# College Math Teaching

## February 12, 2012

### Mathematical Research at “Teaching Institutions”

Filed under: academia, editorial, mathematics education, pedagogy, research — collegemathteaching @ 1:03 am

Now as a professor, I don’t have a “dog in this hunt” so to speak because I teach at a 10-12 hour per semester load institution and I am grateful to have the job. But as a citizen and as a mathematician, I think that the research intensive universities have a place and that it would be a colossal mistake to turn them into “teaching institutions”. We need places that generate knowledge, and one isn’t going to be able to generate top-level mathematical knowledge (say, at the level that gets published in the Annals of Mathematics or in Inventiones mathematicae if one isn’t devoted to keeping current and active on a full time basis.

Now my institution does have a research requirement for tenure and promotion and I’ve developed a modest publication record and am still working to add to my publication list. And yes, many of my colleagues have published far more than I have and I salute them for it.

But let’s face facts: mathematical research at institutions like ours consists of
1. tackling spin-off problems from areas opened some time ago
2. working with another medium level scholar in another discipline to solve some of the mathematical problems related to that discipline
3. working on “nice to know” things that one discovers (or rediscovers) when preparing for class.

As a colleague at a similar institution said: “I dabble here and there; there just isn’t time to learn something that takes 5 years to master”.

The fact is that teaching classes, doing service and meeting with perplexed students soaks up the vast majority of one’s time. Add to that the fact that one’s “upper division” class might be a class that one has never taught or one that you last taught a decade ago; in reality one has to relearn much of the material that has faded from memory.

Then, there is the basic brain rot that occurs from mostly dealing with trying to explain to students that $\int e^x dx \neq \frac{e^{x+1}}{x+1} + C$. One also has the baby-sitting of getting the poorer performing students to not text in class and to explain to them why their course average of 65 doesn’t entitle them to a B (or even a C) and to do so in a way that doesn’t have their parents complain to the department chair.

Then there is the brain atrophy that comes from not reading anything hard for months at a time; then when you try to read something hard you often only have a few minutes of uninterrupted time to do so.

Hence the research that you can do, while it can require cleverness, really can’t require that you master the new sophisticated techniques.

On a side note: this is part of the purpose of my writing this blog; it encourages me to learn stuff that is “new to me” or “what I should have learned a long time ago.” After this next round of exams, I hope to talk about quartic splines that produce increasing, convex curves.