Future predicters
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Every year I stand in front of a group of new fourth or fifth grade students and face the most challenging teaching task I’ve ever had: training them to be telepathic.

I always begin with a magic trick. Each student chooses a two-​digit number. Then I walk them through a series of simple calculations resulting in a new number. On that page in their math book, they choose a picture and memorize it.

Earlier in the day, a mysterious envelope had arrived in the classroom, marked “DO NOT OPENTOP SECRET.” I now open that envelope, revealing a duplicate of the photo they all have memorized. I can read minds!

Of course, it doesn’t take long for the class to realize it was a trick, and I don’t deny it. In fact, I remind them that I began the exercise by telling them I was going to do a magic trick. The point is why I had to do a trick: teacher’s can’t read minds.

So what does this have to do with math?” they ask me.

Ah, excellent question,” I reply. “When you put an answer down on a math test or a homework problem, how does your teacher know what you were thinking when you solved it?”

Uh…she doesn’t?”

Precisely. But for us to teach you, we need to know how you’re thinking so we can help you learn how to solve problems better. Since we can’t read minds, what’s the only way for us to know what’s going on in your head as you’re solving a math problem?”

If the lesson were outside at night, this question would normally be answered by the sound of crickets chirping. One brave soul usually raises a cautious hand: “Uh…we tell you?”

A simple concept. A difficult task. Actually getting the thoughts from their heads into words—and eventually onto paper—is something that takes much practice and many examples. Yesterday I talked about one of the ways to begin this process by teaching and using the correct vocabulary.

We need to teach students that math is not about rote manipulation of abstract symbols. Those symbols, and the terminology that goes along with them, are tools with two purposes: solving problems, and communicating ideas.

I’ve developed a structure that helps students organize their thinking and chunk the way they communicate it. I tell them, “Wear Your C.A.P.E.”:

C Calculations Show all of your math work and computations
A Answer Be sure to answer the question or questions that the problem asks!
P Procedure or Plan Show each step of how you solve the problem, including drawings, tables, etc.
E Explanation Explain your math reasoning—tell why you did what you did

The most difficult aspect of this, of course, is the explanation—describing the why, not just the what. In order to help with this, I teach them the Magic Words. Just like using clue words to identify the operation in a word problem (like “all together” signifies addition), these words can help to signify their mathematical reasoning when they talk or write. (This list is based on an article by Diane Hurst published several years ago in the PA Math Assessment Handbook, but no longer appears to be available):

to get because
to find since
to figure out therefore
to show so that

Students who learn to use these words correctly will begin to unpack the reasoning that is going on in their heads.

How could you adapt this to your situation? What other subject areas might it work for? Do you have other ideas about teaching students to be “telepathic” and communicate their thinking to other people?

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