Confusion in the Classroom

For the second time this semester, I ended up floundering over a problem in Modern Algebra. The first time was only partly my fault. I was taking questions, and someone asked about a homework problem that I hadn't thoroughly thought through. (I know, in the ideal world, I wouldn't assign them before I thought them through, but in this world, I do.) This one was even worse, since it was just an example that I picked out before class. I thought I knew how to do it, but I was wrong, and I didn't figure that out until I was halfway through presenting it.

On the one hand, this is very embarassing. It ruins my image as a master of the material who knows all. It also takes a lot of time. I think I spent about 35 minutes on this one example. We're in the last 100 minutes of class time, so that's an awful lot to spend on one problem. It also throws a scare into the students. One young lady -- one of my best students -- said when we were done, "Please don't put one of these on the exam." They get the idea that if I can't do the problem, how do they have any hope?

On the other hand, I really do think it's good for them to see that these problems take work. Too often, we present the easiest method of doing something, and we bypass all the floundering around that we do trying to find that easy method. I hope that, whatever else, it was a good lesson in how to peck away at a problem when you don't see immediately what the answer is. And I did get the answer. It just took longer than I had originally planned.

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