28 November 2011

Opposing thoughts on teaching

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.

21 November 2011

Khan Academy

Before reading this post, go to khanacademy.org and click on “Practice”. Play around with it for a while. Neat, huh?

I turned J loose on it for a few hours. (J is eight years old, homeschooled, and way ahead of his age cohort in math.) He was absorbed for a surprisingly long time, he said it was “kind of fun”, and he learned a few things. Not bad!

A few points to curb your enthusiasm:

  • Khan Academy started out as a collection of videos. Now it’s a game with available video tutorials.

    I watched my eight-year-old open a video, watch enough of it to guess the answers to the current problem set, then close it, cutting Sal off in mid-sentence. “And the interesting thing about—” Click. This is on day one. It’s very simple: the goal here is to get points and fill out the map.

  • The curriculum is the U.S. math curriculum. To whatever extent the curriculum is the problem, Khan Academy isn’t the solution.

  • The system punishes mistakes. That’s bad teaching already, but it punishes mistakes disproportionately to the point of being inhumane. To clear a topic, you have to answer five questions in a row correctly. If you get the fifth one wrong, you start over—five more questions. A sign error can cost you fifteen minutes of your life. It’s hard to believe this system got into production. No human teacher would be so cruel.

  • Not all of the problem sets are good. As of this writing, the problem set on shifting and reflecting functions is about as bogus as standardized testing gets.

  • The system awards badges for things like answering 75 problems in a row on the same topic, without any mistakes. Gross! I’m not sure why Khan Academy needs badges at all, but if it does, they should reward behavior that the site wants to encourage, right? Don’t we already discriminate enough against non-OCD-sufferers in math education?

  • Putting this work in the commons is the right thing to do, but I think it’s a long shot to hope that it’ll flourish there. This kind of courseware is hard to develop; I imagine it will be hard to modify and reuse. I hope I’m wrong.

All this may seem kind of devastating, but I dunno. Some of my criticisms are easily addressed. Some are just points of disagreement. On the whole it’s good for a lot of people to be attacking the problem of education from different angles. I don’t think Sal Khan would dispute that there’s a long way to go.

I don’t think I’ll be using Khan Academy with my kids. So far J and his younger sister are motivated by innate curiosity. I think we should ride that current as far as it takes us. For now, maps and points and badges, like grades and tests, are just a distraction.