Why I Roll Invisible Dice

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.

Why?

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.

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4 Responses to Why I Roll Invisible Dice

  1. ndroock1 says:

    Is teaching math about the professor getting the attention of students? I may be wrong about this but I don’t trust teachers ( or anyone else for that matter ) who put their statements in writing. Imho teaching math is all about students learning to read ( math ). Initiate them, do not entertain them.

  2. ndroock1 says:

    ( Corrected version )
    Is teaching math about the professor getting the attention of students? I may be wrong about this but I don’t trust teachers ( or anyone else for that matter ) who don’t put their statements in writing. Imho teaching math is all about students learning to read ( math ). Initiate them, do not entertain them.

    • Cap Khoury says:

      I think perhaps you misunderstand my point. I’m not saying my classes are just mime shows. I write down plenty: I fill blackboards, I post online supplements to lectures when this is called for, depending on the course I even have slideshows. And I like your word “initiate”: I tell all my students that in this class, everyone will be treated as a mathematician; in that spirit, I am not afraid to introduce higher math concepts, even in a basic calculus class, when they can illuminate or clarify the material. I think that the dumbing down of mathematics perpetrated by so many of my colleagues is born of an underestimate of what students are capable of and does a disservice to everyone; I resist it at every turn.

      No, this post was talking about just a specific little piece of my classroom practice: the example problem or situation which kicks off a section or topic. There’d be a couple of these in a week, each lasting a few minutes. I firmly believe that mathematical content is more meaningful for students who have, in advance, thought or played with the kind of problem which the new ideas were created to solve. This kind of pre-thinking from students cannot be coerced (though I’d like to), but it can be stimulated.

  3. Mom says:

    Mike, I love this entry. I think you could publish this blog. That from a mother.

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