# mathematics

## An Indirect Journey to Indirect Impact

#### Looking for Signposts

A colleague of mine once told me, “The teaching of teaching is teaching.” That statement followed the more succinct statement, “T^{2} = T,” which made sense to a couple of mathematicians who were passionate about teaching. Both statements refer to what I now do professionally, which is not what I set out to do when I started graduate school. Back then, the goal was to teach math at a small liberal arts college. These days, I direct the Vanderbilt University Center for Teaching, working with faculty, graduate students, and other members of the university teaching community to develop, refine, and expand their teaching skills. In this essay, I will describe my professional journey from mathematics, a traditional academic field, to my current, non-traditional field of educational development. I will share a few key decisions I made along the way in the hopes that academics interested in teaching or just branching out beyond their current field will find signposts in my story that will help them navigate their own journeys.

### Venturing Outside the Math Building

I was bit by the teaching bug my freshman year at Furman University in South Carolina. Having done well in calculus in high school, I tutored several fellow first-years who were struggling in the course. Finding ways to explain calculus concepts and techniques to my peers and seeing light bulbs go off when those explanations made sense to them was very satisfying work. By that December, I had decided to major in math (and computer science) and pursue a career as a college math professor. That meant going to graduate school to obtain a PhD in mathematics.

Not surprisingly, my choice of graduate school turned out to be a key decision in my career. I chose Vanderbilt’s math program for two main reasons: it was a small program where professors knew students’ names (not unlike the liberal arts environment I had experienced as an undergraduate), and I would have plenty of opportunities as a graduate student to teach. Beginning in my second year, I taught my own section of calculus every semester. Other than the requirement to cover particular chapters from the textbook the department had adopted, I had full responsibility for the course. I led class sessions, held office hours, created problem sets, wrote exams, and assigned grades. Unlike graduate students at the other programs I considered, I wasn’t just grading papers as a teaching assistant; I was the instructor of record for my courses.

This meant that by the start of my fourth year, I had four semesters of college teaching under my belt. With this experience, I applied to be a graduate fellow at Vanderbilt’s Center for Teaching (CFT), the center I now direct. As a graduate fellow, I helped lead the center’s orientation for new TAs, offered workshops on various teaching topics throughout the year, and consulted with other graduate students from across the university on their teaching. Many were from the humanities, the other area of campus where graduate students served as full instructors. Thanks to some excellent training and mentorship by the CFT staff, I learned ways to teach about teaching, helping other instructors better understand their students as learners and select teaching strategies that served those students well.

Working for the CFT as a fellow gave me my first experience in the field of educational development, and I started to get a sense of the indirect impact on student learning this kind of work could have. It was only a vague sense, however. I believed that my consultations with fellow graduate student instructors led to their students having more engaging classroom experiences, but I really didn’t know what ended up happening in those classrooms. I rarely observed my “clients’” classrooms after our conversations nor did I often meet more than once with the same instructor to hear updates. It was primarily the “light bulb moments” my graduate student colleagues had during our consultations that made the work fulfilling.

I also found that I really enjoyed having conversations about teaching with other teachers, particularly those teaching in other disciplines. I remember a fascinating conversation during my first week of training at the CFT with graduate fellows from English and sociology, in which we explored some of the similarities and differences in teaching in these very different disciplines. Although I enjoyed similar conversations with my peers in the math department, these multi-disciplinary conversations, along with the exposure to the literature on teaching and learning I gained at the CFT, helped me to see new aspects of teaching and to appreciate it as a scholarly practice. More than just a collection of tips and tricks, teaching was a subject worthy of academic study, just like mathematics or literature or sociology.

### And Now the Job Market

In spite of my CFT experience, when I went on the job market my final year of grad school, I still had my eyes set firmly on a faculty position at a small liberal arts college. I learned, however, that such jobs were becoming increasingly difficult to land straight out of graduate school. These colleges, ostensibly focused on teaching, were looking for applicants with very strong research records. A few years as a research post-doc could get me there, but that seemed a long time to wait to do what I was really passionate about: teach. Nor was it clear to me how two or three years of mathematics research—likely with no opportunities to teach—would help me succeed at a teaching-focused institution. My search for a tenure-track faculty job wasn’t entirely fruitless—I had several interviews at the Joint Mathematics Meetings that January, two of which led to on-campus interviews. But I also landed a couple of on-campus interviews for somewhat different kinds of jobs. One of those interviews led to an offer from Harvard of all places, and, when Harvard offers you a job, you can’t really turn it down, can you?

My official title was “preceptor in mathematics,” but I often describe my position at Harvard as a teaching post-doc: definitely off the tenure track, but a position I could keep for three or more years. There were about a half-dozen of us, including my “T^{2} = T” colleague, Matthew Leingang. Our job was to run the calculus program, more or less. At Harvard, as at Vanderbilt, calculus is taught in many small sections, each led by a graduate student or post-doc. As preceptors, we taught some of those sections, but, more importantly, served as course heads for the various flavors of calculus. We trained, mentored, and supervised the more-junior calculus instructors, work that leveraged my experience as a graduate fellow at the Vanderbilt CFT. I didn’t interact much with the math majors—they were taught by the senior faculty—but I enjoyed teaching the excellent students we saw from the natural and social sciences who were required to take calculus as part of their concentrations.

The preceptor position also sharpened my sense of the indirect impact on student learning that educational development work can have. In contrast to my experience as a Vanderbilt CFT fellow, at Harvard I was able to work with my fellow instructors over the course of one or more semesters, which provided me opportunities to hear from them how their developing teaching skills were affecting their students’ learning. I also had the chance to interact directly with their students through exam review sessions and other multi-section activities I led as course head. Given this, I felt confident that the hundreds of undergraduates taking calculus were having more engaging and productive learning experiences, thanks in part to my work as a preceptor.

As I indicated above, it’s tough to turn down a job offer from Harvard. In fact, I received the offer via phone while walking to pick up my rental car on the first day of another on-campus interview. I almost turned around to go back in the airport and fly home, but I decided I would give the non-Harvard university a fair shake. The interview was for a non-tenure-track faculty position in a mathematics education department. It would have been a good fit for me, but it wasn’t nearly as exciting as the Harvard option. That left one more on-campus interview on my schedule, this one for a tenure-track position at a small liberal arts college—my dream job.

What then sealed the deal for Harvard, other than the fact that it was Harvard? For one thing, all the people I met at Harvard, faculty and students alike, were fantastic—or at least fascinating. The other preceptors, in particular, seemed like they would provide the kind of teaching community I had enjoyed while working at the Vanderbilt CFT (and they did). The work itself built nicely on my graduate student experience, blending the teaching of math and the teaching of teaching in interesting ways and in roughly equal measures. The small liberal arts college tenure-track job? After the interview, I wasn’t sure that I wanted to commit myself to a career there. I certainly enjoyed meeting the faculty during my interview, but the experience didn’t have the same energy and excitement my Harvard interview had. The Harvard interview gave me a sense that my career could be perhaps something more than a typical tenure-track math professor. I wanted to explore that potential. Timing played a role, as well. The liberal arts college had interviewed me, but hadn’t made me an offer. Harvard’s offer was on the table and the clock was ticking. I went for it.

My biggest concern about the Harvard position was what would come next. This is, I think, a typical concern of those pursuing alternative-academic careers. There are few signposts for our career paths. The Harvard preceptor program wasn’t that old. There weren’t many alumni of the program available to show me what I could do with myself after a few years at Harvard. Would being a preceptor help me land that ideal liberal arts math professor gig I wanted, the one with the energy and excitement? There was no way to know. And if the preceptor position sent me in a different direction, towards a career based on the teaching of teaching, what would that career look like? I was unsure, but I figured that since this Harvard opportunity had come out of nowhere and seemed to be such a good fit for me, perhaps something else would turn up serendipitously at some point down the road. Sure enough, something did.

Sidebar: After that first year as a preceptor, I was privy to the discussions happening on the other side of the preceptor hiring process. I was struck by how challenging it was to find many candidates that possessed the right blend of skills for the position. I note this not to say how exceptional I was as a candidate, but to point out that the particular interdisciplinary space between the teaching of math and the teaching of teaching is (relatively speaking) sparsely populated. To be more explicit, we saw many applicants who were very talented mathematics teachers, but few of them seemed to possess the experience or mindset that we felt would equip them to be effective teachers *of* mathematics teachers. Just as being a talented mathematics researcher does not imply that one is an effective mathematics teacher, being a skilled mathematics teacher does not imply that one would be suited to training and mentoring other mathematics teachers. Successful candidates were highly reflective about their own teaching choices, could understand the perspectives of other teachers who might make very different choices, and were able to help other teachers make more intentional, reflective teaching choices in a non-directive way.

### Something Has to Change

After about a year and a half at Harvard, it became clear that, as much as I liked my colleagues, my students, and my work, living in Boston wasn’t sustainable. It was expensive, certainly, but more important, I hadn’t found any community there. And with a one-year-old and some health issues in my immediate family, I needed community. An assistant director position opened up at the Vanderbilt CFT, so I took a good look at it. Moving back to Nashville sounded great, certainly, but the job itself? Shifting from a faculty appointment to a staff appointment, moving out of a math department to a university-wide center, teaching only one course a year—those were all significant career moves to make. And, just as it wasn’t clear where the preceptor job might lead, the career path for an assistant director in a teaching center wasn’t well marked. Sure, I might get to be director someday, but who knew when that might happen? It wasn’t like progressing from assistant professor to associate professor—the teaching center only had the one director. Timing played a role, too. I didn’t fully realize how much my family needed to move until January, too late to join in the traditional math faculty hiring season. I could have waited until the next hiring season—and test my theory that a couple of years as a Harvard preceptor would make me more marketable as a tenure-track math professor—but another year in Boston didn’t seem feasible. Personal concerns clearly needed to take priority over professional ambitions.

Back to Vanderbilt I went. The work itself was similar to that of my Harvard job, but the emphasis shifted away from the teaching of mathematics and towards the teaching of teaching—in an expanded domain. In addition to supporting graduate students and post-docs in their teaching, I consulted with faculty members, too. I worked with colleagues in the math department (mostly post-docs—I’m not sure the senior faculty knew what to make of me), but also with faculty in other departments, particularly those in the natural sciences and engineering. One-on-one teaching consultations, come-one-come-all workshops, ongoing working groups—the teaching of teaching took many forms. Since I only taught one course a year, my direct impact on student learning was fairly small. But thanks to my work with faculty and graduate students all over campus, my indirect impact on student learning at Vanderbilt was significant. It took me a couple of years to realize that and to embrace that indirect impact, but once I did, I found the job very satisfying.

At Harvard, I appreciated the ongoing interactions I had with the instructors I mentored to give me a sense of how they were refining their teaching practices and the effects those changes had on their students. At Vanderbilt, I found I didn’t need my faculty colleagues to “report back” as much. They let me know what kind of changes they were making to their teaching, and, thanks to an increasingly familiarity with the literature on teaching and learning, I could predict what kind of an impact those changes would have on students. Of course, I always appreciated hearing back from my faculty “clients” at the end of the semester, and some faculty worked with me semester after semester, which was particularly rewarding.

And yet, I still had my eye on my original goal. Could I leverage my work at the Center for Teaching toward a tenure-track faculty position at a liberal arts college? I had no worries about convincing a hiring committee that I could teach well, but my mathematics research wasn’t going anywhere. I tried to fit in some research with my advisor (two buildings away from the CFT), but math research wasn’t part of my job description and it’s hard work to fit into nights and weekends. What about a career in the world of teaching centers? It was great work, and I thought I was pretty good at it. But the lack of a clear career path bothered me, as did the fact that the job market was a thin one, with few job openings each year compared to those for math faculty. On the fence between two potential futures, I worked hard to build a CV that would serve me well either way, going to math conferences and teaching conferences, squeezing in some math research while also writing about teaching. I had found the community I was seeking outside of work in Nashville, but now my work life wasn’t sustainable. I had to pick a path.

### Picking a Path

So I did. I decided that staying in Nashville was my priority. Given that, Vanderbilt presented me with the best options for a career, even if that meant leaving the CFT at some point to find interesting work in some other part of the university. So I walked away from the math research and math conferences and jumped into the teaching center world with both feet. In fact, just a few days after I made this decision, I submitted my application to run for the board of directors of the Professional and Organizational (POD) Network, the largest professional association for educational developers in North America. I had long wanted to take a leadership role in POD. The community had been such a helpful resource for me over the years—from conversations about teaching on the POD listserv in grad school to networking and discussing educational development at the POD conference every year since returning to Vanderbilt. But I didn’t feel I could commit to serving on the board of directors until I made up my mind about my career. After I threw my hat into the ring, I was elected to a three-year term on the board—a nice reassurance that my career choice was a wise one!

As for my concern about a career path, about a year and a half after walking away from my dream of being a college math professor, the director of the Vanderbilt CFT left to take a position elsewhere, after a very successful 13 years at Vanderbilt. I was offered the director position. Accepting that position was the easiest career decision I’ve ever had to make! Learning the ropes of directing a university-wide teaching center has been challenging, but I’m getting there. I’m now one more step removed from the students at Vanderbilt, since it’s my staff that lead most of our faculty and graduate student programs. But being able to shape those programs, direct resources to teaching and learning initiatives, and influence important campus conversations on teaching means that I have an indirect, but significant impact on student learning at Vanderbilt. Since I don’t consult with faculty as much as I did as an assistant director, I depend on my senior staff to give me a sense of the perspectives they hear in their conversations with faculty. I spend much of my time thinking about faculty and how I can leverage the resources of the teaching center to remove barriers they experience in their teaching and create opportunities for them to teach with excellence. Perhaps because I must focus so much attention on faculty, I find myself drawn to the interesting and creative work that students produce in the courses they take from those faculty. Exploring the idea of students as producers of knowledge, not merely consumers of information, centers my work in the student learning experience, and I find this emphasis on student learning resonates at my research university.

I still get to teach one class in the math department each year. I wouldn’t have much credibility as a teaching center director if I weren’t in the classroom myself, facing the same kinds of teaching challenges my faculty colleagues face. Moreover, I still really enjoy teaching math! I don’t think I could have accepted a teaching center position that didn’t involve at least a little math teaching. My math courses also give me the opportunity to try out some of the innovative teaching practices I encounter in my work at the CFT. Doing so is usually rewarding for me and for my students, and the experience informs the work I do with faculty and across campus.

My key career choices—selecting a graduate program that would allow me to teach, putting one foot in the world of educational development as a grad student, gambling that an interesting position at Harvard would pay off in some unknown way, leaving behind a math department faculty position to work at a university teaching center, and saying goodbye to a decade-old dream of being a math professor—only make sense in hindsight. Along the way, I constantly felt I was stumbling along, with only a vague sense of where my career path would take me. Wonderful opportunities kept opening up for me, but it was stressful to have to plan on serendipity. I could see the tenure track not far away, with its clear signposts: assistant professor, associate professor, full professor. I knew it wasn’t an easy path—landing a tenure-track job and achieving tenure are no easy feats—but at least it was well marked. My path? Not so much. I just kept looking for interesting work that made a difference in student learning and hoped that such work would be valued—perhaps not with tenure, but valued nonetheless. So far, that hope has not been in vain, thanks to a few administrators who put high value on the teaching mission of their universities.

Looking back, I can see how valuable an experience it was during graduate school to venture outside of mathematics research and engage seriously with colleagues in other domains—mathematics teaching and educational development. I would suggest graduate students reading this look for such opportunities. Doing so enabled me to expand my horizons and my possible career paths. Key to my success in navigating this expanded world, I think, were the connections I saw between these multiple domains. My training as a mathematician helped me see patterns and structure in the messy details of student learning in and out of the classroom. My experience practicing learner-centered instruction in my own classroom equipped me to approach my teaching consultations in a similar manner, in which the faculty member or graduate student is the learner, developing his or her teaching skills. And I would even argue that my writing skills, when applied to mathematics research, are stronger because of the discussions I have had about teaching with many different audiences, discussions in which I have needed to explain complex ideas in ways that made sense to those audiences.

As my work expanded across these multiple domains, I ran into a challenge: I saw two careers in my future, but only one of me! I had to find a balance of work in these domains that was interesting to me, valuable to others, and sustainable. During graduate school, I expanded my horizons to multiple domains, but later in my career I needed to contract those horizons, at least a little, and focus more on one of those domains than the others. This meant making some trade-offs with which I had to become comfortable. I teach far fewer students than I would as a tenure-track faculty member, so my direct impact on student learning is not what it would be on that career path. But thanks to my work with faculty, graduate students, and administrators all over my campus, I have an indirect impact on the learning experience of far more students, which makes my work very fulfilling.

- Tags: educational development |
- mathematics |
- teaching