Disclaimer: let me be clear: these are MY thoughts. Not everyone is like me.
I have served on several search committees and have chaired several of them as well. My university: an undergraduate university where we have a very modest, but mandatory research requirement (much less than what an R1 has). Teaching loads: mostly service classes; maybe an upper division class; typically 10-12 hours per semester. Service loads are heavy, especially for senior faculty.
These thoughts are for the applicant who wants to be competitive for OUR specific job; they do not apply to someone who just wants to make a blanket application.
General suggestion: Proofread what you submit. You’d be surprised at how many applications contain grammatical mistakes, spelling errors and typos.
Specific suggestions:
Take note of the job you are applying for. We have two types of tenure track positions: assistant professor positions and tenure track lecturer positions.
One can obtain promotion from the assistant professor position; one cannot be promoted from our lecturer position.
Assistant professor position: has a research and service requirement and involves teaching across the curriculum (lower and upper division classes)
Lecturer position: has a service requirement and involves teaching freshman courses..occasionally calculus but mostly pre-calculus mathematics (college algebra, precalculus, perhaps business math, non-calculus based statistics).
Teaching: What I look for is:
1. Relevant experience: how will you do when you walk into the classes YOU are teaching? Can we reasonably predict success from your application?
2. References: if you are applying for the lecturer position, you should have a teaching reference from someone who has observed your teaching in a pre calculus class (algebra, trig, pre calculus, etc.). Letters that say “X is a great teacher” and is followed by the current buzzwords really don’t stand out. Letters that say “I observed X teaching a precalculus class and saw that…” get my attention.
If you are applying for the assistant professor position, I’d like to see the observation from, say, a calculus class.
Observations of how well you lead a graduate student review for the Ph. D. exam on the topology of manifolds really isn’t helpful to us.
3. Teaching statement: I don’t care about all of the hot buzzwords or how you want to make the world a better place. I’d like to see that you thought about how to teach and, even better, how your initial experiences lead to adjustments. Things like “I saw students could not do this type of problem because they did not know X..” catch my eye as do “I tried this..it didn’t work as well as I had hoped so I tried that and it worked better ..” also catch my eye. Also, “students have trouble with these concepts and I have found that they really haven’t mastered…” are also great.
4. Please be realistic: if you ware applying for the lecturer position, it doesn’t help to state your heart is set on directing student research our teaching our complex variables class. If your heart IS really set on these things, this job is not for you.
Research (assistant professor position only) What I am looking for here is someone who won’t die on the vine. So I’d like to see evidence of:
1. Independence: can you work independently? Can you find your own problems to work on? Do you have collaborators already set (if appropriate)? What I mean: you cannot be too advisor dependent at our job, given its limited resources and heavy teaching load. An advisor’s letter that says “student X suggested this problem to work on” stand out in a positive way.
2. Plan: do you have plan moving forward?
3. Realism: you aren’t going to in a Fields Medal or an Abel Prize at our job. You aren’t going to publish in the Annals of Math. If you have your heart set on working on the toughest cutting edge problems, you will likely fail at our place and end up frustrated. And yes..staying current at the cutting edges of mathematics is all but impossible; they best you’ll be able to do is to tackle some of the stuff that isn’t dependent on heavy, difficult to learn machinery. You simply will not have large blocks of uninterrupted time to think.
College Math Teaching 