What I Learned From the Guy Playing Guitar at 3AM in the Amtrak Dining Car

So I was on the train from Boston to Chicago, and (it being a train rather than a bed) I couldn't sleep.  I headed down to the dining car, and found a few restless folks reading, and one guy loudly playing guitar.  In between his second and third renditions of Folsom Prison Blues, he was talking about writing songs.  One time, he said, he'd got access to a bunch of nice guitar gear, but try as he might he still couldn't play the song that was in his head.  He said he'd been so frustrated that called up his dad (who was also a guitarist) and yelled at him "you did this to me!".  He was stuck, but that didn't stop him from playing on, trying to get that song out.

I'm not a musician, but I know that feeling too.  It's the same feeling I get when I'm trying to learn a new math concept.  It's horrible, knowing that the key that will unlock new understanding is just right there, but there's some kind of block - maybe I'm looking at it in the wrong way, or missing some previous point, or maybe just not in the right frame of mind.  But I endure the frustration because I know that it all become worth it when I finally do get it.

That's also the feeling I want my students to have.  Doing math in school isn't about the answers, it's about the process.  About knowing how to deal with a problem that seems impossible.  About experiencing defeat followed by the thrill of success.  About not giving up.  Then it is our job as teachers to deliver the kind of problems where students can have these experiences.

In this video, Paul Lockhart describes mathematical arguments as "reason poems."  I think he's right - math is more than just solutions.  It's an art.  It's no coincidence that I identified on some level with the frustrated guitarist - after all, we're both in the business of creating beauty.


Edit/PS: I experienced one of those moments of mathematical revelation just this morning while reading the Wikipedia article on Hypercubes.  I'd seen the cool/trippy animations, and heard explanations before, but never really got it.  It was this picture that did it:









It's amazing how just one change in perspective can bring on whole new worlds of meaning.  Yay math!