What's wrong with math education

If I could say it better than Tom Henderson, I would. But I can't. So here he is:


In a nutshell, what is the problem with math education in the US?

I have no idea. Let me instead describe the attitude that students have that is problematic, and you can reconstruct what must be wrong with it from that angle.

“Show me the steps.”

Many students want teachers to “show me the steps.”

They want a sequence of steps that they can perform that will give them an answer. This is not unreasonable; they know that their performance on exams, and therefore their performance on the All-Seeing Grade Point Average, is largely determined by being able to Do The Steps.

But “The Steps” are cargo cult mathematics.

The Steps are seeing the sorts of symbols that count as “right”, and trying to replicate that dance of steps. It turns out that the easiest thing in the world is to look at a student’s work, and tell the difference between “Knows what’s going on, made mistakes and dozed off” vs. “Can memorize steps, has no idea what’s going on.”

Now, the way that I explain mathematics, it sort of looks like I’m torturing the poor bastards. I handwave. I refer to certain groupings of symbols as “Alphabet soup” and write it down as a wild scribble with one or two symbols around it.

Because I’m trying to avoid showing The Steps and instead show them enough of The Idea that they can reconstruct what the steps MUST be.

Many students want to know the formulas, so that they can float them on top of their short-term memory, ace the exam, and then skim them off. Why do they want to know that?

Probably because, for their entire mathematical careers, math has been a sequence of Steps, and if they get them wrong, they get red pen, bad grades, No No No Look What You Did. Plus, bonus, there is no apparent relevance of these algorithms other than To Get The Answer.

What’s wrong with math education in the US? What’s wrong is, Whatever it is that makes my students uninterested in learning any more math than is required to minimize feeling stupid.

So that we’re clear, lots of my students are totally awakened to the interesting weirdnesses of mathematics. But, it takes some doing, and I can’t do it by myself. Hence the podcasts and the lunatic twitter stream and the plans for TV shows and online games and godknowswhat else.

I’m trying to get across that if you are highly motivating, if you have a high degree of fire and “**** yeah!” and “What, that’s impossible, but true!”, you can get students to express interest in theorems named after dead Hungarians.