Something else that has been on my mind for many years now, that I think has impeded my mathematical development: the whole business of how to actually go about proving something. I feel that, and I am probably not alone in this, I was never really taught strategies for how to develop a proof. Sure, I was taught about some very general techniques: proof by contraction, induction, etc. But no one ever really sat me down said, how are we going to develop this proof. Obviously I was shown the proofs to all sorts of famous theorems and other homework problems. But they just showed us the proof after it was already concocted. But rarely the messy business of how we might have come up with proof. Never the false starts, the random walks, and sheer examples of genius that are required pull the whole thing together. Because, to me, the presentation of the completed proof in a nice linear story-telling manner is a complete distortion of the actual reality that went into creating it.
So, does any one know of any resources that actually address this issue? Am I alone in thinking that this is a real pedagogical problem in mathematics? Or am I just too aware of my own limitations in this area?