I recently stumbled upon a link to Lockhart's Lament.
You should stop and read this right away, if you haven't already. It's a fairly harsh and biting attack on the state of math education (and more specifically K-12 math education) in the US. His main point is that the focus of the K-12 math curriculum has essentially nothing to do with the actual practice of mathematics, which is true. It's not perfect, but there's almost nothing I actually disagree with in it – its only real sins are sins of omission. Here are my thoughts:
Lockhart does an excellent job of talking about the problem, but says nothing about ways to solve the problem. I strongly agree that the state of education in general, and math education in particular, is fairly bad in the US. However, just saying that over and over isn't going to fix anything. I'd be curious to hear what he thinks about ways to fix the system, other than the obvious – just overhaul the whole thing. I'll save most of my ranting for another post, save for this: I don't see how we're going to fix the system until we find a way to make being a teacher – especially a teacher at a public school – an actually desirable job.
I think Lockhart also gives a bit more credit to teaching in other areas than they deserve. He speaks as though the curriculum in english or the sciences is great – clearly he didn't have my middle and high school experience. :) That said, it does fit with his primary theme – I think there was much more similarity between my high school english classes and the job of a literary critic than between my high school math classes and the job of a mathematician, especially a research mathematician in pure math.
I think that Lockhart also underplays the value of some amount of rote exercises, especially for younger math students. However, I think the point that he's trying to make is that rote exercises without any motivation whatsoever are pointless – and I agree.
Lockhart seems to take the point of view that the reason for doing math is to do research in pure math. He doesn't seem to take much time to talk about math as a tool for physics or engineering, which is just silly. Of course, his attacks still apply – my experience is that students of engineering take calculus classes because they're required, but don't actually understand why they're doing it until later on. Sadly, because they had no idea what they were doing or why, they also generally don't remember any of the techniques they learned, either.
I want to say again, though, that I loved this article. Even if there were things that were missing, there was so much good in it. Of course, I don't seem to be the only one … here's a link to the blog post that first pointed me to the article, and another link with info about Lockhart himself.