I have some honor students who are really strong. Way stronger than I was in high school. Most of the time that's an awesome challenge for me as a teacher, but sometimes it forces me to confront my insecurities.
I've been doing math on my own for fun.* It's great. Highly recommended. I've been going through old PCMI problem sets and having tons of fun with them. Last Thursday I gave my Algebra 2 students a quiz. I projected a problem on the board that I had printed out for myself and told students that I was stuck on number 3, and asked for some help. As they finished up the quiz, some of the stronger students grouped up and started battling it out among themselves.
*Yes, I read comic books and like Community. Yes, I teach math and computer science. But I don't want to be a big nerd. No -- I want more. MORE. I want to be the biggest nerd. Ever.
Here's the problem, by the way. I hadn't had a chance to spend a ton of time on it when I showed it to the kids.
That night I got an email from one of those students with a solution. He was right-on. He made a fantastic observation that had eluded me when I was working on it.
My first reaction was pleasure in the collaborative relationship I had fostered with my student. Oh, wait, actually my first reaction was the exact opposite of that. Thoughts went through my mind, like, "He got it before I did!" and "Is my student smarter than me?" My old insecurities as a learner rushed back to the fore and I felt ugly and embarrassed. And in that moment I worried, "Should I be teaching these kids?"
I have colleagues who think that appearing smarter than students is an important part of their job. They've spoken about how it's important to appear knowledgeable to students, and they have plans about what to do when a student asks a question that they don't know.
And though I've given lip service to a different conception of the teacher/student relationship in the past, now I'm really facing up to it. Because my students really do know things that I don't. Not just about math, but about everything. My job is not to be smarter than my students. My job is to make my students smarter. And if you think that teaching is all about transferring knowledge, then I guess I should worry just a bit about what I can provide extremely bright students. But I'm finally really getting what it means to facilitate learning, and it's in my gut, running through me like adamantium.*
* HUMONGOUS NERD.
Teaching, as I understand it now, involves checking my ego at the door. Sure, I know some things. But only those things that will help my students grow.
Saturday night I got a message from that student about the problem he had solved. He was having trouble proving that his observation held. Outside of that interaction, yeah, I knew a proof. But as soon as we started talking about the problem I no longer knew the proof. Instead, I just knew a general strategy that is helpful for such situations and, hey, here's a link that you might find interesting, and let me know if you figure anything out. Five minutes later, I've got a proof in my inbox.*
*By the way, I've ripped off this asterisk/footnote thing from Joe Posnanski, who you should read if you like sports. You should also read him if you hate sports, because he's got a shot at changing your mind. Linkety link: http://joeposnanski.blogspot.com/