## Our Value

Robert Campbell and I were discussing why/if we are valuable to the students, and how we could maximize our value to the students (we are probably really talking mainly about nonmajors here). We started with the agreement that almost all students are not going to remember the details of the mathematics from our courses for more than a few weeks after the final exam. Calculus students might retain some broad notations of what derivatives and integrals mean (or not), but most students do not seem to remember the antiderivative of $1/x.$

This is disputable. For instance, I am certain that my students know a lot more mathematics—including the details of things akin to the antiderivative of $1/x$—than a seventh grader. So at the very least, there is probably some cumulative effect. However, let’s take this as an axiom: students do not remember details from our course.

Given that, how valuable are we? I teach about 50 students a semester right now, and I am guessing that I only make a large difference in 2–3 of those students lives. That is not bad, but it also suggests that my courses might not be working too efficiently. Is there a better way of doing this? If my goal is to positively affect students’ lives (in a mathematical way, broadly defined), then I have a much better success rate with advising and undergraduate research.

For instance (this is only a thought experiment), perhaps I should spend almost no time planning and grading for my courses. I can just follow the textbook, cook up a lecture for each class day (which does not take very long for 100-level courses), and just grade three exams over the course of the semester. This would cut down on my planning significantly. Then I could put the time saved into high-impact activities like advising and engaging in student research.

This is not something that I think is a good idea, and it is certainly not something I am planning on doing (I enjoy course planning too much, at the very least).

So this is something I have been thinking about. I suppose it boils down to a couple of questions.

1. What is the real purpose of my job?
2. What parts of my job make real progress in achieving the real purpose?
3. What parts of my job do not make much progress in achieving the real purpose?

Once these questions are answered, how do I spend my days to best do my job? I suppose that this is similar to the idea that IBL can give students a transformative experience. In an extreme case, IBL might give students a transformative experience without teaching them much content. Is this a win? I was fortunate enough to be able to have lunch with David Walmsley this weekend, and he said he heard of an example where a real analysis professor had the students discover the students discover (with very little guidance) the definition of limit. These students owned the notation of limit when they were done. But it took half of the semester to define limit. Is this a win? I think the answer is probably “yes,” but I am not certain.

### 9 Responses to “Our Value”

1. thehabyss Says:

1. Advise and mentor me. I suppose also occasionally hold my banner.

2. TJ Says:

Okay, I guess. But if you follow this too far into “maximizing utility” you will lose me. Does your work have value? I mean TO YOU? Is someone willing to pay you enough to live an acceptable life for doing that work? I hope you can say yes twice. Now just do the best you can and don’t sweat the details too much.

• bretbenesh Says:

Yeah, we don’t want to go too far. The reality is that I love my job—almost all aspects of it. So it is a little dangerous to start trying to improve it.

That said, I want to make sure that my job is not essentially Kakuro. I love doing Kakuro, but my doing Kakuro helps no one else. So I just want to find a good balance.

3. mrdardy Says:

This post makes me reflect on some of my most valued compliments I have received in my teaching career. I used to think that the measure of my success as a math teacher was based on how much math/what interesting facts my students might remember years after my class. I have now moved to thinking that the most valuable indicator of success is whether my students remember that they thought differently, that they asked questions or were asked questions that they did not think of before. In general, if your careful course planning is obvious to your students, and I suspect that it is, then your impact is that you are a careful, thoughtful adult in their lives. The rest is gravy, I’d say

• bretbenesh Says:

That is kind. I am guessing that a smaller proportion of students notice than I like, though. And that is fine, but I am wondering if I can do something different to help the students who don’t notice.

Do you care to share some of those compliments here?

4. mrdardy Says:

The most meaningful one – by far – was from a student about 10 years after he graduated. I was living near him and we had lunch occasionally. He told me a story of being frustrated by a project at work and he told his boss he’d take a long lunch to clear his head. He returned from lunch to find a series of post-it notes on his file folder. He said to me, ‘You know Jim, he reminds me of you. He asks questions I would not have thought of asking.’
I was SO flattered by this, he remembered me as curious and he was struck by the kinds of questions I wanted to ask.