I love sixth grade math because there is so much room to develop conceptual understanding, and that’s great for kids and an excellent mental challenge for me. But I didn’t realize how much I miss doing math that I, personally, find fun to do. I’ve taken over our advanced math class for a couple weeks, and suddenly I’m getting to do all sorts of new things. This group has already finished most of the seventh grade math course, and they’ve already taken the state test, so I have the opportunity to teach them whatever I want. Should I repeat that? I can teach whatever I want.
They already know a solid amount of algebra, and (like most young kids in advanced math classes) they are champions at learning procedures and regurgitating things. It seems like it would be a good use of our time to start skimming the surface of geometry – I think it could be really valuable for them to have a foundation in that entirely different way of thinking before they hit the upper grades. Obviously I can’t go too high-level with 12 year olds, but we definitely can introduce some great concepts and start working on their logical reasoning.
Plus, I love geometry.
We just started with the Pythagorean Theorem. We spent a day on grid paper, cutting out triangles, drawing squares, estimating hypotenuse lengths (and trying to pronounce “hypotenuse”), creating new squares, measuring, and noticing patterns. While they cut things, I told stories about the Red Sox and Italian food. We worked it until we had the Pythagorean Theorem happening in cut-out little grid squares on each desk, and then I gradually formalized it into the “a squared plus b squared equals c squared” piece.
When I finally had that written on the board, the class literally gasped in recognition and excitement.
You should have seen me bouncing all over the classroom. I know, kids! I’m right there with you! This is exciting! Do you know what this theorem is about to do for mathematics? Just wait for it! Triangles are my favorite shape and there are SO MANY cool things coming up. I used the Pythagorean Theorem to hang my bedroom curtains, and did you see me dressed as Pythagoras on Favorite Celebrity Day? You want to just add the side lengths without squaring them? Soon, we’re going to explore why that isn’t even possible! See this crazy figure? I bet in a few weeks you’ll be able to label all sorts of information on it!
I also stopped class during a spiral review because a kid told me to simplify 25/30 “by dividing by 5″. I had to get in an argument with him about how he was really dividing by 1.
Whew, I am nerding out. And it’s more fun than I should admit to.