Sunday, December 31, 2006

Priming the pump

Here we are again!

It's the last day of the old year, and I'm really starting to get things in order for the start of classes, coming up in a little over two weeks.

I've got (and have had for a couple of weeks now) the syllabus for Calc I put together and posted on-line. I've taught that class often enough that I'm sure I could do it with my eyes closed and both arms held behind my back...which is exactly why I need to challenge myself to do it differently, better, this time around. Not that I've taught it poorly in the past, but I believe that now I'm capable of running this course so much better still that it'll make my previous efforts look like those of a first-year grad student. (I ain't knockin' on first-year grad students, some of them are hella good teachers; what they lack is experience.)

What'll be different about this coming semester? I plan on teaching this course in much the same way I've taught the last four sections of Calc II I've had: lots of application-oriented projects (which are, for the first time ever, built into the syllabus), structured team activities, including the ever-popular team quizzes, carrying over from last semester's MATH 365 course.

Then there's 280, our "Foundations" (read: "Proofs") course. To be honest, I haven't given it much thought, though that'll change in the next couple of weeks.

For 368, the course with the hifalutin' name "Theory of Numbers" (it's "number theory," people! "Number theory"!), I'm envisioning something much more akin to a seminar than a lecture. I may just have to take a page from Maryellen Weimer's playbook and let the students come up with their own course, selecting the assignments they'd like to complete from among a smorgasbord I place before them.

There is one goal I want to lay before them and make a sort of lodestone for the semester: what's the largest number you can prove is prime? I might make it a contest between the members of the class, to see who can come up with the biggest provably prime number before the semester is out. This'll spur them into reading about all sorts of primality tests, involving everything from basic modular arithmetic and Fermat's Little Theorem, through quadratic reciprocity and Dirichlet characters, all the way up to Dirichlet's theorem on prime congruences, and the Riemann Hypothesis itself!

Obviously this is a bit to bite off, let alone chew. But I have a feeling we'll get farther if I let them lead the race than if I serve as a pace car.

I'm off for now...I hope to get a working syllabus up for the other two courses before the week is out and I head down to New Orleans.

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