April 2023
Sarah Sword, Michael Young, and Carl Westine
This post shares findings from an NSF research study, Studying Successful Doctoral Students in Mathematics from Underrepresented Groups, in which the authors, along with a large team of collaborating researchers, sought to listen to and understand the voices of students from historically marginalized groups in doctoral programs in mathematics. Our goal was not to identify characteristics of students who could succeed in existing programs, but to understand– from the students’ perspectives–characteristics of the graduate mathematics environments that promote students’ success.
A team of interviewers talked with seventy-five students or recent graduates, in conversations that lasted between 45 and 210 minutes. We customized interview protocols for students at four stages in the trajectory of mathematics doctoral programs:
- Newly accepted doctoral students and post-baccalaureate students in programs designed to prepare students for doctoral programs in mathematics;
- Early graduate students (pre-qualifying exams) who have successfully navigated the transition to graduate school in mathematics;
- Advanced graduate students who have passed all exams and are working on dissertations;
- Recent PhDs (0-5 years post graduation) in academic and non-academic jobs.
We chose those stages because arriving at each stage means that the student has successfully navigated a barrier to the PhD. Typically we think of exams and dissertations as the key hurdles to completion of a doctoral degree, but we wanted to highlight the ways in which there are earlier barriers that may get in the way of getting to those stages. We especially did not want to limit our study to recent graduates of PhD programs – although we included them – because in order to understand mathematical environments from the point of view of students themselves, we wanted to capture those perspectives at multiple points in graduate programs.
The interviews do offer students’ perspectives on their environments: the challenges they face from their perspectives, what programmatic elements support them and what programmatic elements create additional barriers. We learn about their perceptions of their own pathways: what do the students feel like they need to know? What steps do they need to take to achieve their goals? How can they learn to navigate that pathway? What interactions and structures create environments in which students feel welcome and supported enough to succeed in the many challenges of graduate school, whether those are mathematical or environmental?
The interviews were semi-structured, meaning that we had protocols with questions for the interviewers to pose, but we recognized the ways in which interviews might veer from our written protocol. Sample questions included:
- Getting to know the interviewee: What does success in graduate school mean to you?
- Mentorship: Do you have mentors? How do they support you?
- Academics: Can you tell me about your school’s qualifying exam structure?
- Practical needs: How did money play a role in choosing your university?
- Race: How do you think race has played a role in your experience?
- Network: What is your connection to the larger community of mathematicians of color?
- Finally: What are the systemic issues that aren’t being addressed and that should be?
Each of these questions served a specific purpose. For example, asking a new graduate student about their school’s qualifying exam structure sometimes just yielded information about that structure. Sometimes that question surfaced frustration with multiple sets of written and unwritten rules, and not knowing which applied when. Similarly, asking about money surfaced issues that were likely invisible to faculty and administrators who were not checking in with their students about money, and how money plays a role both in students’ selection of graduate programs and how they navigate it. Asking about connections to the larger community of mathematicians of color often surfaced joy – those connections matter.
But why did we gather so many perspectives? A doctoral student describes this well in her own interview:
But for example, my department, I think they clump us [minoritized students] all together and forget that we might need different things. So I think part of the issues I have with my department even though they had very good intentions, they didn’t really spend the time to look at the layers of what it means to be a minority student. It’s like, “Okay, you’re all minorities. This is what you only need.” Instead of, “Well, depending on who you are, you need … different things.” And for me… I thrive when there’s a sense of community and I was able to find spaces or create spaces for that or, I don’t know, places where you can talk about things that are not math but affect your math work in a sense.
On the surface, this student’s statement that you need different things, depending on who you are, seems obvious. And yet students in our study report their sense that “what [they] need” has been predetermined before they ever arrived at the department, simply because they are people from historically marginalized groups.
What emerges from our analysis is that there isn’t one “what they need” for any group of students. No one support structure is going to work for all students – so to support the individual students in any given program, talk with the students. Find out what their particular barriers are and help them resolve those. In particular:
- Talk with students individually, one on one.
- Talk with faculty who are already doing #1, and draw on collaborative teams to support students.
- Put yourself in situations where you can hear from students and faculty from historically marginalized groups.
The students we interviewed agreed to contribute to the project partly to support #1, #2, and #3. By sharing quotations like the ones we share in this column (see below), we lower the threshold for faculty who wish to put themselves in situations where they can hear from students and faculty from historically marginalized groups. Each student’s experience has unique elements, but the general experiences of systemic barriers, microaggression, and racism persist in university and college towns, post-secondary institutions, and mathematics departments. Knowing this may make conversations like those in #1 and #2 more productive.
For example, many students shared experiences of isolation and invisibility – in classrooms, in departments, and in their communities. One student reported on his experience this way:
I sat at the front of the room and we had sort of like these… It was like a grid of tables that sat two people per table. And I was the only person at my table in the front, and then everyone else sat at the remaining tables behind me. … And I just remember that [the professor] never once made eye contact with me. And there were a couple of times when I raised my hand and it seemed like he totally didn’t even see that I was raising it and I was just like, okay, lower that back down, I guess. … does anyone else see me raising my hand? Am I a ghost right now?
This student also reported on how dismissed he felt in office hours; how when he talked with some of the white males in his department, they did not relate to his experience of being dismissed and some of the women he talked to did relate to that experience. And this student is not alone in feeling this way. Again and again, we hear from students about feelings of isolation.
A different student – one who did have mentors she trusted for some aspects of her professional growth – wondered if there was any point in even raising her sense of isolation with any of her mentors. She wasn’t sure that her professors – even the ones she trusted to care about her success – would have any way to make sense of that feeling and the implications of that isolation on her sense of whether or not she was in a productive environment.
There are other factors that contribute to students’ sense of living and working in productive environments: adequate funding, funds and access to resources for mental and physical health, personal safety on and off campus, clear pathways through their programs–especially things like knowing where there’s flexibility in schedules for passing qualifying exams, access to internal university networks for students of color and external national networks of other mathematicians of color. Systemic barriers that students face can feel incredibly daunting. We can’t fix all of those systemic barriers.
But even in the face of those systemic barriers, advocacy, as another student describes, has value, and does help students feel seen and supported. Another student describes this phenomenon:
…another professor was actually amazing to me. He was actually interesting, amazing, because he was the best kind of… He was even keel to everybody, right? I’m not going to say that he was the warm and fuzzy person that would just come and hang out with you, but if you wanted to talk math and if you wanted an advocate, he was the person, and he was never afraid to fight for [me].
Similarly, a theme present across many of the interviews is the importance of individual people they had met along the way–teachers who took them seriously as mathematicians, or recognized their spark of interest, or just shared their own passion for math. One student shares that experience this way:
It must have all started with my high school Calculus teacher, because when I started in his class, it became clear to me that math was something that people could just enjoy… people actually think about it, and find joy in it and want to know more, and there’s math that happens outside of a classroom and people get excited about it. And it made me want to explore how I could get excited about math outside of the classroom.
Students shared endless examples of individual high school teachers, mathematics professors, formal and informal mathematical mentors, and advisors who advocated and provided mathematical support and ongoing inspiration. It wasn’t uncommon in the interviews for students to reminisce about bonds they formed with faculty and how those bonds continued to inform their graduate experiences.
We give the final word of this column to a student who felt the presence of many such people in her department – she shares a view of what is possible, with advocacy and allyship and listening:
… there is a lot of love and warmth in [this] department, and a lot of room to just be who you are. Being in this department has been very helpful for me in accepting who I am as a person, and who I am as a mathematician. And that I don’t need to imagine what a mathematician is, and then try to be that. I just need to imagine who I am, and try to grow in that as a mathematician.
Acknowledgements: We would like to acknowledge the following people who have contributed to the research:
- Research team: Maya Bartel, Miriam Gates, Pamela E. Harris, Christian McRoberts, Simone Sisneros-Thiry, Dwight Williams II, and Aris Winger.
- Interview team: Maya Bartel, Nakia Rimmer, Vanessa Rivera-Quiñones, Simone Sisneros-Thiry, Shanise Walker, and Dwight WIlliams II.
- Advisors: Lillie Albert, Federico Ardila, Robert Berry, Alina Chertock, Maisie Gholson, Edray Goins, Chris Jett, Loek Helminck, Regan Higgins, Illya Hicks, Danny Martin, Robert Megginson, William Velez, Erica Walker, and Shelby Wilson.
- The unnamed, generous, brilliant students who have trusted us – not just the CORE team, but all of us in mathematics – with their stories so that math departments can create real and lasting change.
Finally, we acknowledge that this work is supported by the National Science Foundation under Grant Agreements #1920753 and #2207795. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.