I've raised before in this blog the question of how important understanding is when you are teaching new methods in maths. I have a suspicion that for many people understanding actually follows rather than precedes the ability to carry out, say, an algorithm in multiplication. Does it matter if we don't understand the theory behind it? Well, some say it does, and in parts of the US new curricula are being developed that attempt to remedy this seeming problem.
I have to say I'm worried.
I thnk we've been here before, with the idea that pupils are meant to "discover" maths for themselves. Don't get me wrong, I like an investigative approach as much as the next mathematician... but there are surely limits to what can usefully be created in the time available. To put it another way, if you want the students to discover the maths, you'd better give us a lot more time in which they can do it. And besides, are the standard algorithms really so bad?
But hey, why listen to me on this, when you can see what I'm on about here.