathematical Sciences, 19801998 (in thousands of current dollars)
Year 
USDA 
DOD 
DOE 
DHHS—NIH 
DHHS—Other 
NASA 
NSF 
Total 
Percentage NSF 
1980 
282 
16,121 
2,921 
3,671 
0 
1,344 
24,686 
49,025 
50 
1981 
1,492 
20,991 
3,350 
3,975 
0 
862 
28,815 
59,485 
48 
1982 
1,107 
24,362 
3,163 
4,079 
0 
937 
30,630 
64,278 
48 
1983 
1,051 
27,493 
3,972 
4,074 
0 
834 
34,869 
72,293 
48 
1984 
1,032 
30,181 
3,393 
5,251 
0 
416 
38,133 
78,406 
49 
1985 
973 
32,239 
11,384 
3,733 
0 
833 
47,816 
96,978 
49 
1986 
833 
35,066 
12,812 
4,615 
0 
761 
51,079 
105,166 
49 
1987 
704 
32,526 
17,051 
4,520 
0 
953 
55,784 
111,538 
50 
1988 
615 
33,152 
15,958 
5,759 
0 
1,115 
61,199 
117,798 
52 
1989 
497 
32,165 
13,727 
4,666 
0 
998 
63,155 
115,208 
55 
1990 
353 
36,551 
17,155 
5,642 
0 
989 
68,501 
129,191 
53 
1991 
867 
25,829 
16,280 
6,477 
0 
623 
71,834 
121,910 
59 
1992 
678 
39,961 
15,122 
5,299 
467 
873 
88,045 
150,445 
59 
1993 
632 
39,716 
7,575 
6,473 
456 
684 
80,351 
135,887 
59 
1994 
466 
48,030 
9,070 
7,433 
353 
689 
74,997 
141,038 
53 
1995 
567 
35,190 
0 
19,984 
128 
917 
76,368 
133,154 
57 
1996 
297 
35,019 
0 
24,290 
7 
641 
75,716 
135,970 
56 
1997 
203 
20,263 
7,297 
9,320 
381 
841 
79,862 
118,167 
68 
1998 
610 
29,183 
7,280 
9,993 
308 
816 
84,326 
132,516 
64 
NOTE: Acronyms are defined in Appendix F. SOURCE: National Science Foundation, “Survey of Federal Funds for Research and Development,” accessed via WebCASPAR, http://webcaspar.nsf.gov. 
The second concern raised by the four important national studies cited was the concentration of funding. The Odom Report suggested that NSF had a high level of responsibility for the stewardship of the mathematical sciences (NSF, 1998, p. 38). This is clear from Table 21, which shows support for the mathematical sciences from several federal agencies. The David Report put it somewhat differently, suggesting that NSF might inadvertently have had too much control over policies that should be made by, or with, the broader research community. NSF’s proportion of federal support for graduate students rose from 30 percent in 1980 to about 37 percent in 1998, with most of this occurring between 1984 and 1985, and irregularly otherwise (see Figure D1 in Appendix D, “The Mathematical Sciences Since 1998,” in this report).
The third point of concern was that federal funding in the mathematical sciences was imbalanced in major ways that hindered the support for and development of young people. As Figure 22 shows, most graduate students were supported by nonfederal sources of funding (about 70 percent), followed by selfsupport (about 20 percent). Federal sources only supported about 10 percent of fulltime graduate students in mathematics and statistics during the 1980s and 1990s, and that support was relatively flat as a proportion of total support (although the number of graduate students changed over this time, as noted in Table B4 in Appendix B, “The Mathematical Sciences in the 1980s and 1990s,” in this report).
The Odom Report noted: “Despite the excellence of the U.S. graduate programs in the mathematical sciences, the students of these programs are provided substantially less federal funding than are students of the other sciences. They depend almost entirely on teaching assistants stipends and on their own resources” (NSF, 1998, p. 31). As Figure 23 shows, most students who received support relied on teaching assistantships (TAs) or other mechanisms of support. These mechanisms tend to lengthen the time to degree.
In terms of support mechanisms, federal sources rarely funded fulltime graduate students through teaching assistantships—99 percent or more of TAs were funded by nonfederal sources such as state
university funds. On the other hand, about half of research assistantships were funded through federal sources, as indicated in Table 22.
The NSF (1996) report noted that the funding approach had helped to create an imbalanced focus on research.
Since the main criterion for judging grant applications has traditionally been the quality of the research to be performed, along with the success of past research, this is necessarily where the attention of grant applicants must be focused. Not only does this affect the principal investigators, who may believe they are expected to give lower priority to other aspects of the education of their students in order to keep the funding pipeline open, but it affects graduate and postdoctoral students themselves, who perform most of the labor involved in such research and who are often effectively discouraged from spending time on other educational pursuits not directly involved in their advisor’s research project. [Moreover,] [t]he current funding mechanism (where graduate students are supported primarily by Research Assistantships) also has the effect of allowing a lengthening of the time to obtain a Ph.D. Successful researchers are understandably unwilling to lose graduate students when they have finally become highly productive, and these students may, in turn, prefer the protected, known world of the university over a usually unknown “outside” world. (NSF, 1996, pp. xi, xii)
Table 23 shows, for instance, that NSF had used research assistantships most often in supporting graduate students.
Postdoctoral researchers and investigators also faced funding issues in the 1980s and 1990s. According to the Odom Report:
TABLE 22 Percentage of Each Mechanism of Support for FullTime Graduate Students in Mathematics and Statistics in the United States That Comes from Federal Sources, 19801998
Year 
Fellowships 
Research Assistantships 
Teaching Assistantships 
Traineeships 
Other Mechanisms of Support 
1980 
17 
54 
0 
15 
10 
1981 
12 
45 
1 
13 
11 
1982 
12 
45 
0 
14 
10 
1983 
17 
44 
0 
18 
9 
1984 
13 
47 
0 
6 
8 
1985 
14 
48 
0 
8 
10 
1986 
14 
52 
0 
13 
10 
1987 
17 
57 
0 
10 
8 
1988 
18 
54 
0 
5 
10 
1989 
25 
51 
0 
18 
7 
1990 
35 
46 
1 
29 
7 
1991 
37 
47 
0 
36 
7 
1992 
32 
49 
0 
43 
6 
1993 
29 
51 
1 
32 
6 
1994 
25 
48 
1 
28 
7 
1995 
23 
45 
1 
32 
7 
1996 
22 
47 
1 
34 
7 
1997 
19 
45 
1 
27 
8 
1998 
20 
45 
1 
33 
7 
SOURCE: National Science FoundationNational Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://websacpar.nsf.gov. 
Lack of financial support thwarts the careers of many young mathematical scientists. Not only is there a lack of sufficient postdoctoral fellowships for new doctorates in the mathematical sciences, but few young researchers are successful in obtaining research grants. With only 35% of academic research mathematical scientists receiving such grants, it is exceedingly difficult for young researchers to pursue careers in research. This lack of support, especially when compared with support for young researchers in the physical, biological, and engineering sciences, discourages young mathematicians, many of whom have left academia for Wall Street and other nonacademic fields. This loss of young researchers has the potential to undermine future U.S. strength in the mathematical sciences (NSF, 1998, p. 28).
As Table 24 illustrates, during the 1980s and 1990s about twothirds of postdoctorates were supported by federal sources, which mainly provide research funds.
Figure 24, on the other hand, shows little progress in federal support for academic mathematics doctorate holders through 1999. The proposal success rate—one of several criteria used by NSF to determine adequacy of support—was in the same range as for other fields within NSF’s Mathematics and Physical Sciences Directorate (MPS).
These trends led the 1995 NSF workshop to recommend changing the mix of funding:
Currently, the bulk of graduate student support provided by the Foundation is in the form of awards to individual investigators, who use these funds in part to support graduate students. Many participants agreed that this often has had the unintended consequence of limiting the areas in which students take courses and acquire experience. The Workshop recommended that MPS experiment with means to increase gradu
TABLE 23 Mechanisms of Support by the National Science Foundation for FullTime Graduate Students in Mathematics and Statistics in the United States, 19801998
Year 
Percentage of Support Provided by: 
Number of Students Supported 

Fellowships 
Traineeships 
Research Assistantships 
Teaching Assistantships 
Other Mechanisms of Support 

1980 
37 
2 
57 
2 
2 
262 
1981 
27 
4 
67 
1 
1 
227 
1982 
24 
4 
69 
0 
2 
228 
1983 
36 
4 
59 
0 
1 
223 
1984 
27 
0 
69 
0 
3 
279 
1985 
26 
2 
69 
0 
2 
321 
1986 
26 
0 
71 
1 
2 
357 
1987 
24 
0 
73 
1 
2 
436 
1988 
25 
0 
73 
0 
2 
463 
1989 
27 
0 
71 
1 
1 
475 
1990 
28 
0 
68 
3 
0 
491 
1991 
31 
0 
67 
1 
1 
452 
1992 
26 
0 
71 
2 
0 
457 
1993 
24 
1 
71 
4 
0 
470 
1994 
25 
4 
67 
3 
0 
518 
1995 
27 
4 
61 
6 
2 
474 
1996 
29 
5 
59 
6 
1 
435 
1997 
25 
5 
66 
3 
1 
386 
1998 
23 
6 
68 
1 
2 
384 
SOURCE: National Science FoundationNational Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov. 
ally the fraction of graduate students supported on fellowships and traineeships. Further, it recommended that NSF should encourage members of the MPS community in academia to propose new institutional, “thematic” funding mechanisms for graduate student training and support that would involve collective responsibility for groups of students. Funds could be awarded to entire departments, to combinations of departments, or to themeoriented entities that would allocate resources to students themselves. This would have the effect of allowing departments, or other groups, to take greater ownership of the overall quality of graduate education. The criteria for making awards would have to guarantee that special, new efforts would be made to achieve the desired educational improvements. In addition, NSF could reward and encourage such “collective proposals” that exhibit success in the recruitment and retention of students from underrepresented groups, including women, minorities, and, where applicable, domestic students (NSF, 1996, pp. xivxv).
Overall the funding situation in the 1980s and 1990s was characterized by the following:

Rising funding overall, but federal funding declining as a share of total funding (from Figure 21);

Funding for the mathematical sciences being increasingly dependent on NSF (from Table 21);

Graduate students relying primarily on teaching assistantships and other support mechanisms (from Table 23); and
TABLE 24 Number of Postdoctorates Supported in Mathematics and Statistics in the United States, 19801998, by Mechanism of Support
Year 
Federal 
Nonfederal 
Total 
Percentage Federal 

Fellowships 
Traineeships 
Research Grants 

1980 
23 
3 
31 
105 
162 
35 
1981 
20 
3 
41 
49 
113 
57 
1982 
22 
4 
20 
148 
194 
24 
1983 
27 
3 
53 
87 
170 
49 
1984 
46 
3 
83 
71 
203 
65 
1985 
35 
6 
79 
106 
226 
53 
1986 
39 
5 
70 
87 
201 
57 
1987 
42 
6 
81 
100 
229 
56 
1988 
44 
5 
139 
96 
284 
66 
1989 
38 
4 
99 
84 
225 
63 
1990 
41 
1 
116 
91 
249 
63 
1991 
27 
3 
113 
63 
206 
69 
1992 
23 
6 
114 
58 
201 
71 
1993 
34 
8 
124 
58 
224 
74 
1994 
37 
7 
113 
82 
239 
66 
1995 
39 
5 
130 
88 
262 
66 
1996 
54 
4 
164 
104 
326 
68 
1997 
49 
2 
146 
111 
308 
64 
1998 
41 
2 
136 
100 
279 
64 
SOURCE: National Science FoundationNational Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov. 

Federal graduate student support being overly concentrated in the form of research assistantships rather than in a broader array of professional development mechanisms (from Odom Report [NSF, 1998] extract, above).
STUDENTS IN THE MATHEMATICAL SCIENCES
During the 1980s and 1990s, the mathematical sciences community (as evidenced, for instance, by the David Reports [NRC, 1984, 1990] and the Odom Report [NSF, 1998], was concerned about four major issues with respect to students: (1) the number of students receiving degrees, (2) the lack of racial and gender diversity among the mathematics graduate student body, (3) the declining fraction of U.S. citizens receiving advanced degrees in mathematics, and (4) the lack of sufficient postdoctoral fellowships for new doctorates. As Figure 25 shows, during the period from 1980 through 1998, graduate enrollments in mathematics and statistics peaked in the early 1990s and then began to decline through 1998.
While the numbers of graduate students had been changing over time, so too had the demographic characteristics of students in the mathematical sciences. Much has been written about the rising number of foreign students in mathematics higher education as in the sciences and engineering more generally, as well as about the challenges facing the mathematical sciences in attracting, retaining, and advancing a more diverse group of students and scholars. In looking at this group of fulltime students, Figure 26 shows three demographic trends over the period 19801998:

The percentage of U.S. citizens and permanent residents among fulltime graduate students in mathematics and statistics remained level or declined,

The percentage of female fulltime graduate students in mathematics and statistics rose, and

The percentage of underrepresented minorities among fulltime graduate students in mathematics and statistics rose somewhat, but only by a few percent.
Figure 27 shows that the number of bachelor’s degrees awarded in the mathematical sciences from 1980 through 1998 rose and then declined. The apparent flatness in the number of master’s and doctor’s degrees is an artifact of the graph. In fact they increased by about 30 percent and 50 percent respectively during the period shown.
Focusing just on doctorates over the same period, Figure 28 shows the following:

The percentage of doctorates awarded to U.S. citizens and permanent residents declined,

The percentage of doctorates awarded to women doubled, and

The percentage of doctorates awarded to underrepresented minorities rose by a small amount.
Table 25 provides information about the postdoctoral plans of new doctorates between 1982 and 1998. The number of mathematics doctorates with definite plans to move into a postdoctoral appointment had grown somewhat, comparing the early 1980s to the 1990s. At the end of the 1990s, about one in three new doctorate recipients had such commitments.
As Figure 29 shows, the number of postdoctorals grew from 1980 to 1988 but then dipped and rose, ending up in 1998 at about where it was for 1988.
The envisioned role of postdoctoral fellowships in completing the training of new PhDs is well stated in the Douglas Report: “The number of postdoctoral fellowships in the mathematical sciences should be greatly increased so that such positions can be viewed as a logical next step after completion
TABLE 25 New Doctorate Recipients with Definite Commitments to Postdoctoral Study or Research, by Broad Field of Doctorate: 1982, 19931998
of the doctorate for the good student, not as a highly competitive prize for a select few” (NRC, 1992, p. 3). In contrast to laborintensive laboratory sciences in which many research projects require a team of people with differing levels of research experience, there is not a lot of reliance on postdoctorates in the mathematical sciences. Therefore, postdoctoral appointments have never been a common element of career training. In statistics, where there has long been a strong demand for new PhDs in industry, there is scant interest in postdoctoral appointments. And in mathematics, with its tradition of solitary
research, it is not always obvious how to parcel out tasks from a research project to people at different levels of experience. But many in the field recognize the value of a postdoctoral appointment as an opportunity to build research expertise and to develop a track record without the competing demands felt by a junior faculty member. Some see the value of such fellowships as allowing a broadening of training, with “applied, interdisciplinary, or pedagogical components” (NRC, 1992). The 1980s and early 1990s were also a time during which it was difficult to attain a tenuretrack faculty appointment, and a number of new PhDs had to make do with “research professorships” or “visiting professorships.”
The David II Report (NRC, 1990) went farther in emphasizing educational issues by entitling a section of its recommendations “Improve the Mathematical Sciences Career Path.” Recognizing, as did the David Report (NRC, 1984), that “the rate at which young people enter the mathematical sciences remains inadequate to renew the field” (NRC, 1990, p. 5), the report made several specific recommendations. Beyond the need for more funding, it advocated that 10 percent of the new funding should “support coherent programs that directly encourage young people to enter and remain in mathematical science careers. Recruitment of women and minorities into the mathematical sciences is a high priority” (ibid., p. 1). The NSF and other federal agencies “should solicit research proposals for programs that will improve the career path. Such proposals may combine research opportunities for students, postdoctorals and young faculty with increased support for senior researchers who can act as mentors” (ibid., p. 7). Another recommendation was for a change in the reward structure of academic departments, which “should give increased recognition to faculty who act as mentors for students and junior colleagues, who contribute to education, and who interact with collaborators from other disciplines” (ibid., p. 7).
REDEFINING MATHEMATICAL SCIENCES PROGRAMS
Four key issues were discussed in the Douglas (NRC, 1992) and Odom (NSF, 1998) Reports: (1) the need for increased breadth of training for students, including greater emphasis on interdisciplinarity, applied mathematics, and offcampus experiences (e.g., internships); (2) providing a better balance of education and research; (3) decreasing time to degree for students; and (4) creating positive learning environments.
Concerning the first issue, breadth of skills and knowledge, the 1995 workshop on graduate education and postdoctoral training noted: “The skills and knowledge acquired by new Ph.D.’s are too narrowly focused, and are not adequately applicable to the diverse business and industry environments in which most Ph.D. scientists actually work” (NSF, 1996, p. x).
The Odom Report, in addition to recommendations about funding, devoted much of its emphasis to the changing nature of the discipline and the implications of those changes for training mathematicians. Its recommendations to NSF addressed the second issue, improving the balance of education and research: “[E]ncourage activities that connect mathematics to other areas of science, technology, business, finance and government, strengthen the connections between ‘pure’ and ‘applied’ mathematics, broaden the exposure of professional and student mathematicians to problems in other fields, and maintain and strengthen abstract mathematics” (NSF, 1998, p. 43). In particular, NSF should “encourage activities aimed at broadening undergraduate and graduate curricula, with the objective of widening the range of curricular choices, raising the attractiveness of mathematical careers to students, and increasing the vocational flexibility of future mathematicians” (ibid., p. 45).
As noted above, time to degree is negatively impacted by the reliance of many students on teaching assistantships and selfsupport; it could be offset by increasing the number who instead are supported by fellowships. This issue arose because time to degree was growing during the 1980s and 1990s and was raised as a concern in the various reports noted above. As NSF noted in 1997: “In the last decade, the time to degree for a Ph.D. in the Mathematical Sciences has significantly increased from four to
TABLE 26 Median Years from Bachelor’s Degree to Doctoral Degree in Mathematics in the United States, 19801998
Year 
Years Elapsed (median years) 
Years Enrolled (median years) 
1980 
7.0 
6.0 
1981 
7.0 
6.0 
1982 
7.1 
6.0 
1983 
7.3 
6.3 
1984 
8.0 
6.2 
1985 
8.0 
6.4 
1986 
7.3 
6.1 
1987 
8.0 
6.5 
1988 
8.1 
6.4 
1989 
8.0 
6.3 
1990 
8.0 
6.7 
1991 
8.3 
6.7 
1992 
8.9 
7.0 
1993 
8.6 
7.0 
1994 
8.9 
6.9 
1995 
8.6 
6.9 
1996 
8.3 
6.8 
1997 
8.7 
7.0 
1998 
8.0 
6.8 
SOURCE: Adapted from NSF, Division of Science Resources Statistics (2004), Appendix Table 229. 
seven years. This partially reflects that entering students, especially nativeborn students, are less well prepared than before. But also involved is the heavy dependence by the Mathematical Sciences graduate students and postdoctorates on time consuming teaching assignments for financial support” (NSF, 1997). Table 26 shows the median years elapsed from bachelor’s to doctoral degree in mathematics during the 1980s and 1990s. The data in this table are inconsistent with NSF’s quoted observations. The committee was unable to determine how NSF arrived at this conclusion and has no additional data to draw other conclusions; however, these observations by NSF played a role in VIGRE’s original design.
The fourth issue common to the Douglas (NRC, 1992) and Odom (NSF, 1998) reports had to do with the culture of mathematics departments. The Douglas Report (NRC, 1992) studied a number of departments in an attempt to find out what makes for successful graduate and postdoctoral programs in mathematics. It found that there was considerable variation in explaining such success, and the report broadly classified these variations as the standard model, the subdisciplinary model, the interdisciplinary model, the problembased model, and the collegeteachers model. Within this varied landscape, the report distilled three common characteristics of all the successful programs that it encountered: a focused, realistic mission; a positive learning environment; and relevant professional development. The report highlighted the importance of active recruitment, especially for recruiting women and underrepresented minorities. A detailed description is given of what it means to have a positive learning environment; and communication and cooperation, effective advising, and early research experience are emphasized. It was also emphasized that “a positive learning environment is important to all doctoral students but is crucial for women and underrepresented minorities” (NRC, 1992, p. 3). The report stressed: “Clustering faculty, postdoctoral associates and doctoral students together in research areas is a major factor in creating a positive learning environment” (ibid., p. 3). The importance of broadening the training of doctoral and postdoctoral students was underscored, as was the importance of teaching and communication skills.