Preparation, meet Perspicacity

Already I've noticed several signs that this semester's 280 students are a sharp lot, and with a little poking and prodding I'm sure they'll be capable of great things this semester.

For instance, they've already picked up on the subtleties of the proof and disproof of universal and existential statements, which subtleties might make fine fodder for a paragraph or two in the "textbook" chapter they'll be writing on mathematical statements. Namely, they recognized almost immediately, and on their own, that one can disprove a universal statement through counterexample, but not an existential one, paving the way to an easy understanding of negation, the topic for this coming Monday.

I like to think that their effortless mastery of these concepts comes as much from their preparation as from their perspicacity: it certainly helped to make sure all (or at least most) of them had read through the class's worksheet before class had been convened. I'm thinking it's going to pay off handsomely to designate discussion leaders as I've begun to do, also. Today the three discussion leaders provided the majority of the examples on the board, and did a fine job of explaining the choices they made.

This course's structure is in continual flux, but I think I'm more and more closely approximating an ideal design. My only worry at this point is that the "textbook" component of the course, though I'm quite sure it'll work pretty well this semester, would prove too complicated a project to put together in a larger class.

We'll see. I've admitted to the students that I'm not even sure how that aspect of the course will come together, and I'm as curious as they are (probably far more so) to see what comes of it.