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A Current Look at Mathematics Graduate Programs
Communicated by Notices Associate Editor William McCallum
Last Spring, TPSE Math | Transforming Post-Secondary Education in MathematicsFootnote1 commissioned Rutgers Education and Employment Research Center,Footnote2 REERC, to study mathematics graduate programs regarding current challenges for student experience. TPSE Math is a Carnegie Corporation of New York grant-funded program dedicated to enhancing undergraduate and graduate mathematics education. TPSE Math is led by Phillip Griffiths, Professor Emeritus and former Director of the Institute for Advanced Study, and William E. Kirwan, former Chancellor University System of Maryland and University of Maryland Mathematics Professor Emeritus. REERC Education & Employment Research Center in the Rutgers School of Management and Labor Relations conducts research and evaluation on programs and policies at the intersection of education and employment. With TPSE Math input, REERC developed an online survey that combined open- and closed-ended questions. The survey was distributed to mathematics department chairs and graduate coordinators across the country. Survey responses were searched for innovative approaches and were reviewed for themes and patterns. Using these themes, REERC then developed an interview protocol and conducted interviews with a sample of survey respondents from both master’s and doctoral level programs. The final sample included public and private institutions located across 30 US states and two Canadian Provinces. Both Research I and Research II institutions were represented. Survey data was based on 17 terminal master’s programs and 46 doctoral programs. Interview data was collected from Zoom calls with two department chairs from terminal master’s programs and seven chairs or graduate studies directors from seven doctoral programs. The full report is available at Career Preparation in Math Graduate Programs.Footnote3
Quick overview
The study examined recruiting, admissions practices, diversity-equity-inclusion practices (DEI), advising & well-being checks, plus non-academic professional development and career planning for students and training for faculty. The findings included an assortment of considerations:
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a decreasing reliance on GRE scores for admissions;
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72% of doctoral programs provided incentives to promote DEI, while 90% of master’s programs had not provided such incentives;
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51% of doctoral and 70% of master’s programs require semester advising pre-candidacy;
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in spite of a faculty articulated need, only limited professional development is provided to students for non-academic careers;
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some programs are requiring statistics and computer science coursework, while some programs have industry advisory committees;
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94% of doctoral and 89% of master’s programs provided no professional development to faculty or information on non-academic careers.
The report closes by discussing possible areas for enhancement:
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partnering with industry;
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providing professional development around non-academic careers for students and faculty;
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integrating real-world problems in the curriculum and leveraging alumni.
We present a summary of the findings in the full report. The following material is excerpted directly from the REERC report.
On recruitment strategies
Departmental and college websites were found to be the common mechanisms of recruitment for both terminal master’s and doctoral programs. Master’s programs also relied heavily on undergraduate advisers, while doctoral programs relied more on national conferences. The need to shift to remote recruiting during the Covid pandemic created challenges for many programs, but those conditions may have increased equity in both colleges’ access to students (by leveling the playing field between larger, more established programs and smaller, less-known programs) and students’ access to colleges (by increasing conference access for minority and underrepresented students). As part of their recruitment processes, some programs have become more intentional about fostering personal and individualized relationships with potential applicants, e.g., writing personal follow up letters.
One respondent reported “we just saw a large increase in applicants because the job market just had those jolts.” Another respondent opined that the community needs to treat graduate student recruitment similarly to faculty recruitment—by proactively looking for people that will be a good fit for their program.
On admissions factors
Respondents from the plurality of master’s and doctoral programs surveyed indicated they planned to drop the use of standardized exams in their admissions process. In particular 60 percent of master’s programs have already or will soon drop the use of GRE scores; 55 percent of doctoral programs will continue to use GRE scores, but not as a heavily weighted factor. Both survey respondents and interviewees raised concerns about the efficacy of exam results and equity in their use. A respondent opined, “GREs never really seemed that useful. Students with high GREs usually (but not always) did well, but lower scores did not tell us anything about who would succeed and who would not.” Instead, most master’s and doctoral programs emphasized applicants’ prior mathematics experience in their decision-making about admissions. Doctoral programs also heavily weighed prior research experience. The main factors for admissions decisions are described in Table 1.
Tables 1–4 report on questions where respondents were asked to select a designated number of items from a longer list. Percent of Departments is the proportion of departments including the given item as a selection. The full report also includes the proportion a given item was selected amongst all choices.
The Four Reported Factors that Weigh Most Heavily in Determining Admission into Math Graduate Programs. (See the above description of table statistics.)
| 17 Master’s Programs | 46 PhD Programs | ||
| Answers | Percent of | Answers | Percent of |
| Departments | Departments | ||
| Previous math coursework. | 100% | Previous math coursework. | 100% |
| Overall college GPA. | 82% | Research experience. | 76% |
| Other factors. | 53% | Overall college GPA. | 54% |
| Undergraduate student at your institution. | 29% | Area of study. | 37% |
| Research experience. | 24% | Diversity, race/ethnicity, gender, sexual orientation, social class, disability. | 33% |
| Test scores (e.g., GRE). | 18% | Test scores. | 30% |
| Diversity. | 18% | Essay. | 17% |
In contrast to PhD programs, financial aid at the master’s level is minimal. A majority of respondents from master’s programs reported their department provided either very limited or no financial support to their students. As a result, student loans seemed to be the primary way master’s students were “supported.” This is not surprising given the scarce opportunities for research and teaching at this level. The lack of such support may be a factor in equity gaps at this level.
On diversity, equity, and inclusion (DEI)
About 72 percent of doctoral programs surveyed provided specific incentives, supports, or actions to increase diversity in their student bodies. Incentives primarily included scholarships and fellowships targeted toward underserved populations, though these funding lines existed primarily at the college level rather than at the departmental level. Other financial supports included summer stipends, payment for teaching seminars, and involvement in mentor programs. One doctoral program indicated they had leveraged their Association for Women in Mathematics chapter to support and mentor their women students.
Focus on DEI issues in academia has grown in recent years. Nevertheless close to 90 percent of responding master’s programs indicated they generally do not provide incentives, supports, or actions to increase diversity. The survey found some programs at both levels of graduate study have begun to engage in one or more initiatives to increase diversity and inclusion in their programs. For example, some have forged relationships with Hispanic-serving institutions (HSIs) and historically black colleges and universities (HBCUs) and have provided financial support for students from historically underrepresented groups. However, many respondents cited a lack of departmental resources or incentives to actually transform the makeup of their student bodies, particularly at the master’s level. At the same time, several programs observed that their ability to increase recruitment of historically underrepresented students was intimately connected to having diverse faculty members with ties to HBCUs and HSIs. Further, a few programs underscored the importance of recruiting groups of underrepresented students to establish a sense of community for such students which furthered recruitment efforts. A respondent noted, “Part of this is getting a critical mass of people. Once you have a critical mass of women in your department, women find this to be an attractive place to apply.” A respondent noted that networks provide opportunities to recruit: Math Alliance, Joint Mathematics Meetings, Society for Advancement of Chicanos/Hispanics, and Native Americans in Science. Nevertheless, there were no reports on any systemic approach to DEI (e.g., faculty hiring, student recruitment and support, advising, or curriculum changes).
On advising activities
Overall 70 percent of master’s and 51 percent of doctoral programs required pre-candidacy students to check in with their adviser at least once a semester. Few graduate programs represented in the study conducted any advising around career planning or employment outside of the academy. Most PhD students had to wait until they were at the candidacy level to receive such, albeit limited, career advising. Over 70 percent of master’s programs indicated that they do not provide specific career planning or employment information. Although all colleges have campus-based mental health services, many departments, especially doctoral programs, use adviser sessions, for well-being checks to identify and address student stress. Half of PhD programs provided some form of peer mentoring, while only a quarter of master’s-level programs offer peer mentor/support. However, the few that exist involve some innovative strategies including a chain advising structure involving a faculty member, an advanced graduate student, a new graduate student, and an undergraduate. One program indicated they specifically added advising support to address pandemic-related challenges. Table 2 lists the focus areas for master’s and doctoral advising sessions.
The Three Reported Primary Matters in Advising Sessions.
| 17 Master’s Programs | 46 PhD Programs | ||
| Answers | Percent of | Answers | Percent of |
| Departments | Departments | ||
| Course selection, registration. | 82% | Course selection, registration. | 100% |
| Advising about research project. | 35% | Checking on overall well-being. | 44% |
| Academic pathways related career advising | 29% | Advising about research project. | 27% |
| Advising about master’s thesis. | 29% | Academic pathways related career advising. | 22% |
| Advising about further study - second master’s and/or doctorate. | 24% | Advising about specific doctoral programs. | 20% |
| Advising about specific master’s programs. | 24% | Advising about doctoral thesis. | 10% |
| Checking on overall well-being. | 24% | Advising about specific master’s programs. | 5% |
On social networking and math-related associations
Of note, 80 percent of chairs and directors from doctoral programs and 60 percent of chairs and directors from master’s programs reported that “there was a very close and interactive group” among their students. Factors contributing to this included scheduled and ad hoc social activities. In addition, at the doctoral level, programs had established graduate seminars, provided collaborative research activities opportunities, and in some cases, assigned multiple graduate students to the same office. Further, at two-fifths of doctoral campuses, students also had the opportunity to participate in math club/associations, including chapters of national organizations, e.g., the American Mathematical Society, the Association for Women in Mathematics. These groups sponsored social and recreational events, workshops, and panel sessions about current student research activities, and, at times, sessions about career and employment information.
On non-academic career preparation
Curricular changes emerged as the primary way programs prepared students for non-academic careers at both the master’s and doctoral levels. Some programs required applied courses such as statistics or computer programming. Some programs also integrated more real-world problems into existing courses. Other common career preparation activities included career panels, internships, and establishing connections with local industry. In addition, some programs have even established industry advisory committees in their department and allow industry representatives to serve on doctoral committees. However, these activities were not widespread across the programs studied. Moreover, funding support for career exploration and advising activities remains an area of need in both master’s and doctoral programs. Table 3 describes the top four types of positions taken by master’s and PhD graduates.
The Four Reported Types of Jobs Students Enter After Receiving Their Degree.
| 17 Master’s Programs | 46 PhD Programs | ||
| Answers | Percent of | Answers | Percent of |
| Departments | Departments | ||
| College and university teaching. | 71% | College and university teaching. | 100% |
| Actuarial and insurance business. | 47% | Academic research. | 91% |
| K–12 teaching. | 47% | Non-research industry jobs. | 60% |
| Non-research industry jobs. | 35% | Non-governmental research jobs. | 40% |
| Federal government jobs. | 35% | Federal government jobs. | 40% |
| Academic research. | 29% | Actuarial and insurance business. | 22% |
On professional development focused on non-academic pathways
Per the American Mathematical Society’s Annual Survey Report: Employment Experiences of the New Doctoral Recipients on the 2017–2018Footnote4 cohorts, 39 percent of doctoral graduates started in business, industry or government jobs (Figure E.2.), 64 percent of respondents in academic jobs entered in a temporary employment status (Figures EE.1 & EE.2) and 43 percent of respondents in temporary academic positions entered 1 or 2 year positions (Figure EE.4). REERC survey respondents at both the master’s and doctoral levels indicated little professional development was offered in their program that focused on preparing students for careers outside the academy. However, many faculty interviewees cited a need for such discussion and training. Some informants shared that they were trying to develop or expand such training and working to build stronger relationships with industry/government. At the same time, informants stated that professional development initiatives could only be successful if they were paired with larger cultural shifts in mathematics graduate programs. In their view, while younger faculty often understood the need to expand preparation for non-academic career pathways, older mathematics faculty were more likely to hold an attachment to an academic pathway, remaining unaffected by the reality that their students may not want to or simply may not have the option to pursue that career track.
On faculty knowledge of non-academic career pathways
Survey respondents at both levels of graduate study indicated that some faculty in their program have some knowledge about careers outside of academia. However, interview informants clarified that this knowledge was typically based on the individual faculty member’s specialization or prior experience in industry. More theoretical faculty are typically not as knowledgeable about these areas as those in applied mathematics fields. In addition, many programs noted a generational divide in terms of both faculty knowledge about industry and their willingness to encourage students to pursue careers outside of academia, with younger faculty more knowledgeable and enthusiastic in these areas.
The Four Reported Career Paths or Occupational Fields Encouraged by Department Faculty.
| 17 Master’s Programs | 46 PhD Programs | ||
| Answers | Percent of Departments | Answers | Percent of Departments |
| Data science. | 88% | Academic research. | 100% |
| College math teaching. | 88% | College math teaching. | 93% |
| K–12 teaching. | 47% | Data science. | 43% |
| Academic research. | 41% | Tech industries. | 41% |
| Actuarial sciences. | 29% | Federal Goverment. | 39% |
| Financial services. | 29% | Financial services | 32% |
| General statistics. | 25% | General statistics. | 11% |
On career and occupational pathways encouraged by most faculty
Faculty professional development around topics related to non-academic careers seems to be a clear gap for programs at both the master’s and doctoral levels. To date, 94 percent of master’s survey respondents and 89 percent of doctoral-level respondents indicated their departments had not conducted any professional development to help faculty become more informed about careers outside of academia. In most cases, faculty continued to emphasize academic teaching and research jobs over careers in industry and government. See Table 4 above for occupational fields most encouraged by faculty. The faculty emphasis of academic positions took place despite the growing trends of “adjunctification” throughout much of the academy; the decrease in job security in many postdoctoral and faculty positions; and a general decrease in student interest in academic careers as they progress through graduate programs. Master’s programs seem to be more encouraging of non-academic careers than doctoral programs, a difference between these two graduate levels that should be explored further.
There is some disparity between Table 3, jobs accepted and Table 4, jobs encouraged. Advising and curriculum also evidence a separation. The interviews with graduate program directors and chairs confirm national trends. The traditional view of the post-baccalaureate career trajectory for mathematics graduate students—a view that remains widely held by many tenured math faculty—is disconnected from actual labor market conditions. Academic jobs are increasingly precarious, casualized, and underpaid, and they carry with them slim opportunities for advancement or tenure.
The survey demonstrates that mathematics faculty at both the master’s and doctoral levels continue to emphasize academic career tracks over industry and government careers despite rapidly escalating evidence that it may be outside students’ best interest to do so. The harsh realities of part-time adjunct positions afflict most of the academy, including many math departments.Footnote5 Moreover, the kinds of careers math faculty encourage may be misaligned with the occupations students are actually interested in pursuing.
Lancaster, A. K., Thessen, A. E., & Arika, V. (2018). A new paradigm for the scientific enterprise: Nurturing the ecosystem. F1000Research, 7. https://doi.org/10.12688/f1000research.15078.1
Based on the survey responses and subsequent interviews, REERC identified four general areas for enhancement and three general recommendations for TPSE Math and mathematics graduate programs.
Areas for enhancement
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Partnering with industry: Forming partnerships with industry would benefit a department by creating more opportunities for internships for students, finding members of industry to serve on a department’s advisory board, and having industry representatives on some doctoral committees.
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Providing professional development around non-academic careers: It is helpful for departments to have resources for faculty and for students that outline career opportunities in industry. At the graduate level, a major hindrance for making improvements in helping graduate students get non-academic jobs is the feeling among certain faculty that a career in industry is less meaningful than a career doing research at a university. Being able to change this perception would be significant.
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Integrating real-world problems in the curriculum: There are benefits in having students work on mathematics problems that are from today’s industries. While individual faculty in some departments are successful in introducing real-world problems into courses, there is often not a sizable group working on this effort.
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Leveraging alumni: Most departments do not track alumni or if they do, these efforts are done in an ad hoc manner. Having a stronger network of alumni in industry would connect students with contacts and potential careers in industry.
Recommendations
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Professional Development Opportunities: Besides a greater knowledge of non-academic careers, there is a need for a better understanding of what it takes to get such jobs. This includes training in the soft skills (e.g., speaking and writing) that are generally not taught in mathematics graduate programs and are different than the skills needed to communicate the results in a theoretical mathematics thesis. Possible topics for professional development include:
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The Career and Occupational Landscape for Math Graduate Students Beyond Academia
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How to Develop Strong Relationships with Industry
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Equitable Advising Strategies that Encourage Students’ Agency
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Skills Math Graduate Students Need to Succeed in the Twenty-First Century Labor Market
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Integrating Industry/Real-World Problems into Math Graduate Curricula
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Facilitating Stronger Partnerships between Mathematics Departments and Industry: While there are some faculty and departments that do have solid connections with industry, many do not. For graduate students who want a career in industry, this often results in them having to take the initiative on their own to prepare for and get a non-academic job. This situation could be improved by finding ways to help departments develop connections with industry.
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Funding Support for Non-Academic Career Initiatives: Most master’s programs and doctoral programs do not receive financial support to prepare graduate students for non-academic careers. Such funding could be used for offering professional development mentioned above and implementing other programs such as employing a part-time career adviser. Identifying and creating potential funding opportunities would be helpful.
Michael J. Dorff is a professor of mathematics at the Brigham Young University and TPSE Director of Strategy and Implementation. His email address is mdorff@tpsemath.org.
Scott A. Wolpert is a professor emeritus of mathematics at the University of Maryland and TPSE Senior Consultant. His email address is swolpert@umd.edu.
Article DOI: 10.1090/noti2494
Credits
Photo of Michael J. Dorff is by Laurie DeWitt, Pure Light Images.
Photo of Scott A. Wolpert is courtesy of Scott A. Wolpert.