Saturday, September 22, 2007

This week in college mathematics

Where to begin?

The week got off to a rough start with an uncharacteristically stern lecture on my part to my Calc I students. (Musta worked: their homework for this past week, graded this morning, was far more complete and correct. Well done, y'all!) They came back that night for a pleasant review session in preparation for a relatively tough test I'd dish out to them on Thursday. I always enjoy review sessions: the students are awake, receptive, responsive. I wish students would bring the same eagerness and vigor to class as they do to those evening sessions. They finished off the exam with an overall class average of 75.9%; one student nailed it with a clean 100%, and there were several other As. With revisions (I told them to think of the in-class exam as a first draft), they've got the chance to bring the class average up to 84%, and I promised a 3% cherry on top of that if they manage to make it within a couple percentage points of that goal.

I spent a good deal of time (most of it while running) thinking about how I'm going to put Calc I together the next time it falls to me to teach it. I've already created almost all of the resources I'd need to make the course decidedly more student-centered: the plan would be to pare down and tweak the existing class notes to the point where they could be used as effective worksheets for the students to complete outside of class and present to one another in class, much as I'm currently doing with 280. I'd break further away from the text than I have already by eliminating all textbook homework problems (they'd instead be "recommended" as practice problems, alongside illustrative examples from the relevant sections of the text) and replacing them with problem-centered applications worksheets (similar to the first team project I've just passed out to my current classes) which would be handed out and collected on a weekly basis. Completing these worksheets would require students to master all of the concepts discussed in class during the previous week, and would force the students to integrate content with application and to produce realistic technical writing. Exams and quizzes (both individual and team) would continue as at present. Classes would be focussed on student presentations and student-led discussions. With the exception of a handful of appropriate weekly projects, I've got most of the materials made up, the transition wouldn't be too hard for me. I'm ready; it all comes down to one issue.

Class size.

To realistically expect freshpeople to speak up and participate in class to the extent that this course scheme would require, I'd need to establish a relatively small and tight-knit community of learners; this semester has reminded me just how difficult that task is when working with a class of 30 students.

Further bulletins as events warrant.

And then there's 280, with another round of committee reports. They did a bang-up job on Wednesday, raising a number of crucial issues, including appropriate choice of notation, simple vs. short in the context of proofs, writing for a given audience, and the fact that there may be more than one way to skin a mathematical cat. So far I've been impressed with how well the committees have appeared to work. Beyond the great conversations we've had in class, I've no doubt that homework has been made immeasurably stronger as a result of input from the committee members. That's my take on things, and I encourage any of my students to give me their side of the story: how are things going on behind the scenes, folks?

All in all, I'd characterize this semester's 280 class as a friendlier place to work than last semester's was. Not only have the students had little problem in communicating with each other, they've shown willingness to speak up and let me know when I'm full of it, too. This past Wednesday a handful of them objected, quite openly and strenuously, to the way in which I'd worded one of the examples in a worksheet, and sure enough, a subtle semantic oversight I'd made in designing the sheet last Spring came to the fore, and I was forced to change it before we reconvened on Friday. Bravo!

We'll be continuing with set theory for the next couple of meetings, and by the end of the week should be making our way into the realm of relations. I'm eager to see how they handle the first take-home exam, due this coming Wednesday.

Finally, I ought to mention that the first meeting of this semester's Learning Circle, on self-authorship, went down this Monday. I have a good feeling about this group, we had a great discussion concerning the basic idea of self-authorship, and how it fits into our various philosophies. In particular, I mentioned that I appreciate (among other effects) the way in which the concept of self-authorship effectively displaces "content ownership"; my colleague Thibault from the Drama Department concurred and added that he's happy to say farewell to the term "development," a word that simply connotes passivity, as though students just happen to turn into learners, magically, mysteriously. (One of the contributors to Meszaros's volume addresses this mistaken view of development.) I'll likely have more to say on these issues as we continue to meet.

Well, it's after midnight, the Badgers have just beaten back the Hawkeyes (on, Wisconsin!), and it's time for me to head for bed. Until next time...

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