Wednesday, August 13, 2008


Yup, it's that time of year again...Fall's nearly here, classes begin in less than a week, and I'm freaking out that I'm nowhere nearly as well-prepared as I ought to be.

Likely that's not true, but hey.

What's eating at me most this time around is my preparation for Precalc. I've never taught Precalc before (not here, not anywhere...the closest thing I've ever taught was Vandy's one-semester "Survey of Calculus" that took the highlights from a two-semester course of calculus and condensed it into a single semester for the benefit of folks like business majors who didn't want to bother with proofs), for one thing, and for another the course as we teach it involves a substantial on-line homework system with which I have next to no familiarity. It's easy enough to learn, but I'm still puzzling through the details myself and I know it's going to be a few weeks before I'm proficient enough to help guide my students through it.

I'm definitely feeling underprepared. With a week to go, I've got the first couple of days of both of my classes ready: Precalc will start off with a review of the structure of the real numbers, before vaulting into absolute values. Abstract begins with an examination of the Division Algorithm and related results. I'd like to be a week further ahead than this...I've still got next Monday and Tuesday to prepare, though, and with classes starting on Tuesday the hum and thrum of surrounding activity should invigorate me.

Just a couple of days back I was chatting with one of the REU students, and we talked about how we both feed off of the energy of the semester, we get high off of our work and the work that's demanded of us. I'm looking forward to getting that high again.

On a positive note, I've come up with several good ideas for relevant, meaningful Precalc projects that should not only prove challenging and enlightening to the students, but should also give them a leg up when they get to certain cognate problems in their future calculus classes.

For instance, a standard optimization problem in first-year calculus courses is to maximize the volume of a box that can be built from a piece of material of fixed dimensions, according to fixed parameters. The only step that actually involves calculus is the differentiation of the formula the students obtain for volume as a function of one of the linear metrics for the box; deriving that formula in the first place, plotting it and interpreting the graph, and determining maxima and minima visually are all actions that require the skills taught in Precalculus, and students who accomplish such tasks now will be more ready to handle the cognate problems when they recur in the calculus curriculum.

Another plus: while running into campus this morning I finally figured out the general form for the function that governs the work Thalia and I have both kept working on since parting a little over a week ago. I don't know why I didn't see it before, but now with the general equation in mind we might be able to make real progress on actual proofs.

Ah, research.

Here's hoping this semester goes well! Once things get underway, I'm sure I'll slip into the right frame of mind. I always have, for nearly three decades now. I'll be fine. Besides, I've already got pledges of moral support from two dear friends should Precalc prove to be the back-breaking straw.

Much as I know I need to prepare a bit more, I'm having difficulty focusing. I'm feeling very sluggish today. And why should I not be? The weather took a much-needed turn for the rainy overnight, so the sky is a shroud of white. Campus (where I sit as I type this) is dead: my department's a tomb, the building's air is still and warm (the cooler's on the fritz...again), all is quiet.

All right, I'm going to head sense in cocooning myself in this scholarly sarcophagus any longer today. I'm sorry this post has been so scattered and erratic.

To be continued...

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