College Math Teaching

September 16, 2012

Commentary: New Ph.D. in math? Is a “teaching institution” for you?

Filed under: academia, advanced mathematics, calculus — collegemathteaching @ 10:25 pm

I remember MathFest (the MAA summer meeting) and how I enjoyed many of the talks. But one of the talks was rather enlightening. The content of the talk was good enough: it was about the applications of topology to science and engineering problems. The speaker wondered how we might get the research engineers to be more conversant in topics like algebraic topology and wondered if we might…introduce such concepts in our multi-variable calculus and linear algebra courses! Yes…

He made a remark on how calculus was, well, one of those “less-than-desirable” courses for faculty to teach. Oh yes, the speaker was from an Ivy league institution. I had to snicker; at my place the “regular calculus” sequence is considered one of the more desirable courses; the unpopular courses tend to be the non-calculus based statistics, “math for poets” and our “business calculus” (aka “faux calculus”) courses.

So this made me reflect on my career and describe my experience at a “teaching institution that has a research requirement”. I do this to give the new Ph. Ds a chance to determine if, barring a failure to obtain a post-doc position or a tenure track position at a research school, they want to go to academia or retrain for industry or some other area. Life at an undergraduate oriented institution is very different from life at a research institution.

Caveat: I realize that my experience at an “average” undergraduate institution (median ACT of entering freshmen: about 25) is but one data point. People going to an elite undergraduate oriented institution or to open admission caliber places are likely to have a different experience.

My background: Ph. D. in topology from a D-I research place; part of my thesis got published in the Proceedings of the American Mathematical Society. My adviser solved a big problem and has graduated elite students; I wasn’t one of them. This was back in 1991; at the time the old Soviet Union and the market was flooded with Russians with very strong credentials. I feel very fortunate to have landed a tenure track job; I had a couple of nibbles at post docs but nothing worked out.

My university: about 5500-6000 total students; we have a business and engineering department. So we have 15 full time faculty members and most of our load is service courses. Usually we teach two “calculus of some sort” courses (both regular and fake calculus) and one differential equations/linear algebra or upper division course.

Teaching life: students are very needy; they are sold on the idea of “individual attention”. They use office hours. (note: this isn’t a bad thing, but it does eat up time; that is reality). Often most of the students in the class have to take it; most have minimal motivation to learn the material for its own sake and many don’t have a lot of ability. The classes vary; I did have one “fake calculus” class with a median ACT of 22; another one has 10 of the 21 on academic probation AT THE START of the semester.

On the other hand, I’ve had a few classes in which the students were naturally fired up and ready to learn…and had tons of ability to boot. I remember teaching the lesson on Green’s Theorem (integrals) and having a student ask “but…isn’t it true that not all two dimensional surfaces can be embedded in the plane?” Yes, we were ready to go on to Stokes Theorem (ok experts, I know that ALL of the integral theorems are really Stokes Theorem but…)

The stages I went through:
1. Denial: I figured that I’d get started, work my butt off on research (on my own time) and get some publications and get to that post-doc position.

Reality: well, there was a reason I didn’t get the available post-doc positions out of graduate school: ABILITY. I wasn’t as smart as those who landed those coveted positions. Add to that that those in those post-doc positions were teaching lower loads and even teaching advanced classes on occasion (e. g., perhaps an algebraic topology class).

Reality: there were stacks of grading, committees, students seeking help often for problems like \frac{d}{dx} sin(2x) = ?etc.

Reality: I also had to worry about tenure; that meant at least doing a few problems that I had a good shot of solving and getting published. But these publications were the more “routine results”; throw-aways for the big guns but not the kind that would get you noticed at those D-I research places.

Reality: the longer I stayed away, the more techniques I forgot…and the more my discipline left me behind. Staying current is a full time job in itself, and all but impossible to do for someone teaching 12 hours and doing departmental work.

Reality: there were also the “been there forever” colleagues with questionable doctorates (or less) who, well, didn’t see the difference between their courses and those taught at MIT. Seriously.

Reality: some of the old time “researchers” indeed had a long list of publications: in those low-level foreign journals; this was, well, the quality of research that I had to do to ensure that I had something to get tenure. And some of them didn’t understand why research I faculty didn’t consider them to be scholarly equals.

2. Acceptance: many of my colleagues understood and reminded me that we are all in the same boat; I did the same for newer colleagues. They also reminded me that post tenure research is important…for one’s own sanity. Teaching calculus to, well, average students year after year will kill your brain cells if you don’t keep at least some intellectual engagement. You won’t be publishing at Annals of Mathematics and you are highly unlikely to be a lead speaker at a research conference.

And, after tenure, you can afford to do some “fun” filling in the gaps of your own mathematical education and perhaps even publish a paper or two in a new area (not cutting edge research, of course).

Get to some conferences, keep perspective (yes, your discipline HAS marched on without you…yes that hurts but that is reality) and have fun. Don’t pretend to be something you aren’t; that takes too much energy!

A comment made me rethink what I said: I said what I meant but I was incomplete. Here are a few upsides to this situation:

1. We teach across the curriculum. Hence I ended up learning things (or relearning some forgotten undergraduate mathematics and building on it) that I might not have learned as a full time researcher in my field. For example: I never realized how fascinating some of the numerical methods can be! So, when I teach something like Simpson’s rule in calculus, I have a bit more perspective and can point out that the relationship \frac{2}{3} MID(n) + \frac{1}{3}TRAP(n) = SIMP(2n) is really part of a scheme in which previous integration approximations can be averaged to produce a still more accurate approximation (Romberg Integration).

2. I have smart colleagues; they too have had to produce at least a little bit of research and we talk to each other about it. In fact, more than once, discussions with colleagues have lead to minor papers.

3. There are the math major classes too. While these students are not ready for cutting edge stuff, having a bit of research background helps one to provide some perspective on the various major theorems (e. g., what are the ramifications of the various types of convergences of sequences of functions?)

So, there are lots of upsides too and I don’t want to downplay those.


  1. It sounds painful to be where you are.

    I’m in a less prestigious situation, but happier about it. I didn’t finish my PhD because I saw quickly that it would be alienating. I love math, but I want to learn it at my own pace, which is a tad slower than those classes were. I teach at community college, and do what I can to get students coming into my office more. I get intellectual satisfaction from learning more math (I’m sure it’s not cutting edge) and from thinking about how to help students learn.

    I solved a problem related to the game of Spot It, not knowing that it was related to finite field theory. Some day I’ll learn more about that, because it’s connected to a delightful problem that I solved on my own. I’m putting together a book about playing with math (and hoping against all realistic expectations that it will be some sort of best-seller). I do what makes me happy.

    I hope you can find your joy.

    Comment by Sue VanHattum — September 16, 2012 @ 11:17 pm

    • Your comment made me reread this post; I’ll update with some of the upsides.

      Comment by college math teaching — September 16, 2012 @ 11:36 pm

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