My First Small Victory

#31.

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.