The past few weeks have been busy and filled with lots of math as I’ve been teaching a new subject at Unquowa. I’ve never been a math teacher before. Science is usually my thing, but I was surprised at how easily fifth grade math came to me. It’s as if thirteen years haven’t passed since I learned this stuff myself. I love the simplicity of math and I love that it can be easily applied to the world around me and the world of my students. My first lesson at Unquowa involved using a bucket of plastic animals to explain multiplication properties. My students seemed to like the tiny zoo of multiplication properties and I’ve enjoyed finding other ways to make the math tangible and interesting since then.
For the Aldrich lesson, I was tasked with designing something for the seventh and eighth graders to enjoy instead of my usual fifth grade class. I was a bit nervous at the prospect of being filmed as teaching a lesson in front of a camera is a new experience for me. I wasn’t too worried about coming up with an interesting lesson though. As soon as I saw the pans of water in Peter Liversidge’s “Proposals to the Aldrich,” that the artist claims are proportional to the largest freshwater lakes in Connecticut, I figured that a lesson on proportion and direct variation was in the works.
At least, that’s what I thought my lesson would be about. I planned to have the students pretend to be anthropologists from the future on a quest to use art, the one thing that remains when everything else is gone, to figure out the proportions of the long-ago dried up lakes in Connecticut. I gave them two lake measurements and all of the tin measurements and asked them to use direct variation to find the remaining lake measurements. Then, the night before, as I was checking and rechecking the math on my handouts, I kept finding that no matter how I did it, the numbers didn’t add up. The scale factor was not the same for each of the lake-tin pairings, not even close.
I panicked for a bit as I wondered how in the world to salvage the lesson. I emailed my mentor and sat in front of my notes and the giant flip chart I’d be using to show how to do direct variation. Then, it occurred to me that the proportions being wrong was actually a great opportunity to teach more than just proportions. I kept the same science fiction tilt to the lesson, but added in a few of the lake measurements to leave only three blank. I told my students the next day that their job was twofold. They needed to first decide if the artist was correct enough in his claim of proportionality to render the piece a useful source of data, and if so, to use it to find out the measurements of the missing lakes.
Out of the four groups of students, each one worked at a different pace. I was worried that they would doubt themselves and become frustrated as soon as they found that things weren’t adding up. One student said “Mr. Teachey, they definitely have to be proportional because you wouldn’t make up a worksheet about it if they weren’t.” I was hopeful that they would trust enough in their math skills to be able to question the artwork and perhaps more importantly, to question their teacher. I’d never thought of critiquing art as a mathematical endeavor before, but my students ended up doing a good job of it. Each group figured it out, though at their own pace and with their own bumps along the way. My students were surprised when I told them that I didn’t make up the artist’s intentions and showed them the proposal on the wall. Some seemed surprised that the artist had seemingly done his math wrong. Others seemed surprised that I had set up a situation in which their job was not really to solve the second problem but to prove that they couldn’t trust the source of their data.
I felt very satisfied about how it had turned out. Despite the panic of the night before when I realized how things didn’t add up, it lead to a much richer, deeper lesson than I could have hoped for if the artist had been perfectly exact in making proportional representations of the lakes. Knowing how to assess a source, and even to question authority, seems like good value added even at the price of a bit of fumbling and panic during the planning of it.
-Caleb, also known as Mr. Teachey