Doing It Wrong

It is a commonplace to offer the advice to “learn from one’s mistakes” after experiencing a failure and almost as frequent that “one learns more from a failure than from a success.” Yet for reasons that I’m not completely certain of, these prescriptives seem to rarely if ever find there way into teaching. That is, instructors don’t knowingly, via an act of commission, take an incorrect approach to solving a problem or to present new ideas, especially in the case where they don’t advertise to the class ahead of time that they are doing exactly that.

For example, there is much talk nowadays about teaching design and getting design inculcated throughout the curriculum. Consider this simple design problem. There are two rooms in which to put flooring, one gets tile, the other gets carpet. Why not start by putting tile in the bedroom and carpet in the bathroom and have students work through the implications of that, before getting to the preferred solution where it is done vice versa?

My guess is that to protect their own egos instructors guard against making errors that they haven’t planned and are so caught up in that issue as well as the related issue that the students might find them out that they don’t venture into this other terrain where things are topsy-turvy, where the instructor’s expertise and authority are revealed only in a more subtle fashion by making sense of it all. This gives me enough of an explanation for why comparatively novice instructors don’t do this and then, since we are such creatures of habit, why more experienced instructors don’t do this as well. And its likely too that most instructors haven’t given the issue enough attention. But consider what they miss through the “telling of truth” approach that so many do adopt.

If someone takes a wrong turn but believes it to be right, there will be a period of time during which the person is happy in their conviction that they are headed on the true path. But then evidence will start to accumulate which suggests that belief is wrong. What evidence is that? How much evidence must be accumulated before changing direction? And when that evidence has been gathered, then what? Which way to head now?

Suppose that we instructors viewed one of our main jobs to be modeling for the students how they should proceed as they learn and that one key skill is to get oneself unstuck after having gone down the wrong path. How can that be taught unless we ourselves deliberately make mistakes, to put ourselves in a position where we are stuck, uncomfortable and unsatisfied, to be sure, but still with our wits about us and a strong sense that this place isn’t the final resting stop?

Knowing how students seem to prepare for class on my campus, my sense of teaching this way is that if the deliberate mistakes where part of a pattern – start with the mistakes and then move to the correct solution – students would soon learn to ignore the mistakes; they wouldn’t be on the test would they? So I think if one teaches this way one most do it by surprise, in an inconsistent way, where the students are not sure what’s coming. It may be the straight dope or it may be a deliberate error but ahead of time they are not sure which. They have to use their own wits to ascertain the situation. And beyond wit, they have to use their own sense of taste as to whether to be satisfied with what they’ve been told or to question/reject the ideas because there are issues with them. Indeed, instructors developing such a sense of taste in the students would seem to precisely the type of deeper learning skills to which instructors aspire for their students. Doesn’t it make sense to deliberately practice doing that sort of thing rather than have it mysteriously happen (or not) when the students are on their own?

But I believe an instructor is not likely to try this unless one sees the need for some “invention” in the teaching, some departure from an entirely linear presentation. Way back when, 15 + years ago, when I was teaching the graduate economic theory class or the summer math for economists class that was preliminary to the graduate students entering the doctoral program, with all those goodies about Bordered Hessians (a certain matrix of partial derivatives), the Implicit Function Theorem, and the Envelope Theorem, the core math behind the economic theory, I learned to lecture without notes. I did this not to show off, but rather because I went too fast when I paid attention to the notes – I knew the stuff so when I was paying attention to the notes I zipped through them, because I was simply regurgitating what was on the paper, there was nothing new in the process for me. Since I knew the stuff real well but this was not the type of material that one might memorize, without the notes I had to re-derive the results from scratch and much of my lectures ended up being talking through how I did that while doing a lot of writing on the blackboard. Perhpas not we romanticize about as good teaching nowadays, but the graduate students then were quite appreciative of the approach.

I tell this story in part to let regular readers of the blog know that I deliberately “made a mistake” in writing the post up till this point and wondering whether any of you noticed the error. Figured it out yet? Here’s a hint – it has nothing to do with that in my little story I talk about lecturing.

Instead, it’s about positioning the story within the Blog post. Normally, I begin with a personal anecdote. I do so for several reasons – to break the ice and draw the reader in, to illustrate by example the point I’m trying to make in the post, to show connections between my experience and my ideas, etc. I think that is the better way to write, from example to the theoretical point, from the personal to the abstract. It is more closely how we actually think, in my view, and as I’ve written elsewhere, I’ve borrowed the approach part and parcel from Stephen Jay Gould.

But I didn’t do it in this post. I started with theory and made a theoretical argument, albeit in chatty terms. Then I went to the anecdote to illustrate. If you’ve gotten this far in the reading of the post, and if you’ve read other things I’ve written you might very well have a sense of which you prefer. Further, you might make come to the meta conclusion that errors of commission are precisely the examples we need from which to generalize about our thinking; were I such a good teacher I'd do it more often.

Let me close with one last point. It may be harder to do this in “live mode” since to a certain extent you then have to “sell” the error as reasonable and that may require an acting skill that many of us don’t have, but I believe this is do-able in writing, in which case the idea is simply to take a somewhat longer journey to the resting stop, possibly by taking a detour or two in the process, those detours offering potential insights via the deliberate making of mistakes and learning from that. Instructor blogging would seem to provide a nice framework for this, as by its essence there is invention in the writing, and the instructor can be thoughtful about the type of errors he would like to make.