My instructor assigned problem #31, which happened to be the first problem on page 34. There were no problems like it in that section of the text. None. And I had absolutely no idea how to solve it.
In the textbooks out of which I teach, it would have been labeled a "critical thinking" problem.
So on Sunday I started thinking about it. I had a brief idea and gave "part a" a shot--and when I checked the answer in the back of the book, it was right! OK, on to part b.
Buoyed by my success in part a, I thought long and hard about how I might tackle part b. Then I went on to the next section of the book because I can't spend the rest of the semester on page 34 without moving on. But I kept coming back to #31b, just to see what intuition would buy me. Last night (Monday) before going to bed I actually came up with an idea I thought I'd try today. It was based on logic, but it was a complete and total guess. I had no idea if I was anywhere near the right path or not.
So when I got home from school today I set to work on 31b. I checked the section again, but no, no example problem had magically appeared in there. I was going to have to give my idea a try. So as I'm turning from pages 30 and 31 (the lesson) to page 34, on which resides problem 31, I passed page 33, which contained problems 29 and 30--both of which introduced concepts needed in #31. As I said, #31 was the first problem on the page; I hadn't thought to look at previous problems, only the lesson itself, and besides, 29 and 30 weren't assigned.
So I spent a few minutes studying #29 and 30--and I'll be darned, all that thinking and intuition I'd done on parts a and b were definitely on the right track! Armed with my new-found information in problems 29 and 30, though, I tackled #31, and I got the right answer!
My goal is to have many more such feelings of victory in the weeks and months ahead.