The Big Unteaching Experiment: Rebooting the Machine

OK. Sorry for the confusion earlier today folks. I accidentally posted things meant for my classroom blog to this one. And they got automatically tweeted out. Awesome. So, now you know that I keep a simple blog for my students each semester. That way we all have a running account of what happens each day. I find it especially useful for my Moore Method geometry course, but it serves well if a student might happen to miss a meeting.

We are now past the half-way point in the semester. In fact, spring break starts right about…now. I have been worried for some time about the state of my experimental differential geometry course, and today I discussed with my students how we will go forward in a manner different from the first half of the term.

What was the problem?

Too much freedom. I have relatively advanced students who like mathematics. But they are also busy people. Setting a reasonable study pace and keeping up with such a schedule is not something they have ever been asked to do before. And as Robert Talbert noted in some of his recent writing

…this is not something they’re born knowing how to do. They have to be taught this skill — by us.

Quite. That makes it seem so obvious that I am embarrassed for getting us all into the mess we made. I intended to teach them the skill, but I fell into the trap of not structuring the approach. I gave them time and space and responsibility, but I did not help them develop the tool set to deal with the problem. (Hell, I am not the greatest at time management. Why did I expect they would all just “figure it out”?)

Last week was supposed to be the week where students gave presentations on advanced topics in the theory of curves. They were OK. But of course they were generally not on time. Everything spilled over into this week.

I had originally planned for this week to be our “outlining” week for the theory of surfaces. And in a way it was. I asked them to start on this on Monday and today (Friday) we talked about it. I put up some section headings and had the students put what they thought the important items were up on the board while I failed to pay attention. Later we discussed and moved things around. Now we have a workable outline for our last six weeks of study. I proposed a new plan, and they seemed to like it. If you are curious, my hastily assembled version of the outline is here:

Surfaces Study Plan

The New Plan

  • We have six major sections to think about. Each will get one week of class time.
  • Each class meeting will have a clearly defined set of topics for discussion.
  • Each class meeting will have a designated discussion leader who is responsible for prepping 10 minutes of something relevant to get class rolling.
  • Each class meeting will have 2-3 assigned common homework problems so we have something to check our progress.
  • The completed common homework problems will be assembled in a class latex document (we will use writeLaTeX.com) so we will have some sort of record of our work to rely upon

The relief on the students faces when I told them I was going to assign regular homework was a sign. I have never seen students so happy to be given specific things with hard deadlines. Apparently we were so far out of their comfort zone!

I will think more about how to apply Robert’s wisdom throughout what this class is doing. I am starting to re-evaluate in what ways this might have been one of the issues underlying my failure with linear algebra last term. In a way, I think my success with Euclidean Geometry led me into this. I think of EG as a course where I give the students clear expectations and a lot of room, and then I help them adjust on the fly. But that is inaccurate! I spent several semesters learning my student audience and designing the sequence of questions! This makes it look like I am not giving any guidance except for when students ask, but it only looks like it. The task sequence has a lot of hard work buried in it, and that is where I have structured things. Not so with my teaching in the last two terms.

Now, I will do my best to prepare the students to run the show, but not ever take over. In particular, I intend to never pick up the chalk again this term. (I know, fat chance. But I am going to try.) This means that I will have to coach the students on things like

  1. How to read effectively
  2. How to prepare to lead a discussion
  3. How to pick out the nugget of an important or challenging idea so we may focus our attention on it
  4. How to work through an example on the board quickly (what do you leave out? what must you be sure to include?

I am sure I will learn other things that should be on this list when students fail at something I take for granted.

So, that is the deal. I still believe in the goals I set for this class. But even strong students need the right structure and support to help them reach those goals. I will try to do a better job of providing that stuff.

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