Teachers Can't Read Minds!

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 OPEN…TOP 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?