If you’ve ever been in my office (my official office in the math department, I mean, not the coffeeshop which I affectionately refer to as my “Fenton office”), you know that I have lots of stuff. Decks of cards of every shape and size, all sorts of dice, Rubik’s cubes and variations, etc. And if you’ve ever sat in on one of my math classes, you know how often I’ll lead with an example involving a game or a thought experiment involving rolling dice, dealing cards, or counting something.
And if you know both of those things, you’re probably wondering why I almost never bring any visual aids. I roll imaginary dice, I carefully shuffle imaginary cards. Even when I’m wearing my corduroy jacket (which always has at least one deck of cards in the inside pocket), I don’t use them. I pantomime.
Because when I say, “Suppose I have a deck of cards, and I divide it into two piles like this…,” everyone’s eyes are on me. They have to be, and the students know they have to be. They have to follow my every pantomime or they won’t know what’s going on. They can’t take a look-out-the-window break and wait until I’ve finished doing what I’m doing, then look and see where the cards ended up. They have to pay active attention, to imagine the cards and dice and figure out what is happening. Because it’s not true that I don’t use cards. I do use cards. And the cards I use are in my students’ minds.
Students rarely give you their undivided attention, but almost no one wants to give her teacher zero attention. It’s natural to pay at least nominal attention. This gimmick means that students have to decide between paying no attention whatsoever and actively engaging their minds in what I’m saying, doing, introducing; there’s nothing in between.