The thing about teaching, which somehow I always forget, is that there is rarely an “aha!” moment. Even in something like mathematics, which it seems like you would either understand or not understand, the process of learning is more of a slow and painful slog (with plenty of backsliding) than a steady progression with plateaus of understanding.
Even after a year of teaching in Kenya, and a semester of teaching here, I'm still amazed by how little material we are able to cover in every class. I'm teaching a section on prime numbers and prime factorization in my 7th grade class now, and one of the topics that we are supposed to cover is something called the Sieve of Eratosthenes. I had never heard of this before, but looking it up online, I learned that it's a neat little system for eliminating all of the numbers in a given set that are not prime. Since it is in the syllabus, and it's a pretty simple little trick, and it has a pretty awesome name, I figured we'd give it a shot.
Big mistake. The whole concept of prime numbers is incredibly confusing to the students. And with so many other topics to cover that are so much more relevant to everyday life – decimals, fractions, and percents, for example – I'm wishing that I'd scrapped this whole section completely. But, oh well. Too late now.
I feel like I make that mistake a lot here. Somehow, having gone through an educational system that actually functions, I'm always surprised and confused when I discover that something that seems intuitive is in fact exactly the opposite. No matter how well I think I've broken a particular subject into easily understadable chunks, I still always seem to end up discovering that I've made some leap of logic that has left most of the students completely bewildered.
In other news, the six-month volunteers who came with me are leaving next week, which is, first of all, a bummer, and second of all, hard to believe. Time flies when you're having fun . . . or, alternatively, when you're teaching a million classes with a million students each . . .