by Brian Katz
In high school, we had guidance counselors to help us make a plan; in college, we had a mentor or dean to make sure we were on the path to our goals. But who fills the role of career guide during graduate school? The most natural answer is the thesis advisor. The problem with this is that most research faculty who produce students only have experience getting research jobs. So what part of their advice should those of us interested in jobs that balance teaching and research take? Over this past year, while applying for jobs, I have realized that the spirit of their advice is exactly right, though some of the details are a little different: as a graduate student, you are a bit of an unknown quantity, and the mark of a strong application is one that makes it clear what kind of peer, coworker, and faculty member you will be. In the end, you will be measured by the evidence that you can provide to support your CV and the quality of impressions that you have made on other people.
Details. There are five main parts to most applications for teaching-research jobs: a cover letter, a curriculum vitae, a teaching statement, a research statement, and letters of recommendation. Each of these is a chance to give a clear picture of yourself as a future coworker.
CV: In short, your CV should resemble your career goals as closely as possible. Graduate school is a fascinating time when we are hybrids, part student and part teacher. The kind of school that expects faculty to balance teaching and research expects the same from the graduate career of a potential hire. And the kind of job that places full emphasis on research expects you to do a substantial amount of new mathematics while juggling other graduate responsibilities, as you will as a faculty member. This is also the best place to show engagement and involvement in the mathematical community through talks and conference participation. Take the opportunity to do community outreach, attend conferences, collaborate with others inside and outside your university, or demonstrate teaching excellence, depending on what you want from your career. Would you hire someone on the promise that his/her behavior will change upon graduation?
Research Statement: The ultimate benchmark for quality research is publishing in a peer-reviewed journal. If this is possible for you, you should try to have a paper accepted for publication by the time you send out your applications. But this is not the purpose of the research statement. Instead, your goal is to demonstrate that you have done original mathematics, that you can communicate your work outside of the most elite circle of specialists, that you ask interesting questions, and that you have a detailed and realistic plan for future research after you leave the shelter of your advisor’s regular advice. A respected mentor from a small liberal arts college also told me that he uses the research statement to see how well the applicant can teach him about his/her work.
In addition, many teaching-research schools have a strong preference for research that is collaborative, especially with students. You should be able to support claims that you can work with students with specific project ideas and a realistic description of the student who could do the work. This last bit is very unusual for a graduate student, so it takes some planning.
Teaching Statement: The teaching statement should make it clear what kind of teacher you are, particularly in situations in which you have had more responsibility. This means that you must be specific and detailed but connect to the reader, and be sure to support your claims with evidence other than your own opinion. Quote from your student evaluations and email correspondence; it’s not inappropriate to email any former students that you think you made an impression on and ask them how they have faired since leaving your class. I believe that schools that care about high quality teaching are open to many perspectives on teaching, but you should also avoid evaluating other philosophies. Simply describe the challenges that you have met and overcome, and let that speak to the relative merit of your perspective.
I thought of constructing this document like writing a song: avoid waxing philosophical like a poorly written love song, and make sure it’s not just a story that your friends will understand. A wise song-writing teacher of mine once said that good songs contain “furniture”, objects that are universal enough that anyone can relate to them but specific enough to call up a colorful image in the listener’s mind.
Letters of Recommendation: The letters are probably the most important part of the application because they are written by people who have already been vetted by the system. But that means that the recommender needs to convince the reader that they know you pretty well. Your thesis advisor will know you well enough for this, but you should make sure that he/she is clear on the kinds of jobs you want. I would strongly recommend that you find another mathematician in your field to write about your research. If you have a collaborator, that is great; otherwise you will need to cultivate some relationship through repeated conversations and demonstrated response to suggestions. For teaching-research jobs you will also need teaching letters. This can only be done well by someone who has seen you teach and talked to you about teaching. If you’ve been a TA for a good teacher, try to maintain a relationship. Consider talking to that person about your later experiences with more responsibility and then asking the person to observe your class. Personally, I think it take more than one observation to write a personal letter about teaching, and it is a rare faculty member who will sit through more than one session of a class as a favor to a graduate student. Three letters is a fairly standard minimum, but most schools are happy to see more. If you have been involved in an unusual program, a letter from a faculty member involved is a perfect way to make sure it is explained in detail. But remember, it is the quality of the letters, not the quantity that leaves an impression. Personally, I would avoid any letter by non-academic writers unless it’s going to be very strong or directly applicable to the job.
These kinds of relationships are hard to nurture; start early. If you are unsure about the quality of a letter or how specific it will be, ask directly, but be prepared to ask someone else if you don’t get the right answer. Give each recommender the relevant application materials, give them time to look them over, and offer to talk about any part of it.
Cover Letter: This single page is your only chance to communicate that you understand what the job will be like and that you are specifically interested in their job. It should include the highlights of your application, the things that you think will grab their attention and separate you from the pack, and address all unusual details of the school or job. Many places scan for proper nouns on this page; sometimes it’s not even a mathematician who does the scanning. Edit this meticulously as a typo here is disrespectful and hence fatal.
Preparing for the Gauntlet. This kind of preparation can take years. It can be done later, but it will become a full-time job, and you’ve already got two of those. I learned a lot from writing my first draft of each of these documents even though the final drafts are almost unrecognizable in comparison. In fact, I learned a lot about myself as a teacher by writing my teaching statement. I don’t see any reason not to try to do this well in advance.
But let me make one point very clear. It may sound like I’m advocating making personal relationships to strengthen your application. Although that is a good recommendation, it misses the point. I think you should talk to mathematicians about math and teachers about teaching and keep records of your own performance because these are the parts of graduate school that transform you into a better teacher-researcher. It’s a happy side-effect that they also make you a stronger applicant.
I make no claims to have done the application process perfectly, but I did receive a very strong reaction from the teaching-research schools during this year of economic crisis (particularly my teaching statement). If you’re curious, my application materials can be found on my website.