Jason, in a moment of genius, chose a winner of a concrete basis for developing the structure of binomial expansion: the game Q-Bert. There's an outside chance he gamed the judging based on my non-secret, unabashed enthusiasm for all things with a high score and a controller, but I'm ok with that! Here was Sam's take:
Not only for the fact that students can use it to count out things, and really engage hands on with figuring out the numbers -- really get intimate with what's going on instead of just noticing patterns -- but there is something powerful about the physicality of it. I kept on imagining Qbert jumping, instead of seeing things in some abstract algebraic framework. It also, merrily, explains why the pattern we use to draw Pascal's triangle works (why the two numbers above it add to form the next). Jason too saw the power in it, because he kept on referring back to Qbert as the base structure on which he built his lesson, instead of saying "here's a cool thing" and then going into the world of abstraction never drawing the abstract back to the concrete.All of the entries had their own strengths and deserve recognition, including:
Eric Buffington - Who produced a much better-looking, cleaner version of the type of lesson I presented in the original post.
John Scammell - I thought the mathemagic angle was effective for this topic, and well-presented to a live class in his video - a breathtaking act of bravery for a teacher.
James Tanton - Whose approach shared the appealing physical basis of Jason's Q-Bert lesson.
Any of these would make an effective lesson, and made for a competitive field and a difficult decision. Congratulations to Jason, who will be receiving a brand-new Factorial! t-shirt, courtesy me, who decided not to be a cheapskate and send him a hand-me-down, and a lovely book, courtesy of Sam - I think he has his choice of a few.
This was fun! Should we do it again sometime? Maybe better-timed than the end of spring when everyone is super busy? What tough-nut-to-crack topics are begging for the mathedublogsphere treatment? Anyone else want to host the next one?