Reflective Writing for Spring 2012

Originally Posted 05-21-2012

PHhhhhhhhhhhhhhhhhhhhhhwww. Hack, kaff, kaff… kaff. Oh, kaff, my. This is dusty.

Well, this post is a long time coming. When we last left our intrepid hero, he was at that dismal point in the semester where is pre-prepared material had run out. Now, the semester is over, by two weeks, and the craziness is over, and the recuperation time has expired. Now it is time to reflect. As Stan Yoshinobu suggests, I might as well write it down and pretend to share my insights (aka bruises).

The Big Plan was

For those of you new to the conversation, I was running three brand new semester long courses, all in an Inquiry Based Learning format. Well, sorta. And I was trying to implement the use of the free, open-source mathematical software package Sage in a two of them. The courses were these:

  • Math in Decision Making
  • Linear Algebra
  • Dynamical Systems: Chaos Theory and Fractals

First Course in the Hopper: Math in Decision Making

My original plan was to split this into three units. The first was about the existence of uncountable sets, and was mostly stolen/adapted from the work of my colleague Doug Shaw. The second was on the classification of surfaces (compact, possibly with boundary). This one I wrote myself from scratch. The final unit was to be on classifying wallpaper patterns, and would use the Conway-Thurston approach and the previous work on surfaces. Each unit would have a separate exam.

Also, this course benefitted from the participation of Kyle Pitzen, who agreed to be an in-class teaching assistant rather than a grader. Kyle was wonderful and helped me deal with the largish class size (36 students) for a first run IBL class.

The first section went really well. I attribute this to a couple of different factors, but one of them is that I stole Doug’s work. He is amazingly good at writing problems. I’m sure that most people notice Doug’s cutesy, personal touch. He has a distinctive prose style. But that is inconsequential, really. The important part is that he has a gift for recognizing the cognitive difficulties that students will have and writing problems that force students to confront them in a graduated way. I only lightly edited Doug’s task sequence to fit my needs, and everything was wonderful. The first exam showed that most of them basically got the main point.

The second section was fine, but did not go as well as the first. Students found the material on surfaces very challenging (which is OK with me), and it took me a while to figure out what this particular audience’s difficulties are. In the end, I’d say that those who worked hard on this really learned a lot, but a larger than acceptable fraction of the class got frustrated and gave up. I think I can make this material work, but I will have to streamline it. We definitely spent too long spinning our wheels about the kinds of curves you can draw on surfaces. I want to get right to the point of computing Euler characteristic, and maybe leave out the “baby fundamental group ideas.” (It hurt to write that sentence.) This exam showed a split in the class: Some got it, some did not.

At the end of unit two I had four weeks left. I had been talking to lots of my colleagues about expectations for the course, and I started to feel pressure to make sure I covered some basic statistics. No one tried to pressure me, I just felt the responsibility.

So I took two weeks and some of Doug Shaw’s problems on understanding horse race political polling data. This was fine, but a significant number of students had already seen this type of thing. It is not terribly deep, and you have to black-box the main result in a pretty significant way… This was unsatisfying. Then I took the last two weeks and tried to show them some things about continued fractions. Just because they are interesting. Exam results show that the last “unit” was not very successful. Students did not really get the main points, as a class.

I have some SALG data from this class, but I’ll go through that when I prepare my MathFest 2012 talk on how this class went. I hope that it shows that students at least changed their attitude about mathematics to something more positive.

What Changes Do I Make for the Fall

I get to offer this class again in the fall. This will likely be an even larger class (about 65 students wouldn’t surprise me), so I am fortunate to have Kyle back as an assistant. I think that I will keep the first two units. The counting unit will add a day or two to think about the Cantor set (because we can). The unit on surfaces will get whittled down a bit and rewritten to aim exactly where we want to go, bypassing some of the things I couldn’t resist the first time. As for the third unit… I’m not sure.

Right now, I am exploring a suggestion from Jeremey Shipley on Google+ to look at a book by Ian Hacking on different models of probability and how they focus our decision making processes.

Till Next Time

Since this is getting long, I’ll cut off here and resume after a bit with discussions of the other two classes.