Thursday, November 12, 2009

Hall conversations

I spent a lot of time in the Math Lab with my students today, and in the hall outside of it.

Most of that time was spent with my Calc I students, helping them out with the volume maximization problem they're working on right now. It's a barely-unprettified problem demanding a good deal of careful computation and innovative use of derivatives for optimization. They've got to find the least costly means of constructing a collection of dumpsters designed to hold 2000 cubic meters of material, knowing that the dumpsters' shape has to fall within certain parameters. It's a tough nut to crack, whose precise solution involves techniques from Calc III. They students are either loving it or hating it, for the most part. One thing's for sure: they're spending more time on it than they'd ever spend on a set of textbook problems, and they're learning a lot. As I was leaving campus just after 5:00 p.m., two or three of the groups banded together to throw an extemporaneous "dumpster party" in the classroom in which we meet. I almost wish I could have stayed.

I also spent an hour or so talking to a couple of my 280 folks about combinatorial and topological graph theory, and just straight-up topology. I taught Uriah and La Donna how to decompose a torus into a disc with identifications, and showed how this could be used to easily find an embedding of a complete graph on 5 vertices in the torus. It was good fun.

At one point soon after that I mentioned to several current and former students who were there assembled that I'd love to put together an informal reading group (much like the RAP [Research Among Peers] groups we ran at UIUC while I was a postdoc there), and they were all game. I mentioned Herb Wilf's generatingfunctionology, a freely-available text of which I've never read more than a few chapters and into which I'd love to get deeper. I think it would be accessible to some of our stronger students, and they could help the not-so-strong ones along. It could be a fantastic learning experience for us all.

Might could be we could swing that in the Spring.

I also talked to a couple students in the hall outside the Math Lab about my plans for Topology next semester (one's registered already, and the other plans to as soon as she can tomorrow morning). They're both regular readers of this blog, so both were familiar with my portfolio plans, and I asked how they think it'd fly.

Sidney (a student in MATH 280 in Spring 2009) is all for it. "It'd definitely motivate me. What motivates me is proficiency, and you'd be measuring proficiency at achieving learning goals for the course. I'm all about that."

La Donna (a current MATH 280 student) thought it might work well, but was a bit more reserved in her acceptance of the idea. "I have to admit that I'm a little motivated by grades," she said. "A good grade is a signal to me that I'm doing well and getting it."

I suggested that perhaps, as I've posited elsewhere recently, she's motivated by grades because she's been systematically trained to be motivated by grades. She admitted this possibility.

"In any case," I told them, "whether I grade by portfolio or not, whether I hand out numerical grades or not, I know for sure I'm going to permit unlimited revisions. I'm going to let people revise and resubmit, revise and resubmit, and so on, until they're one hundred percent satisfied that they've made their work as good as it can get." Both were excited about this idea.

They're both passionate students, and a blast to have in class. En route to lunch with our speaker the other day Sidney admitted that his mind had been blown on the last day of 280 last Spring when we'd talked about the existence of infinitely many different sizes of infinity.

Crazy shit.

I'm delighted that that delighted him. It's nice to have students like him, and like La Donna. And like Cornelius and Uri and Uriah and Tedd, all of whom were there to voice strong support for the idea of an informal research reading group.

They've got my back as much as I've got theirs.

That's a comforting feeling.

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