> While I agree with this in general, I find that to reall fully understand a problem, I need to attempt to code, or at least formulate, a solution to it.

Me too. Sometimes when I don't feel like I really know how to solve a problem, I'll just write some really hacky code to try to get an answer. Just anything that moves the problem forward.

Then once I understand what I want to do better, I either throw out that code and start clean. Or I just refactor the heck out of it until it is in a good state.