Thursday, November 01, 2007

Harder than it looks

Teaching is hard.

What makes it this way?

After 280 wrapped up yesterday, I was walking back to Robinson Hall with Quincy, and he was rehashing the experience he'd had less than an hour earlier with two others from the class, their committee report on the latest problem set. He was worried that what I had seen as a successful endeavor had gone horribly awry; it hadn't gone as he'd expected it to. It wasn't as smoothly executed, perhaps, and he hadn't been able to clearly get across (pardon my split infinitive) the "subtle nuance" he was trying to point out in the proof they were critiquing.

"It's really hard to lead someone to say what you'd really like to hear her say, without telling her to say it," I assured him. "That's called teaching." From a pedagogical standpoint, I felt that their committee report had been a solid one.

Most heartening to me is the fact that the students have begun to break away from the "here's the right answer" style of committee report with which they began the semester. "We want this to be a discussion, so if you have anything to say, just come out and say it," Nicolette exhorted her peers yesterday. (Like Quincy, I think she feared that their team just wasn't saying whatever it was they'd have to say to get the others out of their seats.) They were aiming at a different model for their presentation: rather than simply hand out the "correct" proof of the indicated proposition, they intended instead to guide their peers to a proper understanding of the weaknesses of the proofs they saw, and of the necessary elements of a valid proof. The second team had the same goal, and they strove towards it with different steps. In lieu of doling out a proper proof, they instead gave an outline of the elements such a proof would need, indicating where they felt people might have tripped up most commonly. Neither presentation was fully explicit, both focused on the process instead of the product, both adopted a more mature attitude regarding the course content than most earlier discussions had.

In case you can't tell, I'm pleased!

I cornered one of the other students in the Math Lab after class and asked her how she would compare this semester's installment of the course with last semester's. (She'd been enrolled in the course in the spring until health issues forced her out about 2/3 of the way through.) She's enjoying it much more this time around, and she feels like she's learning more effectively. The format, she says, is much stronger (what about it? This was unclear. Is it the idea of the homework committees? The structure of the worksheets? The revisions? I'm not sure...I'll have to probe further), this particular group of students is more open to the idea of learning in this way.

Perhaps what's working well for her is the more conscious focus on writing instruction, in particular writing as a discipline-specific endeavor. She indicated that partly as a consequence of our class she's seen her writing improve in all of her classes. (Her partner, who proofreads all of her written work for her [what a kind soul!], has noticed this as well " 'I only had to add a couple of commas for your last paper,' " my student reported her partner's words.) With the clearer writing has come a clearer understanding: her scores this time around are noticeably better than her scores in the spring. As I told her yesterday, I'm so happy I could hug her.

I am dying to find out what kind of responses we get on the exit surveys for the writing assessment project. This is an exciting study!

Yesterday too I had the first of two interviews with one of the Writing Center's new student consultants. I prepared myself by going over the interview questions I'd been sent in advance, and when Beulah came by, I was all ready...perhaps too ready...with my responses. I actually printed out the abstracted answers to her interview questions that I'd typed up for myself, and asked if she'd like a copy. She accepted them happily. "That's fewer notes I have to take!" she said.

"I hope it's okay that I give you those," I said. She assured me that would be fine.

Our subsequent interview was a brief one, but she asked some good questions. "In what math classes do you feel that writing is important?" I warned her that I was answering for myself and not for my colleagues up and down the hall, and I told her I felt that writing was of pivotal importance in any class, including any math class. It wasn't until I said it out loud that I realized how strongly I feel that way, and how rare that feeling might be among my colleagues. (By "colleagues" I mean my colleagues in the profession, not necessarily the other folks here on the Third Floor.) I cannot imagine teaching a class in which writing didn't figure into the curriculum in some way, whether it's a conscious focus of the class, as it is in 280, or whether it takes the form of a few simple papers on vaguely mathematical topics, as in Calc I.

What else do I need to say right now? I thought to make a dent in the list of topics about which I wanted to say a little, but it seems like I'm running to stand still. (This is a good thing, to be sure, but a frustrating one...I need to invent a way to increase the length of the day by 20% or so.)

With the help of my students, I'm busily amassing good ideas for activities to take place in existing classes, and for classes we could offer as a part of our curriculum:

  1. Last week the idea of math-themed poetry arose from two completely unrelated sources. We batted the idea around a bit in both of my Calc I sections, and it came to the fore as a topic of discussion on listserv of the MAA Special Interest Group on Math and Art, of which I am a member. I've decided I'm going to make math and poetry the focus of the last of my Calc I projects for the semester, a short one that'll cool the students down after the leviathan efforts they'll have expended on the Newton v Leibniz project. I'm going to incorporate a bit more guidance and instruction into this project than I did the last time I asked students to construct mathematical poetry, a sad little project I put into action during my grad school days at Vanderbilt. (Totally unrelated note: Vanderbilt, at 5-3, has the same record right now as Florida. Go 'Dores!)
  2. I'm liking more and more the idea Quincy pitched a couple of weeks back regarding a "Random Seminar," in which participants, students and faculty alike, did research into and subsequently constructed classroom exercises around mathematical topics pulled from a goldfish bowl placed at the center of the room. It could work. It would take some fine-tuning, but it could work.
  3. Quincy pitched another good idea to me by e-mail. A bit less ambitious, this one involves a component exercise for the 280 course: each student has a turn in which she presents a particular nasty proof she's been struggling with to the rest of the class, receiving feedback, suggested revisions, and so forth. Sounds kinda Moore-ish to me. Maybe we'll get a chance to do this a little bit before this semester's over. (Quincy, you're gonna love next semester's graph theory course!)
  4. Another course idea that'll take some work to clean up is an "Unmath Seminar": students are asked on the first day of class to make an alteration to some fundamental axiom of mathematics, somewhat akin to denial of Euclid's Fifth Postulate. From that point on, students are asked to construct an internally consistent mathematical system that obeys all laws that are consequences of the assumptions made at the outset. If inconsistencies arise or inordinate difficulties ensue, seminar participants would be allowed to return to the starting point or some other point intermediate in the construction in order to modify their assumptions to make the resulting system more amenable to analysis. This whole project would be hard, and would require a good deal of advance planning to make the exercise worthwhile. Moreover, the students taking the course would have to buy into the project completely to make it work.
  5. On a less ambitious tack, at some point I'd like to offer special topics courses on lattice theory and set theory.
So much to do!

I've got lunch this afternoon with Quimby and a couple of our cognition folks over in the Psych Department. I have no idea what they're going to spring on me, but I've no doubt it'll prove to be interesting. I've yet to send an e-mail to my colleague in mass comm whom Quimby recommended to me as an interested partner, regarding my idea for a "communicating mathematics" course.

For now, I'm off to be continued!

1 comment:

TIM said...

doc, I KNOW things about the number 9 that no-one knows and I have tried diligently to contact a mathemetician to disclose said to and discuss the huge tip of the iceburg too.

Try me if you will
e-mail me at if ye so will. Tim