SIAM News Blog

Mentoring the Missing Millions

By David Goldberg and Padmanabhan Seshaiyer

The National Science Board’s (NSB) January 2022 biennial report on “The State of U.S. Science and Engineering” identified the need to increase representation from the “missing millions” in order to strengthen the nation’s research enterprise [1, 2]. To do so, the NSB estimates that the science, technology, engineering, and mathematics (STEM) workforce must undergo the following necessary changes: the number of women must nearly double, Hispanic and Latino individuals must triple, Black and African American individuals must more than double, and individuals of Native American and Alaska Native descent must quadruple [3]. Here we argue that mentorship is the key to increasing diversity and reducing the significant talent gap in all STEM areas.

One of the main draws of the scientific enterprise is the opportunity to meaningfully contribute to the breadth of human knowledge within a given discipline. The fact that such a large portion of research occurs in academic settings indicates that the process of teaching and training new scientists is an important component of scientific advancement. Many of us seek to institutionalize our own contributions by guiding students through the process of becoming researchers and/or instructors. The importance of mentorship is widely recognized; for instance, award recipients nearly always acknowledge the valuable influence of several mentors.

When we mentor the next generation, we are often drawn to students who remind us of ourselves. However, we should also recognize that we are mentoring all the time — whether we know it or not. As such, we must be intentional about offering adequate advice and direction to everyone. To harness society’s full potential, we need to purposefully reach out to students from backgrounds that are different than our own, offer encouragement, and expose them to the vast array of opportunities for graduate study and employment. When programs and faculty undertake such deliberate mentoring, they more effectively mentor all students, not just women and underrepresented minorities.

Figure 1. Growth of the Math Alliance community from 2007 to 2022. Blue bars represent faculty members, red bars represent the cumulative total of Math Alliance Scholars, and yellow bars represent active participants.

A good mentor supports students in their personal interests and passions. Doing so can be challenging for researchers who must then connect student enthusiasms to their own fields of expertise. Students often want to solve problems that impact their communities, so mentors should be prepared to help them navigate the connections between such real-world challenges and mathematical thinking [5].

When the COVID-19 pandemic disrupted well-established structures around in-person mentoring, many individuals took advantage of virtual mentorship. Several research and internship programs pivoted online and successfully mentored students at all levels. For instance, the National Science Foundation (NSF) invited proposals for rapid response research grants to better understand COVID-19, which provided further opportunities for faculty to engage in mentored projects with students [4, 6].

Now we will discuss the Math Alliance: a successful mentorship program that continues to serve as a national model. The Math Alliance evolved from an NSF-funded project called The Alliance for the Production of African American Ph.D.s in the Mathematical Sciences. It comprises a community of student participants (known as Math Alliance Scholars) and faculty mentors who believe that any student with the talent, desire, and ability to earn a doctorate in a mathematical, statistical, or quantitative science should have the chance to do so. The community has continued to grow organically since its inception in 2006 (see Figure 1).

Figure 2. The number of doctorates earned each year by Math Alliance Predoctoral Scholars.

One key to the Math Alliance’s success is that every scholar must be nominated by a mentor. One former NSB member remarked that the Math Alliance has institutionalized, within itself, the scaffolding that moves students from where they are to where they can achieve their potential. We continue to build this scaffolding even as our Math Alliance Scholars climb it, and thus constantly try to stabilize the infrastructure. Figure 2 charts the increasing number of Math Alliance Predoctoral Scholars—participants who became part of our community before entering a doctoral program—that have earned Ph.D.s each year, and Figure 3 provides a breakdown of the positions that Predoctoral Scholars have obtained after completing their degrees. The program has led to more than 220 Ph.D.s to date, while 175 Math Alliance Predoctoral Scholars and 59 “doctoral only” scholars have earned doctorates — the overwhelming majority of which were in the quantitative sciences.

Several key Math Alliance programs evolved as our community steadily grew. The Facilitated Graduate Applications Process (F-GAP) provides undergraduate seniors and terminal master’s students with the advice and assistance to successfully apply to and thrive in graduate programs. William Vélez (University of Arizona)—who was on Math Alliance’s Executive Council until 2020 and continues to serve as the Associate Director for Undergraduate Programs—spearheaded this initiative. A year and a half before receiving their undergraduate or master’s degrees, students are paired with Math Alliance Doctoral Mentors who help them select the disciplines they wish to pursue in graduate school, assist with their application materials, and discuss the programs to which they should apply. Math Alliance staff then track these applications and ensure that Math Alliance Mentors at the programs/institutions in question are aware of them.

The annual Field of Dreams Conference unites roughly 200 Math Alliance Pre-doctoral Scholars in the quantitative sciences; approximately 80 to 90 percent of these scholars are members of minority groups that are traditionally underrepresented in STEM fields. About half of these students are participants in the F-GAP program. Other conference attendees include doctoral students; Math Alliance Mentors; Math Alliance staff; faculty members who are not (yet) mentors; and representatives of funding agencies, NSF-funded Mathematical Sciences Institutes, professional organizations, industry, and government. In 2020 and 2021, the conferences convened virtually due to the COVID-19 pandemic. The virtual format allowed for many more participants than in previous years, with over 500 people attending each event. The Field of Dreams Conference will return to an in-person format in 2022 and is scheduled to take place from November 4-6 in Minneapolis, Minn.

Figure 3. Outcomes of the Math Alliance mentoring program as of March 2022, in terms of the employment breakdown of Math Alliance Predoctoral Scholars who earned their Ph.D.s.

Graduate Program Groups (GPGs) consist of a significant assembly of faculty in a quantitative sciences graduate program who have agreed to provide a welcoming and nurturing environment for students. The Math Alliance certifies these groups based on proposals that include explicit mentoring plans. There are currently 42 Doctoral Program Groups and 12 Master’s Program Groups, the latter of which comprise terminal master’s programs with a demonstrated, successful track to a doctorate. GPGs provide Math Alliance Scholars with consistent mentoring throughout their pursuit of graduate degrees.

Initially, we thought that Math Alliance programs would essentially conclude when participating students earned their doctorates. However, we are learning that Math Alliance Scholars can benefit from our community’s continued support throughout their careers. We must ensure that scholars who pursue academic professions receive adequate mentoring in regard to research funding, grants and fellowships, tenure and promotion processes, and other cultural aspects. We have discussed the formation of a program to provide this type of support and expect that it will include several F-GAP features, as we aim to ensure that upcoming doctoral graduates are paired with mentors who will complement the advice of their thesis advisors. Students who are interested in nonacademic positions will connect with mentors in industry who can help them chart a career path.

Serving as a mentor is a rewarding experience that is pivotal for the success of every student’s academic journey and intellectual growth. Through effective mentorship, we can build a living and learning community of student scholars in STEM and create a systemic change to reach the missing millions.

All figures courtesy of David Goldberg.

[1] Blatecky, A., Clarke, D., Cutcher-Gershenfeld, J., Dent, D., Hipp, R., Hunsinger, A., … Michael, L. (2021). The missing millions: Democratizing computation and data to bridge digital divides and increase access to science for underrepresented communities. Alexandria, VA: National Science Foundation.
[2] Burke, A., Okrent, A., & Hale, K. (2022). The state of U.S. science and engineering 2022. Alexandria, VA: National Science Board. 
[3] National Science Board. (2022). The U.S. is a keystone of global science and engineering (Report #: NSB-2022-2). Alexandria, VA: National Science Board.
[4] Ohajunwa, C., Kumar, K., & Seshaiyer, P. (2020). Mathematical modeling, analysis, and simulation of the COVID-19 pandemic with explicit and implicit behavioral changes. Comput. Math. Biophys., 8(1), 216-232.
[5] Seshaiyer, P. (2022, March 1). Preparing future generations to address global pandemics with innovative mathematical thinking. SIAM News, 55(2), p. 2.
[6] Wang, W., & Seshaiyer, P. (2021). Engaging students in applied mathematics education and research for global problem solving. In R. Buckmire & J.M. Libertini (Eds.), Improving applied mathematics education (pp. 27-49). Cham, Switzerland: Springer.

David Goldberg is a professor of mathematics at Purdue University and has served as executive director of the Math Alliance since 2016. He works in the broad area of the Langlands program and focuses on the confluence of number theory and representations of p-adic groups. Padmanabhan Seshaiyer is a professor of mathematical sciences at George Mason University and chair of the SIAM Diversity Advisory Committee. He works in the broad area of computational mathematics, data science, biomechanics, design and systems thinking, and STEM education. Seshaiyer also serves as vice chair of the U.S. National Academies Commission on Mathematics Instruction and as Associate Director for Applied Mathematics of the Math Alliance.

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