Problem Solving

It occurred to me recently that I have this notion of programming as a process that involves breaking a problem down into a sets of smaller and smaller problems until I have something I know how to solve. (I mentioned this to Steve yesterday which reminded him of a joke about an engineer and a mathematician.)

I have previously just assumed that I therefore follow this process when I'm actually problem solving however, on reflection, I'n not so sure. More specifically, I'm either not doing it at all or, at the very least, I'm doing it intuitively.

I wonder how many people do (or have done) this as an explicit part of their own problem solving and if so, what effects they've noticed as a consequence.