By Diana Davis

As a mathematician by nature and by trade, I like to approach the world in terms of trying to optimize things: minimizing the time I spend walking to the math department in order to maximize the amount of time I spend being productive, for instance. As I’ve been teaching for the first time this semester, I’ve thought more about what I’m trying to maximize, and how my goals will affect what I do in the classroom.

Last summer, when I was thinking about teaching calculus but before I had actually done it, I decided that my goal would be for all of my students to be able to solve at least six out of the eight problems on the final. My thinking was that each student might not end up understanding everything that went on in the course, but whatever they did learn (those six topics), I wanted them to understand very thoroughly.

When we maximize one thing, other things may suffer. I happen to be teaching a mandatory pass/fail class, where 50% is the passing grade. One of my goals is for all of my students to pass. If I maximize the number of my students who pass (ensure that no one fails), this likely comes at the expense of the best students, who could use more enrichment.

As the semester has progressed, I have changed my goals slightly. Now, I want to maximize my students’ intuitive understanding of the topics that we cover. I don’t want them to memorize anything; I want each of them to understand what is going on, before we move on. Maximizing their understanding comes at the cost of our pace. Rather than simply stating the second derivative test and doing several examples, I spent all of today working on an intuitive understanding of the second derivative, drawing lots of pictures and doing only two examples. Will this help my students learn? I hope so.

My students fill out end-of-semester evaluations. I have wondered, if my goal were to maximize my evaluation scores, would I be doing anything differently? I am not too worried about this, because I think that if my students are engaged in the class and they are learning, then the ratings on the evaluations will fall into place as well.

What are your goals when you teach, and what are you seeking to maximize?