Why I Teach Such Good Classes (2003)

Right. Here's some old paperwork, alpha-tized as usual; do please maintain the order as it circulates so everybody can find their own work. Exam 1 is a week from tomorrow; Friday the I don't know what—28th, thanks. Chapter 6 and the first part of 7; I'll be more precise by about Wednesday or so.

Okay, check it out. Apparently there's been some dissention in the ranks and somebody's gone over my head to the chair to complain about how how things're going in here. Obviously, I'd rather talk about mathematics than, whatever, classroom management—and we'll get back to that real soon—but I guess I'd better say a little bit about this business.

So. If I was to stand up here every day with a perfectly prepared lecture and write out a crystal-clear set of notes, and if you were to all copy it all out into your notebooks... then I claim that would be pretty much a waste of time: you might just as well be watching TV.

Obviously a lot of teachers do work this way: "I talk, you listen"... and there must be a few students that it works real well for. But, doggone it, if it worked for anything like a majority, then you'd mostly know this stuff already and we'd be here talking about Algebraic Number Theory or something.

The best thing I can do every day, as far as I can tell, is maybe talk about some new trick, maybe something about common mistakes in recent work, maybe look at a few questions as usual... but then, and this is where I get a chance to really do something right: ask some question that about half of you will have some pretty good idea how to begin to answer.

Now, I've tried to be that guy that dresses up nice and dots all the tees and crosses all the eyes and always has beautiful slides for the overhead and ends 30 seconds before the bell. But I gave up trying a long time ago: I am not that guy. A really good day for me—and we've had a few—is when I'm moving around the room troubleshooting and I can overhear a whole bunch of different conversations about the Problem Of The Day. Then I know I've asked the right question... and, for me, that's the most important skill I've learned over my, whatever, n years as a teacher. Try to have some faith: I might know what I'm doing.

OK. Yesterday we were looking at rational functions...