Some thoughts on teaching by Bret Victor.
I used to think that to be a good manager of engineers, you first had to be a good engineer. I could name several particular managers in support of that theory, but that’s anecdotal evidence, right? And believe it or not I have a few counterexamples too. Now I think that management is many things, and there is more than one way to be great.
Bret says that to be a good teacher of mathematics, you must first be a good mathematician, scientist, or engineer. I think the claim is way too strong, and it’s a good thing, too, because we need many times more math teachers than there are mathematicians, scientists, and engineers who want to teach. It’s easy to suspect that Bret, who has an MS in electrical engineering, is harboring a romantic notion here. The structure of the essay isn’t encouraging—five anecdotes followed by a lot of undirected personal incredulity and vague analogies.
Look, if I have to choose between a teacher who “lives math” and one who can tell when a student is perplexed and find another way to explain it, I’ll pick the latter every time.
Of course you have to actually understand the material quite well to be a good teacher. Not just well enough to pass a test on it! You have to know it well enough to know what is actually interesting about it, to invent good demonstrations, to turn it around when you need to explain it a different way, to inspire kids to turn it around in their own minds, to recognize when a student gets it. But you don’t just have to know math well enough to do those things. You also have to actually do those things.
Many engineers are horrible teachers. Many math teachers who are obsessed with teaching, and not math so much, are great. Teaching is many things.