Reflection on Spring 2012; Part III

Originally Posted 05-22-2012

Dynamical Systems

I had taught dynamical systems once before, in the spring of my first year at UNI. Then I used a textbook (Alligood, Sauer and Yorke) which turned out to be too advanced for my students, and I asked them to do too much. The class was lecture/homework with a big final project that involved reading a scientific paper from when Chaos was just being recognized everywhere. Mostly, the class was too hard, but the project bit went pretty well.

This time was going to be different! I planned an IBL approach and I wrote my own notes. Also, as an experiment, I went with a structure described to me at an IBL workshop at UT Austin run by Mike Starbird and Carol Schumacher: each meeting the class was responsible for a small snippet of tasks (usually 4 or 5 of them), and we would spend the first 25–30 minutes of class working in groups to solidify our ideas and refine arguments, and then discuss/present to the whole class.

I won’t try that particular structure again. It didn’t work for me. That is, students didn’t seem to take the personal responsibility to get all of the work done each meeting. Many used the group meetings as a way to avoid coming to grips with the material on their own. Etc, etc. All of this made it hard to evaluate some of my students, as they really did their best to hide and nothing in my written expectations said they couldn’t. In retrospect, one thing I changed from the structure as it was described to me likely made a big difference: I did not require them to turn in written work every class period for evaluation. I don’t have a graduate TA for this type of class, so the workload wasn’t feasible for me. But I see now that this might be a key part of making that particular IBL structure work.

Also, I was trying to get them to use Sage for the numerical work required. Basic dynamical systems has a nice experimental feel, where you can get the computer to do some basic things for you and then poke around the data looking for patterns. What I learned is that even fairly advanced mathematics students who otherwise seem comfortable with technology will balk at having to do something that requires a simple “for” loop. I’ll have to write code snippets for them next time. I had a few computer science double majors, and they got the class limping through that portion of the course. But really, that is when things hit a wall. The class never really recovered. I realize that I have to work on how to teach how to use the computer to do mathematical investigation. Computers are an incredibly powerful tool, but only if you have some basic way of using them. (Like Sage/Python confidence.)

In the end, we did not get through all that I think we could have, but we did “enough”. I certainly want to do more next time.

What will change?

First Item: More structure to the learning of how to use the computer.
Second Item: Pre-written scripts to hand out so that the computer is not the obstacle.
Third Item: Back to a structure I am more comfortable with–one that involves more personal responsibility on the part of the students.

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