State of mind

A few months ago Zima, one of my grad school colleagues who now teaches at Kennesaw State University in Kennesaw, Georgia asked me to present at an undergraduate research conference for which she'd just received MAA funding. (Said conference is this coming weekend; it's the one Ino and Ned are presenting their findings at.) I'll be giving a run-of-the-mill plenary talk on some of the graph theory I did with a couple of REU students this past summer, and I'll be presenting in a workshop on inquiry-based learning (IBL) at the outset of the conference.

I offered Zima a title that's so generic I really could talk about anything: "Guided discovery in the mathematics classroom." I feel confined by this generality. Indeed, when I actually sat down a week or so ago to try to figure out what in the hell I needed to say about IBL, PBL (problem-based learning), Moore method, etc., I had a hard time coming up with much to say other than expressing my feeling that all too often these techniques are too "formalized." That is, I get the sense sometimes that the people who apply these techniques look on them as an all-or-nothing process: "if it ain't straight-up Moore method, it ain't anything at all" or "I use guided discovery every single day to address every one of my students' learning outcomes." So I put together a half-hour laundry list of things to say along these lines: be open to using guided discovery in moderation; it's not the be-all-end-all any more than any other pedagogical paradigm may be.

Then just now, while lying in bed unable to sleep (though admittedly probably needing to), I realized that I can say more, for I realized of a sudden why I've had such a hard time trying to come up with something practical (and original...I suspect that the folks I'll be addressing in this workshop are going to make up a choir to whom I won't really need to preach) to say about guided discovery: in my mind, guided discovery is not so much a pedagogical process as it is a state of mind.

I find more and more that in teaching it's not so much what I do with my students as how I do it that matters most. Put another, perhaps more practical way, effective teaching comprises a gestalt-like complex of actions and not a single action individually. Guided discovery is what might be called an emergent operation which cannot be broken down into its constituent parts without losing much of its energy and effectiveness. So it is that I don't necessarily engage my students in singular activities, each of which forces students to lead themselves to original, new-to-them, conclusions, so much as I try to treat them in every way, in everything I do, as co-learners, co-discoverers, seekers of authentic knowledge.

Practically, this realization makes it possible to grow opportunities for genuine discovery in the most infertile academic soil, for every simple textbook problem becomes, if viewed from the right angle (like anamorphic art) a chance for authentic "research-like" engagement. Guided discovery is an "angle" from which these problems may be viewed.

I'll try to say a bit about this on Friday when I'm leading my portion of the IBL workshop. Are these views original? Meh...perhaps not. But they're more original, and, more important, more meaningful, than whatever else I will have to say. We'll see how they're received.