Will the (Learning) Circle be unbroken

I'm in Clemson for a couple of days, very much enjoying the 24th Annual Miniconference on Combinatorics and Algorithms. I'll be speaking tomorrow about a topic I've thoroughly enjoyed working on for several months now, with the help of one of this past year's REU students. Despite the research-heavy atmosphere I'm breathing down here in Tigerville, I've been reflecting deeply on teaching philosophy and practice in the last several hours.

You see, I've decided that I'd like to offer to lead a Learning Circle for Spring 2010, and I'd like to base it one of two books, both by the same author. I'm trying to decide between Alfie Kohn's No contest: the case against competition (1986) or the same author's collection of 1990s essays, What to look for in a classroom. The former I read a couple of years back when it came up in the reading I was doing to supplement the reading a Learning Circle I was taking part in (I don't remember which Circle it was now); the latter I'm reading now. (I took in about 50 pages as I whiled away a couple of hours this morning by the giant fountain at the center of Clemson's lovely campus.)

Both books are compelling and offer frank examinations of questionable classroom practices that leave our students in the lurch. I think both would make for wonderful multilogues between faculty and staff.

Which to choose?

While working my way through one of Kohn's more challenging essays in What to look for, I began to envision a way in which Calc I could be taught authentically and in a purely problem-based and student-centered manner. It might go something like this:

Day One. "Holy shit! Here's an economics problem we've got to solve! XYZ Megacorp, LLC needs to find all of the maxima on this profit curve!" [Shows students real data, with very messy numbers...so messy that guesstimating by eyeballing a graph ain't gonna cut it.] "What's all that mean?" "Well, let me brief you on XYZ's portfolio..."

Day Two. "So, how are we going to find these maxima, y'all? Any suggestions?" "I dunno...those are the places where the graph goes up and then comes down..." "Yeah, if we could find the places where the slope goes up and then down..." "Well, how do you find slope?" "Uhhh..."

Day Three. "Okay, so we need to find slopes, right?" "Uh...yeah." "How?" "Uh..." [A timid voice, as yet unheard, comes from the back.] "It's rise over run...right?" "Cool...can you compute those?" "I guess. Let's try to get some formulas..."

Day Four. "So now we've started computing rises over runs. But so far they're giving us rises over runs on intervals, not at specific points. How's that going to help us find the exact point where the slopes go from increasing to decreasing?" "Uh..." "We've got some formulas we can work with..." [Another timid voice, this one from a different student.] "What if we take two points that are really close together?" "All right, what does that do to the formulas?" "Is that the right way to go?" "I don't know. What do you think?" "Uhhhhhh..."

Day Five. "Okay, so you've got these formulas...I give you two points...two points that are really close together, and you can give me the slope. Let's try it out for a bunch of different functions. Which ones would you like to try?" "How about just y = x?" "That's too easy, man...let's do y = x²." "And square root of x!" "Dude." [There is much scribbling and crushing of paper.]

And so forth.

This whole enterprise would be messy, sporadic, anxiety-inducing, and would require the patience of a boatload of Jobs to do it effectively. Moreover, I can't see it working with a class of more than about 12 students.

I wanna try it!

More later, to be sure. And I'll update you on the Learning Circle situation once I've figured out which Kohn I'd like to roll with.