Warming

I had a good time with my Calc I kiddies today, mostly because they did the lion's share of the work. (We spent the day working through several archetypal examples of tangent slope computations, observing patterns along the way.)

So far (six class periods in) several students have expressed mild apprehension regarding the structure of the course. It's noteworthy, though, that they're all enjoying the class and are clearly willing to ride it out and let themselves grow more comfortable as the semester goes on.

Most unsettling to them, I think, is the decentering of formulas that's gone on. There's no call to memorize formulas...in fact, there have been almost no formulas needing memorization. Central, instead, is concept: rather than hand them ready-made formulas for computing slopes of tangent lines to the graphs of various families of functions, I've asked them to derive those formulas from scratch from a single formula, emphasizing constantly why that formula works and where it comes from.

Most of the students are used to being told to memorize; they're used to "theorem proof theorem proof formula formula formula definition example example theorem proof" math courses.

Most of the students are not used to being told to understand; they're not used to "why is that what are we looking for how can we find it how does that formula work how can we use it to our gain" math courses.

I give them tremendous credit: they're patient, they're hard-working, and they're doing great.

They're also fun to talk to, in class and out of class. We jawed a bit today about the following pretty well-documented pedagogical fact: though it's painful (for both the professor and the pupils) to sit in a silent classroom in which everyone's staring at everyone else, when a greater lag time is allowed for between a teacher's question and a student's response, the response that comes is generally richer, more complete, and more meaningful than the one that will come from continual once-every-few-seconds prodding on the part of the professor.

As a part of that same conversation, I mused out loud about why it is that students seem more eager to write a solution on the board when I'm out of the room than when I'm sitting right there in front of them. "Is it because you feel safer making mistakes in front of each other than you do making them in front of me?" I asked.

"No," someone said. "I think it's just because we feel bad if you come back in and we haven't written anything."

There could be something to that.

In any case, I'm looking forward to following up tomorrow (limits!), and to continuing our discussion of matrix algebra in Linear.

For now, I've got to finish a few more paragraphs of my book (tonight: the unique challenges faced by writers in quantitative disciplines) before calling it a night.