A Guide for Mathematics PhDs: How to Incorporate Education into Your Scholarship

Let me introduce myself: I am an assistant professor at Auburn University, where I was specifically hired to conduct discipline-based education research (DBER) in a mathematics and statistics department. While my current research is solely in mathematics education, my undergraduate and graduate work, as well as my postdoctoral research, was in Mathematics. You may be wondering, why the drastic change? In the second year of my postdoc, I realized that I was fascinated by math as a verb, rather than math as a noun. To clarify, while I found mathematical objects to be interesting (math as a noun), I was deeply enthralled with the different ways people do, learn, and teach mathematics (math as a verb). Fortunately, I didn’t need to go back to grad school to earn a second PhD in mathematics education; I have been able to pick up the tools and techniques of education research as I go, while also continuing to leverage the skills I developed as a mathematician.

In this article, I will share lessons I learned making the transition from research in mathematics to research in undergraduate mathematics education (RUME). I assume most readers won’t want to entirely leave their mathematics research program to become education researchers and, accordingly, will provide advice on how you could build familiarity with education research or how you might incorporate mathematics education research as a portion of your overall research program.

Blurring “Teaching vs Research”

In 1990, Ernest L. Boyer, a former US commissioner of education (i.e., secretary of education) argued that academia should reconsider the siloing of teaching apart from research activities Boy90. A variety of initiatives, such as the scholarship of teaching and learning (SoTL) movement, have since emerged as a way for faculty to combine scientific inquiry with their own teaching practice. This is precisely where I recommend you start your journey, by considering teaching and learning in your own courses.

One way we can blur the line between teaching and research is to purposefully bring our mathematics research skills into the context of our teaching-related activities. In particular, in mathematics research we strive to be systematic by verifying and proving claims. We also share the results of our work broadly with our community, for example through seminar talks or posting our preprints to the arXiv.

Let’s consider how we might be more systematic and public with a teaching-related material, which could be your lecture notes, a digital demonstration (e.g., GeoGebra), a handout for group work, or an assessment. While one may be quite careful and thoughtful in designing something to use in a class, if it is used over and over again without explicit consideration of an outcome goal and evidence that it will achieve that goal, then I will position that activity as informal and private. I’ve also been very vague here in terms of outcome goals. You could, for example, intend an assignment to support students in developing understanding of a concept or in developing a positive outlook on mathematics.

One way to be more systematic in the creation of your classroom materials is to collect feedback from a colleague. Alternatively, reading literature could help you think about your course materials to see if anyone has written about your scenario and desired outcome. You may find numerous suggestions that you can leverage when developing or refining your teaching. To be even more systematic, you can collect information that will suggest if you achieved your goal or not. For example, if you want a handout to support students in developing their understand of a concept, you might ask them to answer a short question at the beginning and at the end of class to see if there was a change after engaging with your handout.

The other important consideration for scholarship is dissemination. You can share your teaching materials online, either on your personal webpage or in a widely used repository such as AMS Open Math Notes. If you have collected data concerning the effectiveness of your materials in achieving your outcome goal, you can analyze your data and publish it in a wide variety of outlets, depending on both the scope of your data collection and the rigor of your methods. To delineate between SoTL and RUME, SoTL research tends to be more limited in scope, for example by focusing on one person’s classroom. What we call RUME or DBER generally aims to make broader generalizations, for example by studying a learning phenomenon with college students coming from many types of institution—liberal arts colleges, universities, and community colleges. Frequently, the data and methods presented in RUME or DBER publications will be reviewed more critically than if they were to be presented as SoTL.

There are numerous grant opportunities that support education research. Seeing what education-related grants have been funded can provide you with a broad perspective on the current state of the field and help you in developing your support network. The most relevant NSF solicitation is called Improving Undergraduate STEM Education (IUSE); I recommend typing “IUSE” and “mathematics,” or a more specific search term if you are interested in say linear algebra, into the NSF award search: https://www.nsf.gov/awardsearch/. Note that you do not need a grant in order to engage in education research.

Above, I focused on creating and disseminating teaching materials, but you might be more interested in teaching-related activities that fall outside of the classroom, such as professional development for instructors. The private and informal version of this activity might be reflecting on your teaching by yourself. This could become more systematic by writing a teaching statement, reflecting on your student course evaluations and adjusting your teaching practice accordingly, or participating in a workshop on teaching and learning. To leverage your interest in this activity for scholarship, you can explore organizing teaching professional development for your community and reporting on the impact. Teaching professional development can range from resource-heavy options, like organizing a seminar series or a weeklong workshop with external experts, to low-cost options, like forming a community of colleagues that meets regularly to discuss teaching or visits each others’ classrooms to provide teaching feedback.

After reading about these two possible directions, if you would like to start incorporating education into your scholarship, you will need to build your support network. In the next section, I will share the communities that supported me in making my transition from mathematics to mathematics education research.

Building Your Support Network

Locally

If you are at a large university, your institution will likely have seminars or workshops related to teaching and learning that you can attend. If you are at a smaller institution, you may not be able to attend this type of event on your campus, but you can find virtual opportunities on the AMS or Mathematical Association of America (MAA) webpages. These resources likely focus on practical tips for practitioners which has been distilled from research. I highly recommend these; they will help you to develop as an educator and you will meet others who are focusing particularly on their teaching. On the other hand, this type of event will not reveal how to do education research. To gain familiarity with the mechanics of research, you should look for talks that are specifically intended to communicate research. You may have to work harder to find these events, for example by reaching out to another department on campus to see if you can join their colloquium email listserv. Even better, if your department has a seminar/colloquium budget, you could ask if you can invite an undergraduate mathematics education researcher to visit and give a talk.

As I mentioned before, SoTL as a movement is gaining a lot of traction. You may be able to locally find a SoTL institute/academy, an organized group with a facilitator to walk you through the steps of conducting your first research project. This could provide you with a cohort of colleagues who also are interested in engaging in education research and who come from different disciplinary backgrounds. A SoTL academy would likely walk you through the process of securing Institutional Review Board (IRB) approval for human subjects research, which may be required if you publish data related to a class. IRBs were put in place as an ethical safeguard after numerous instances of research abuse came to light in the 1900s (e.g., the Tuskegee Syphilis Study); you can read more about the history of IRBs in the the Belmont Report.

By federal law (Title 45 Code of Federal Regulations Part 46), every academic institution that receives federal funding is in charge of forming their own IRB, so it is important that you find a local “IRB mentor” who can share their experience of the process with you. While it may be tempting to ask a friend who you know has an approved IRB protocol at another institution about the process, don’t do it! What may be true for me at my home institution is likely to not be true for you at your home institution. The forms you need to fill out and the training you must complete will be different.

Nationally

If you are attending a national meeting, such as the Joint Math Meetings or MAA Mathfest, try attending some sessions on education research. As I discussed above with respect to seminars and workshops on your local campus, some of these sessions will be more about relaying information and less about how to do research, so you may need to ask around about the purpose of the session.

You can also attend a conference specifically dedicated to education research. My two favorites are the Annual Conference on Research in Undergraduate Mathematics Education put on by the Special Interest Group of the MAA on RUME (http://sigmaa.maa.org/rume/Site/Conferences.html) and the annual conference of the Research Council on Mathematics Learning (RCML) (https://www.rcml-math.org/). RUME conference attendees have a variety of academic backgrounds; there will be mathematics PhDs and Mathematics Education PhDs presenting on their education research. I enjoy the RCML conference because it focuses on mathematics learning for both children and adults, broadening my perspective on what is happening at all levels of mathematics education research, not just in my particular area of focus. Similar to the annual RUME conference, researchers with a wide variety of backgrounds attend the RCML conference. You’ll meet mathematics education faculty, mathematics faculty, and K–12 school leaders.

If, after attending some research talks, you feel like education research is something you would like to try, I would strongly encourage you to apply to attend a weeklong NSF-funded field school called Professional Development for Emerging Education Researchers (PEER) (https://peerinstitute.org/). These field schools typically happen in December or over the summer. Some locations may be more competitive to get into based on local demand, so I encourage you to apply again if you don’t get invited the first time (One of my graduate students had to apply twice in order to participate). I attended a PEER field school in Rochester, NY, and it felt like summer camp for DBER! The program is extremely well-thought-out and hosted by a team of highly dedicated facilitators. I formed a pod of mathematics education researchers at PEER that I still keep in touch with.

Audacity and Its Challenges

At this point, I’ve given you a mixture of terms all to describe education research: SoTL, DBER, and RUME. For me, these areas are not well-defined in the mathematical sense. I’ve experienced that what one person calls DBER, another will call RUME. For me, these terms have been most helpful in identifying myself and how I relate to a particular education research community, as well as helping me to set reasonable expectations for my work.

For those just getting started in education scholarship, SoTL can be a useful identity. SoTL is intended for faculty from noneducation backgrounds to become more reflective and scholarly teachers and to share their findings publicly. Because the focus of SoTL is on your classroom and your teaching practices, SoTL is a friendly introduction to education scholarship.

On the other hand, DBER/RUME have more expansive aspirations, meaning the skills will be much more challenging to learn. I currently identify most with DBER, because this identity acknowledges that I am coming at education from a disciplinary background. In math grad school, we slowly learn the norms of our community, from the conventions of mathematical writing to the structure of a research talk. We have a structured program of study, that makes sure we develop a common foundation of skills that will prepare us to be independent and successful mathematicians. As a discipline-based education researcher, I am learning new skills in a very ad hoc way, meaning I make mistakes that would be obvious to a second- or third-year mathematics education PhD student.

This is why I have called this section “Audacity and its Challenges.” Audacity can mean both willingness to take a big risk as well as impudence. It is a testament to the welcoming and nurturing culture of the research in undergraduate mathematics education community that my audacity and I have been able to thrive.

Why Try Education Scholarship?

The vast majority of mathematicians employed at a college or university are also responsible for teaching undergraduate or graduate mathematics courses. Additionally, many faculty members in mathematics departments will have to do teaching-focused service, making decisions about a broad range of issues from textbooks and course placement exams to teaching professional development and awards. Engaging with education research can open new opportunities and increase the effectiveness of your efforts. If you feel drawn to put a lot of effort into teaching and learning, writing up your work to share it with others could help you to meet your expected annual scholarly contributions (make sure that your department will count this before deciding if or how much you want to work in this area!). Most importantly, by engaging in this conversation, you can contribute your unique insights to our generalized understanding of mathematics teaching and learning.

As a mathematician, I’ve found that learning how to do education research is definitely challenging, but with perseverance and patience, it is doable. If you choose to integrate education into your scholarship, there are supportive communities waiting to welcome you!