I think you need to separate two things that are going on here. Intuitively knowing how to tackle a problem, inventing methods for oneself, is a strength, not a problem - it may be worth demonstrating more efficient methods sometimes, and discussing different ways more generally, but that's all. So "odd, more complex than necessary" methods don't bother me, though when he gives such a method I'd try to discuss it. (Watch out for methods that are not over-complex but just different from what you were expecting!)
Not being able to explain, though, is another matter, and it mystifies me why adults sometimes seem to admire this (not you necessarily). It's actually the explanations that are the maths, tbh. I wouldn't count a question as answered unless the child can explain why the answer is correct. That doesn't have to mean "show your work" in a tedious way. It can be more useful to play an "I don't believe you" game - push for a gradually more elaborated argument by questioning selected steps. If there's really no explanation available I'd reframe the answer given as a guess: "OK, so you guess the answer's going to be ... Let's see if we can work out whether you're right."
ETA one thing that can cause impressive leaps is being really good at visualising, and then it can be hard to know where to start in explaining method. Might be worth explicitly suggesting beginning by drawing a picture, if you think that might be happening.
Last edited by ColinsMum; 08/26/13 01:23 AM.
