Mr. Quinn was my favorite high school math teacher. He was quintessentially nerdy cool. He would roller-skate to school, he had a calculator case on his belt, and he knew how to use a slide rule. I also thought he was brilliant. We all did. He seemed to know everything there was to know about math and could answer almost any question we asked. In part that was because he had heard them all before, but we didn’t know that. He taught my freshman geometry class, my junior pre-calculus class, and was the advisor (head coach?) for the math team.
Many years later, well after I’d graduated from college, I went back home to visit, and talked to Mr. Quinn about my life and a tricky stats problem I was working on. He had no idea how to even start to help me. That’s when I realized he wasn’t actually a brilliant mathematician. He knew the high school math curriculum very well and was an excellent teacher, but in this particular area of math, I’d passed him.
It was only a matter of time before the same thing happened to me, and the other day it did. One of my former students came by my office to visit and ask a few questions about a project he was working on that was inspired by a class I co-taught (with Luke de Oliveira) introducing a few machine learning algorithms. After a few minutes it became very clear that my former student knew more than I did about these methods, and I didn’t have much to contribute. Maybe I was imagining it, but I thought I could see the disappointment in my student’s eyes as I fell from the pedestal.
Human knowledge is vast and growing ridiculously quickly. Of course no one can know everything. At the same time, it’s easy for students to over-estimate just how much their teachers know. To be honest, it feels good when students think we’re geniuses, but we do them a disservice when we consciously let this happen. They need to trust us to know what we’re talking about, but also know that we all have a lot to learn. When they see that we are human, our expertise becomes that much more attainable. We also need to show them problems we can’t readily solve so we can demonstrate our problem solving process. That’s how they will know how to approach questions when they don’t have answers. And there are an awful lot of those out in the real world.