Friday, December 26, 2008

Chapter 5. Blueprint

My first exposure to Moore method instruction came during my first year of graduate school at Vanderbilt University, back in 1998. My graduate-level topology course was taught using the Moore method, and as there were only four of us in the class, our going was painful: often every one of us would be called on to present a problem on every single day.

Of the four of us, two had seen a good deal of advanced theoretical mathematics already: I came having finished a Masters degree and having taken just about every math class offered at my undergraduate institution, and my colleague Oleg came from a European nation where his undergraduate training had been much more focused and intense. We had a decided advantage on our less-experienced colleagues. Erdrick and Tara were fresh out of American undergraduate programs and had had little more than the standard course of study one would find in such a program: both were smart, but relatively fresh.

As one might expect Oleg and I had a far easier time than our two friends: we came upon our solutions more quickly and we had an easier time presenting them. Although this advantage dwindled and then disappeared almost entirely by the time we got to algebraic topology, a topic none of us had dealt with before, for a few months Oleg and I were able to set the cruise control and drift along breezily while our friends struggled.

But about three months into the Fall 1998 semester, during one of Erdrick's more protracted proofs, I noticed something striking: his presentations were richer than mine were, they involved themselves with more details, and they provided a thicker description of the underpinning concepts and computations than my own presentations did. Moreover, they were clearer, and contained a more cohesive and coherent argument and were therefore more well composed. Even as he professed his lack of understanding of this or that topic (often one with which Oleg and I had dealt in earlier classes), it was evident that he was taking the time to dig more deeply into said topic, uprooting it and holding it up to the light to better see it and better get at its meaning. And as he held a topic up for his own examination, so he held it up for all of us to see and analyze and understand.

His relative lack of knowledge was making him a better teacher than I could ever be.

If one is able to unashamedly confront one's ignorance in front of others, one is acting in the manner of an effective educator: teaching is little more than a practiced and public examination and remediation of ignorance.

Fast-forward ten years, nearly to the day.

While I was talking on the phone with Griselda a few weeks ago, the conversation turned (surprise, surprise) to our teaching and our classes and our colleagues and our colleagues' teaching of their classes. Not shockingly, we've both had colleagues with whose methods we don't agree, and about whose teaching we've heard students say decidedly negative things.

"Isn't it funny," Griselda said, "that when students complain about a teacher not being very good or not being able to explain something at all, they take that to mean that that teacher is really smart? 'I can't understand Professor X at all...she's really smart, but I can't understand her lectures.'"

"I know!" I agreed. "The assumption is that if you can't explain something it means that you're operating at such a high level that you're unable to 'bring it down' to the level of the students."

We all know the stereotype of the absentminded mathematician whose dwelling in the realm of functions and formulas precludes any meaningful interface with the world around him. This hapless researcher wanders about the "real world" clumsily, muttering apologies to those he jostles and jabs with his elbows, even as he crunches numbers ceaselessly in his head. This professor may have difficulty in "bringing it down" to the level of his students, simply because he's often incapable of understanding just how little his students understand. (Incidentally, you'll find this type of teacher most often at research-intensive universities where the publish or perish mentality ensures faculty need not give a rat's patoot about teaching, and where even if good teaching isn't actively discouraged it's certainly neither actively encouraged.)

There's a different sort of delinquent educator, though, and one that's much more common at schools like my own: the one who has become detached from her own discipline to the point where she's no longer engaged in active research; who has ceased the active pursuit of new knowledge in her discipline and so has lost the ability to discern, to analyze, to interrogate the stuff that is the quintessence of her field; for whom academic inquiry has become static and devoid of new and novel points of view...for this one teaching will be an arduous and sometimes insurmountable task, as she will find it difficult to show her students anything more than an unchanging road map. If a new and more convenient highway is built, she may stubbornly drive on down the old routes as though unaware of the new one's existence. Who knows what sights she and her students might miss?

For this reason I believe that the highly active researcher who values teaching above all else will make the most effective educator. Let research dominate and one risks becoming an ivory tower-dwelling hermit; let research die away and one risks becoming a theorem-spewing robot stuck on autopilot.

This is an oversimplification, to be sure, and as there are exceptions to every rule so we each will be able to identify examples that defy the schema I've laid out above. Nevertheless, the rule is proved by its exceptions, and time and again I've noticed that my colleagues who excel in the classroom are generally those who excel as researchers in their respective fields.

The above observations suggest the following blueprint for teaching excellence:

An excellent teacher is one who

1. is unafraid of professing ignorance and who can confidently confront that ignorance publicly with

2. a rich skill set developed in the course of active disciplinary inquiry, and who

3. values her students' understanding above all else.

Let's see how well this blueprint poses a solution to the following question: "How can someone not trained in writing instruction provide effective writing instruction to his students?"

Following the blueprint mechanically in lockstep, were I to wish to teach my students how to write well, I would

1. admit to myself that I don't know a whole lot about teaching writing and be honest with my students about that fact,

2. take it upon myself to learn what I can about writing (in my discipline, or to learn, or to meet some other end) and the teaching of writing, engaging in the creation of new ideas on writing should the need arise to do so, and

3. keep in mind that the ultimate goal of this procedure is not to publish a paper on writing but to instill in my students a greater understanding of writing so that they may make use of the tools I've helped myself develop and so that they too can help themselves and each other to develop their own tools.

Note how process trumps product, particularly in this last point.

Does this seem a satisfactory solution to the problem I posed above?

I think so.

I have to admit that I'm really thinking out loud here, but it seems to me that the best teacher is a courageous learner, and that as each of us is fully capable of learning should we dare to, so too each of us fully capable of teaching.

To the point I'd originally meant to address, at the risk of belaboring it: any person well-trained to perform in her discipline (whatever "performance" may there mean) will be well-trained to instruct her students in that performance, so long as she keeps her own performance skills sharp. As "performance" in nearly every discipline involves the creation of a textual record of some sort, any able and active disciplinary performer will be well-trained to teach her students to write about her discipline. Indeed, who could do a better job than she could? That is, who could better teach math writing than a mathematician who is skilled in the use of writing to perform mathematics?

Put this way, the whole question of "qualifications" becomes a silly one on its face, and the idea of "writing in the disciplines" makes a hell of a lot of sense.

(As an aside I might note that perhaps the theory above could be used to prove qualifications to perform other disciplinary duties as well: who better than a sociologist to train students to use statistics as they would be used in a sociological setting? Who better than a chemist to train students in the physics that describe the commonest molecular interactions that occur in a chemical lab? How far off-base am I here?)

Perhaps one reason "qualifications" came to be questioned in the first place is that all too often we hold to very narrow and circumscribed notions of "writing" and "writing instruction" in the first place. If we demand that all academic writing take the form of five-paragraph essays whose construction is governed by a rigid set of rules, we might then consign all writing instruction to the realms ruled by composition theorists and rhetoricians.

But not all writing, not even all academic writing, takes this form. There are many more modes of writing than there are disciplines in which one can write, and we forget this at our own peril: one would never write a policy paper where a lab report is required, and a poem will generally not do for a mathematical proof.

Nevertheless, it's not always easy to remember writing's rich diversity. Even the "experts" may forget. I'll have more to say about this in this series's next chapter as I ponder the steps and missteps my colleagues and I took as we attempted to design a rubric for assessing students' mastery of writing in a particular discipline.

For now, as ever, I invite your feedback on my rambling thoughts. I came further than I'd originally hoped to in this post, and I'd really be interested in hearing others weigh in.

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