Friday, January 25, 2008


I've got mixed feelings about today.

Calc II felt all right: the first section was a little sleepy, but the second was more engaged and seemed to enjoy the sugar fix provided by the shortcakes used to illustrate the method of cylindrical shells.

Graph Theory?


After Wednesday's class got a bit rowdy, with lots of cross-talk, overdubbing, interruptions, and just plain ol' mayhem, we decided that maybe we ought to try out a means of directing the discussion. I suggested the possibility of getting a small plush object to toss around: she/he with the ball was the one who got to speak. It seemed a bit puerile, but I didn't want discussion to get out of hand, lest people start zoning out, not understanding what's going on, what's being said, what's being proven.

So Theodoric brought in a plushy soccer ball, and we tried it out.

The atmosphere was...

...well, to me it seemed a bit dead. I'm not sure the deadness was completely unwelcome, but I don't want to kill off the natural enthusiasm that folks are having for the course.

I think some people had difficulty getting the attention of whoever it was who had the ball at any given time, others felt like they weren't going to stoop to "playing the game" of getting the ball before speaking and so said nothing...for the most part we stuck to the plan and didn't speak until given the ball...but it felt stilted, juvenile.

Having to choose between lively and occasionally cacophonous debate on important mathematical topics and stultifying silence, I'll take the debate, even if it means a little chaos every now and then. As I put it to the students in an e-mail exhorting them to write to me and let me know how they felt (their comments will be posted here as they trickle in):

My own two bits, for what it's worth: we've got a room full of 16ish smart, eager people, and I know that there are time when we've all got something to say. I want to keep the class lively and the discussion excited, but I also don't want it to descend into utter chaos. I'm not doing my job well if I let the class devolve into a kindergarten class. That said, if people are overwhelmingly for it, I'll be open to trying to use the soccer ball again (thanks for bringing it, Theodoric, by the way), but my feeling is that (a) you're all mature enough to not interrupt one another and to not crack jokes when other people are trying to explain something, and (b) I can do a better job at moderating discussion should it need moderation. I'd like to come in on Monday and try to go without the soccer ball, we'll let the person at the board lead the discussion (opening it up once he/she is through presenting), and if things begin to get rowdy, I'll exercise my authority and rein it in.
We'll see what they have to say.

Mathematically, we finished off a single problem today, proving that a subgraph of a simple graph is also simple. Our proof, built up in bits and pieces, was ultimately a careful one. One person starting things off with an intuitive explanation, a second tag-teamed with a more solid justification, and a third stepped in to nail it down with some clear notation. The result was a pretty clean proof, and I'm glad we took the time to make it rigorous. Remember, folks: I'd like you to be able to understand these theorems, but you should also be able to prove them.

That's all for now. I'll post student comments on the Great Soccer Ball Fiacso of 2008 as those comments come in.

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