I know that I'm inviting trouble with this, but something that Reader wrote in a comment on another thread piqued my interest. I would like to discuss only a narrow question. Please don't expand the discussion.
Writing about Everyday Math and Singapore, Reader wrote: "The fact is, the newer curricula stress more problem solving and discovery. That is, it's doing more than a lot of older curricula."
Here's my question: can problem-solving be taught?
I mean this in the nicest possible way and I don't have an answer myself. I'm not sure, I'm asking. Can people be taught or trained in problem-solving techniques or is it a talent that some people just natively have more than others? Problem solving requires a certain amount of creativity, doesn't it? It can require a flexibility of perspective, curiosity, persistence, and pattern recognition. Can these things be taught or trained?
I suppose anyone can be taught to play a musical instrument, but not everyone will do it well and not everyone will choose to pick up the instrument and play it of their own initiative. For me, problem-solving is a compulsion. And I have a knack for it. But I'm not sure if I could teach anyone how I do it. I certainly don't have many systems for it and I only resort to them when my usual perception fails me. I solve the Jumble every morning and usually couldn't explain how I found the solutions - at least not the ones I got right away. I just see them.
Setting up math problems is the same way. I just see how to set them and how to approach the solutions. I sometimes wonder if this isn't a contributing factor to the failings of Reform Math - the impossibility of teaching something that is actually a talent. There are others - and there are strengths. Let's try to focus the discussion on get this question: Can problem-solving skills be taught?