How I Know

There's a certain turning point in my learning process that I'm coming to recognize.

When I stop concentrating solely on what on earth something is supposed to mean, (and why textbook writers never explain anything with one sentence if they can use five, and why does it matter whether I learn this or not?), (all of these are important questions, but I've never found an answer to the second one), and start thinking about how I would explain it to someone else, then I know I'm beginning to get it.

This shift from learning to teaching never marks the end of learning. Usually when I ask myself how I would teach this principle or that idea, I don't have a good answer. This is good, because when I keep studying in order to teach, the textbook seems like it's been rewritten in a way that actually makes sense. I think there's a secret dimension of knowledge in every book that hides in the binding and only leaks out when you read the book as a teacher and not a student.

I think it's this shift in perspective that let me do as well as I did in College Algebra this semester. The girl who sat next to me somehow got the idea that I knew what I was doing and asked me questions about the material before every class. I usually didn't have a good answer, but she kept asking me, and so it was like being kicked right into that turning point. I don't know if I actually helped her, but I'm certain that she helped me.