(N is studying calculus. She has just completed an induction proof of the power rule for negative exponents based on the quotient rule.)
N: Induction feels like cheating.
Me: I know, right?? You only prove 2 things, and then you’ve proved an infinite number of things.
N: It’s not just that, it’s that you already assume you’re right. It’s like you’re borrowing against your own rightness.
Research in Practice 
Yes! Get her to read Wittgenstein!
Really great quote.
I just wrote about how our curriculum handles induction from the perspective of failed recursive rules. It works pretty well!
http://patternsinpractice.wordpress.com/2011/05/25/induction-through-failure/