Wednesday, June 10, 2009

Stand and deliver

Day Three has come and gone, and though they're still quite quiet, they've begun to strut their stuff, mathematically speaking.

Yesterday evening I presented them with the most substantial "homework assignment" I'll be giving them during these first couple of weeks of the program (the dreaded list of 34 terms and concepts from graph theory for which they were asked to find definitions and examples they would then take turns presenting to each other in seminar), and they completed it well. They'd divided the work up almost perfectly evenly, each taking about four of five of the terms for her or his own, and working together to produce a single Word document (by Friday it would be LaTeX) containing all of their findings. Impressive! They're the first group we've had who's created, unprompted, their own lexicon at the stage in the game. (Or at any stage, for that matter...)

The first few turns taken were orderly ones, each student presenting on several subjects appearing consecutively on the list.

Demeter started things off with a discussion of the many different sorts of sequences of vertices and edges one can consider: walks, paths, trails, circuits, and cycles. Her presentation was straightforward and confident. It was solid, and left little room for questioning.

Dora's presentation on cliques and blocks and related ideas raised a few more questions, which she handled smoothly. I appreciate how hard it is to think on one's feet in any setting, and I can't imagine how much harder it is when the questions you're being asked to answer (on the spot!) involve high-level math you began learning about just two days earlier.

Next it was Daria's turn, and her introduction to independence and domination led to good many more questions, which she too fielded handily.

Nigel's turn came, and he approached his presentation a bit more lightheartedly then his peers had before him. He was particularly adept at using the board and the colored chalk, and he seems very at ease working in front of his peers, providing clear and correct descriptions for each of the terms he'd been assigned. I hope he can build upon that confidence.

After a break for lunch, the rotation became more scattered. Billie's presentation on coloring and all matters chromatic stood at the center of a scattered maelstrom of turn-taking by Omer, Ole, and Nils, who traded off with one another as they discussed everything from graceful labelings to adjacency matrices.

Billie, who comes to us having taken a graph theory course (the only one of the bunch to have done so, I believe), had no trouble at all searching through her old course notes to root out a good working description of the Deletion-Contraction Algorithm. Like Demeter and Nigel before her, she was confident and clear.

To be honest, the tag-teaming trade-offs the guys made made it hard for me to get a good grip on their presentation styles. Even though they spent as much time at the board, cumulatively, as had their colleages, they weren't up before the class for a long enough chunk to get a sense as to how they'll be in sustained presentation.

Ah, but that will come later!

All around, the students did well. There were several minor slips, but that's to be expected. As I'm fond of saying, truthfully, hardly a day goes by without me making a dozen mistakes at the board. Sure, there were a few misstatements and a few definitions that might have been made clearer, but in the end it was good.

One thing I would like to see more of: the students challenging each other and asking questions that serve to further the work their colleagues have done.

And I'd like for the student who's presenting to not look at me when she or he asks "does this make sense?" or "is that right?" Who am I to say? I don't want to be thought the only expert in the room. I realized earlier this evening that in the last couple of days I've made the mistake of sitting at the center of the room's semicircular arc; tomorrow I'll decenter myself by moving to one side. (Funny: it took precisely one day for the students to fix their places in the classroom. From the near side to the far side, they sit thus: Nils, Ole, Dora, Billie, Daria, Demeter, Nigel, Omer; the last two days I've sat between Daria and Demeter.)

I find myself wondering what it is that's interesting them, mathematically...what sort of projects will they opt to undertake this summer? We've now posed maybe a score of open problems (with another score or so lying in wait), but I've no sense as to which ones they're finding appealing. I'm excited to find out.

For now, speak up, my young colleagues! Let us know what's caught your eye.

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