Thinking Analytically About Thinking Analytically

This is perhaps the most meta topic this semester, and, more than likely, the most difficult to talk about.  You are all here for a variety of reasons, and while you might all think it was because you're good writers, I'd wager that there were other things that marked you as a potentially good tutor—and one of them had to do with the way you think about things.

So here's this week's freakishly-meta prompt:  when you think about a problem you're writing about, how do you think about it?  What kinds of questions do you ask?  What kinds of questions do you try to avoid?  How do you push your thinking on subjects?