Teaching as Performance

"You don't choose your personality when you're on the box."

These words wore heavy on me as I took to the podium for the first time. I looked out at all the eyes on me, over a hundred eyes in total, all focused in my direction. It was the first time I had been at the front of the orchestra, seemingly miles away from my usual home in the oboe section. For a long time, I had wanted to try conducting, because it seemed like fun, and after a whole semester's worth of practice in front of five other students and a faculty member, here was the real deal, leading a short rehearsal of Tchaikovsky's Waltz of the Flowers from The Nutcracker.

I was terrible. And I felt terrible about it.

All my preparation - articulation, tempo, dynamics, balance - all of it careened out of reach from my mental grasp in an instant, and I stood there giving downbeat after downbeat without a coherent musical thought in my mind. I opened my mouth to say something, and I felt naked in front of those hundred eyes. The tempo was dragging, and I needed to fix it, and the words croaked out of my vocal cords shyly. And we rehearsed it again, and it still dragged. And again. And again. And I was frightened and embarrassed and that was death.

Three months earlier, I was leading my first ever recitation for a math course, covering both single variable and multivariable calculus (it's a kind of weird one-and-a-half semester course). I can still remember the first time I taught. I stood at the front of the class, and looked out at all those freshmen, their eyes still bright and optimistic, over fifty eyes in total, all focused in my direction, ready to listen to my every word.

What kind of teacher would I be? At the very least, I knew that I cared about teaching, which felt like a step in the right direction. But caring doesn't necessarily mean that you teach well. Caring doesn't necessarily mean that you're engaging. Caring just isn't enough.

Indeed, I was terrible. And I felt terrible about it.

These two experiences, conducting and teaching for the first time, were extraordinarily similar. The nakedness. The mental lack of clarity. Feeling judged in front of a decent-sized crowd.

For that first recitation, I had very much under-prepared and misunderstood my goals as a teacher. Of course I knew the material well, but it translated into a somewhat incomprehensible jumble of a recitation, which I'm certain was ultimately confusing for the students. Perhaps even worse, I spent way too much time philosophizing about the material, even though it was only day one. Sure, enthusiasm is useful and encouraging, but my version of it was very much misguided, focusing on extraneous thoughts instead of ensuring the class was following along.

I was confronted immediately with the fact that I needed to change how I approached teaching. I completely changed my routine, first and foremost trying out a variety of levels of preparation, finding that when I over-prepared, I spent too long on easy material, and when I under-prepared, my lectures were quite garbled. I re-learned how to think like a freshman, gradually obtaining a better sense of what sorts of questions I might have if I had never seen the material before, which in turn helped me to answer those questions in a more meaningful way during class time.

 My teaching improved dramatically, and I'm of the opinion that if you care enough about your teaching responsibilities, then you can become a good teacher with a little bit of practice. But if you're anything like me, "good" isn't enough. Even as I was improving that semester, I felt like it was the beginning of a quest towards finding the most effective method for teaching I could possibly achieve.

I was lucky that by the end of that semester, I had embarrassed myself attempting to conduct in front of an orchestra. Because of how similar that felt to screwing up my first recitation, I had a powerful realization.

Teaching is Performance

There's a famous problem in probability called the Monty Hall Problem. Monty Hall was the host of Let's Make a Deal, a game show which ran in the US in the 60's, 70's, and 80's. Actually, when I was young, I used to watch lots of reruns of the show, and I ended up with a pretty inaccurate 1970's-based sense for prices of refrigerators. I've never updated my mind with current prices since I've never bought my own fridge. Anyways, the problem describes the following situation. You're a contestant on a game show, and you're presented with three doors. Behind one of them is a car, and behind the other two is a goat. You want to win the car (in case that wasn't clear), but you can't see which door contains which item. The host asks you to pick which door you think has the car. Once you've done that, the host then reveals one of the other two doors, behind which there is a goat. Is it advantageous to keep the door you originally picked, or to change it? Most people would guess that regardless of whether they stay or change, they have a 50% chance of winning the car. But it turns out that's not the case! (In case you haven't seen before, it is important to note that the host knows that the door which is revealed after you've made your choice will contain a goat. The solution, which gives you the probability of winning the car if you keep your door, can be found in the linked Numberphile video.)

So let's say you're teaching a probability and statistics course. You could describe the problem, and solve it, and that would be a standard lecture, but that kind of ruins the fact that the answer feels surprising. Instead, last semester, I turned my classroom into a game show! I was the host, and I had a student come to the front of the class and play the game! And another student. And another student. We ended up with about 15-20 trials, really milking the game show aspect in the first five or so, but just running through them more quickly so there were a reasonable number of trials. Before class, I had used a random number generator to help dictate for each trial which door had a car in it and which door I would reveal, depending on the door the contestant chose, so that I was also being faithful to the mathematical material. My awful Monty Hall impression aside (which was so bad I don't think they knew I was doing a Monty Hall impression at all), I suspect those students are never going to forget the experience of coming to the front of class and picking a door.

I'm not suggesting doing something theatrical like that for every lecture - it'd be impossible to get through all of the material! But performance is about being dynamic. It's about making sound effects and associating them with certain concepts. It's about using consistent colors across different lectures so that the ideas are color-coded. It's about inviting the class in and involving them in the material.

Thinking back to my first semester of recitations, I had only heard of variants of a single model - start by recapping the material from lecture, and then give the students problems to work on. But how engaging is this model? It's really quite boring, isn't it? How much feedback do you actually have from the students? Not much, just whether they can solve the problem or not, and then even upon presenting a solution, there's not really much feedback to see if they understand. Does it really benefit all the students in the recitation? Again, not really, because the people who are behind will struggle, while the people who are ahead aren't learning anything.

Here's a very different model for recitations, derived from the idea that a classroom is a performance space, which I think is infinitely better, and which I instigated by the end of that very semester. (This model is specifically for recitations of about 20 students.)

Again, I started with a mini-lecture, summarizing what was covered in class. (Even here, I tried hard to make the summary more engaging, asking more questions, and trying to get students involved.) But then, for the "working on problems" portion of the class, I separated them into small groups of about four students. I was lucky to be in a classroom where there were many chalkboards around the room, so I sent them to different corners of the room, and gave them the problems to discuss with each other, walking around as a moderator, like being the emcee of a math-themed party. Like good performance art, the emphasis is not necessarily on the artist (the teacher in this case), but on the spectator's experience. Here's how it compared:

Was it engaging? Absolutely! The students were forced to be involved, and importantly, to discuss mathematics, instead of simply keeping it in their heads. That kind of active involvement catalyzes more thorough comprehension. Even if they had solved a problem easily, the setting was perfect for asking "what if"-type questions.

Was there a lot of feedback about the students' understanding? Yes! This structure completely clarified whether students' issues were computational or conceptual. And whenever I approached a group, I tended to ask those students who weren't holding the chalk to explain any solutions their group had written on the blackboard. Very quickly, the class learned that their group was only as strong as its weakest member, and that really helped ensure nobody was being left behind.

Did it benefit every student? 100%! Of course there are going to be weaker and stronger students. In my recitation, the weaker students were forced to engage in the material so that they weren't stumped if I asked them to explain a solution. Meanwhile, the stronger students had the chance to act as mini-teachers, which helped them to think about the ideas much more thoroughly. As many a teacher can attest, you don't really understand the material unless you can explain it to someone else.

And last of all, almost all of the students enjoyed it! I had played around with a few variants of this model over about two weeks, asking the class for anonymous feedback. For the version I chose, almost every student preferred it to the standard model for recitations, and that preference certainly showed up in my teaching evaluations.

It will be interesting attacking teaching in a world afflicted with a pandemic, and I've been spending a lot of time thinking about how to develop the performance aspect in the long-distance classroom. I think the most important part will be incorporating dynamism into lectures. For months, YouTube kept on recommending to me this video of Cedric Villani giving a lecture entitled "Of triangles, gases, prices and men," and eventually I clicked on it. I guarantee that if you play from any point in the video, there will be an entrancing, captivating aura to the performance, even if you don't understand the words. (To me it feels like a scene in a David Lynch film, but minus the dark, surrealist tone, but I'm probably alone in this somewhat bizarre assessment.) I hope I can give my students something close to that experience, even when my usual stage has been suddenly pulled away from under my feet.

I enter every lecture feeling like I'm an actor, about to give a performance. My job is not just to memorize my lines and recite them. It's about breathing life into the words. It's about having an artistic vision for the lecture. It's about reacting and listening to the crowd. And for the rest of the semester, it's about not just rolling with the punches, but transforming the chaos into a fresh perspective which can captivate an audience, even through the bright glow of a computer screen.