By Art Duval, Contributing Editor, University of Texas at El Paso
When I started teaching, I wanted to be the very best teacher. Not just “the best teacher I could be”, but the very best teacher, the one students would tell their friends about and remember fondly years later, the kind of teacher they might imagine being the hero in a movie. I don’t know what your movie hero teacher looks like, but mine is beloved by all the students (more Robin Williams than John Houseman). So naturally, I wanted all the students to like me. I also wanted them to share my love of mathematics, and see it as a joyful endeavor, not just a requirement to be checked off. As a result, I started including more humor in my classes. What I eventually realized, and had to confront, was that at least some of what I was doing was more about making me look like that movie hero teacher, or about making the class fun, than about helping my students learn mathematics.
My first years of teaching, I would prepare for each class by writing notes of just about every word I would write on the board. (Like a low-tech Powerpoint presentation.) However, this greatly facilitated the sort of class where, as the saying goes, the ideas travel from my notes to my students’ notes, without having to pass through the brains of any of us. Because the other trait I imagined in my movie hero teacher was making the students truly understand (and not just memorize) the material, over time I brought in activities to encourage more active learning and interaction, which also made my classes less tightly-scripted.
I also started loosening up and allowing more of my personality and sense of humor to show, for instance slipping in more clever cultural references or ironic asides. This is part of who I am, how I communicate outside the classroom, even when discussing serious mathematics with colleagues. Sometimes it’s just hard to avoid. One of the small ways I have of making class more interactive is to ask students to help me with a proof or equation. After watching countless episodes of Blue’s Clues when my son was little, I find it almost impossible to do this without saying “You will help me, won’t you?“, just the way Steve, the show’s host, said it.
If I thought of anything amusing related to what we were discussing in class, I would share it. The payoff for this sort of thing is immediate, in the smiling or laughing faces of students. I could justify it by noting it made class more enjoyable, and maybe helped students remember ideas better. And it made me feel more like the movie hero teacher.
Now, shortly after I started teaching, I served on the jury for a trial. The lead attorney for one side had very much the attitude in court I was trying to cultivate in the classroom. He seemed to want to be friendly with us on the jury, and, while I don’t think he introduced any actual humor, he was certainly very relaxed and smiled a lot. The attorney for the other side was more down to business. I definitely liked the first attorney more, but I found myself sometimes a little irritated at him for being less serious.
I would occasionally remember this trial as I grew more comfortable injecting humor in the classroom. And I eventually started questioning my motives. Was I doing this because it helped students learn mathematics, or because I wanted them to like me? Here’s the final note of cognitive dissonance that made me confront myself. I would tell students we didn’t have time in class for some things, such as a review for an exam. But if we don’t have time for a review, how do we have time for a joke?And here’s another concern. The clever wordplay and cultural references that I love so much have a special risk when dealing with students from another culture, or who are still mastering the language. I am especially aware of this, being on the border with another country. (It is literally true that I can see Mexico from my office window.) A number of years ago, teaching Game Theory, the textbook referred to the two players of some game as “Norm” and “Cliff“. I asked my students who understood this reference (click on the links to see the answer); all the students who grew up in the U.S. did, but none of the students who grew up in Mexico did.
So what did I change? I’ve kept in my cheerful outlook and my sense of wonder at mathematics (for instance overreacting for dramatic effect when some calculation yields a surprising result). But for anything beyond that, I now have two criteria for including anything entertaining:
- Does it take away precious class time? Class time together is one of our most limited resources, and so I want to reserve it for the most important things, the ones that cannot be done individually or outside of class.
- Does it unnecessarily distract the class from important mathematics? Does what I am thinking of reinforce the mathematics, or is it just funny? Very rarely, it is worthwhile to take a short mental break to give everyone a chance to catch their breath. But I also recall Gian-Carlo Rota’s observation that a valuable trait for doing mathematics is Sitzfleisch, the ability to sit and concentrate for long periods of time.
And, with some practice and careful attention, I have now pretty much trained myself to avoid anything that fails either of these tests. I can now think of a funny idea, and consciously choose to not share it. For instance, here is a joke I used to tell when the idea for uniqueness came up:
How do you catch a unique rabbit? You “neak” up on it.
How do you catch a tame rabbit? “Tame” way, u-nique up on it.
The problem is, students may remember this joke, and so may remember the word unique, but does it help them understand the idea, or remember how to show something is unique, or anything mathematical at all?
On the other hand, some jokes help make a point.
Two campers are in their tent in the woods when they hear a bear. The first camper starts putting on shoes, and the other camper says, “You don’t have time for that, shoes aren’t going to help you outrun a bear.” The first camper replies, “I don’t have to outrun the bear, I only have to outrun you.”
I tell this in Calculus I as we are starting global optimization, to make the point that sometimes it’s not enough to just have a very good solution or almost the best solution, but you have to have the best solution, second to none. Here, the joke may help to drive home this larger point, which some students may overlook in the thicket of algebra and derivatives that will shortly arise when we get to practice problems.
One final anecdote: In Linear Algebra, I was trying to make the point that even though we can’t put all matrices into diagonal form, we can at least put all matrices into Jordan canonical form (of which diagonal form is a more special case). I reminded students that not all matrices are diagonalizable, and wrote on the board, “You can’t always get what you want.” I realized only as I finished writing it that, without intending to, I was quoting the Rolling Stones. But in this case, it worked out perfectly because the next line (as realized by some students, who then practically sang it to everyone else) is “But if you try sometime, you just might find you get what you need,” which reinforced exactly the point I was about to make about Jordan canonical form.
And, come to think of it, this is a pretty good summary of where I am now. There will always be a part of me that still wants the adoration that comes from being the movie hero teacher. But what I need, what my students need, is for them to learn mathematics. And, as the song says, if I “try sometime,” I can give my students that opportunity while still sharing my enthusiasm for mathematics.