I learn from my students every day. I learn about the pain of learning and the joy of growth. I learn about the similarities and differences between and among people. I learn about some of the ways to make mistakes and the infinite patterns it is possible to see in the chaos of marks on the page and sounds in the air. I learn about boredom and confidence, fear and trust. I learn about math.
Now that my semester is almost over, I have realized that my students taught me that I love math more than I thought I did. They showed me by reflecting my own excitement for the ideas as I try to express them. They said things this semester like: “You should see the look on your face!” or “I can’t believe he gets that happy about math”; or “How can you like this so much?” When they said such things, I shrugged it off as acting; I told myself it’s a role I intentionally play in the classroom. The theory is that if I can infuse enough energy into the subject, the students might absorb some of it and do more work—work being one of the fundamental elements upon which learning is built.
The more I thought about it though—the more I explored my motivations and thought about my limitations—the more I realized I’m not that good an actor. No, if I’m projecting that kind of passion for math, it’s mostly because I really feel it.
So, this semester my students have taught me more about why I teach math rather than some other subject. I teach math because I love the way it fits together, the elegance and beauty of the thing. It is a powerful story that leads me to feel an interconnectedness in the world and that I am getting a glimpse of those connections, of the world’s mysteries. It’s funny, too, because intellectually I believe this feeling is an illusion, that these mysteries are not mysteries at all; in fact, I believe the universe is random and the connections we create are purely comforting stories we tell ourselves. But they are very satisfying stories. Compelling, alluring—the promise of revealing the underpinnings of “reality” is so powerful that it doesn’t matter how much math speaks to any actually “reality.”
Math gives me this feeling partly because of the way that, once we choose some simple assumptions (e.g., once we decide that (-1)(-1) = 1, and not -1 or anything else), math takes us on a journey of finding consequences of our assumptions. The path can lead to unusual and even startling results. We start by creating simple numbers because of the need to count objects in the world, an act that is descriptive and useful (we wouldn’t want to leave one of the group of children behind at the zoo, would we?). Before long we see the need to create negative integers and then suddenly we need the square root of negative one. Math took us there and showed us how to deal with this strange object, seemingly so far away from one, two, or three, yet also descriptive and useful in the world.
My students reminded me that math is a powerful story because we make it and because it does work in the world. Math is powerful, not because it probes the mysteries of the universe, but because we believe it probes the mysteries of the universe.