How to Handle the Math

Thursday, March 19, 2009

By Wray Herbert

I used to play chess with an excellent chess player, far superior to me. But he had this maddening habit in the endgame. He would start uttering, softly but aloud: boom, boom, boom-boom, boom. And with each boom, he would gesture in the air, kind of like a conductor with an invisible baton. Whenever he started this ritual, I knew it was over. It meant he saw the inevitable chain of moves that would lead to checkmate.

He was always right, though there was nothing triumphant about his gestures. It was more like he was searching for the solution rather than announcing it. Indeed, at times I had this bizarre sense that he was observing his own hands to extract the answer.

Well it may not have been so bizarre, as it turns out. Psychologists have recently become very interested in how we embody meaning in our movements. Why gesture at all? Do we use hand movements to convey information to others, as a kind of rudimentary sign language? Or are we really gesturing to ourselves, perhaps as an aid to memory or learning? What is the link between gesture and sound and words and meaning? Or to put it more scientifically, what was all that boom-boom-booming about?

University of Chicago psychologist Susan Goldin-Meadow and her colleagues decided to investigate these questions in their lab. They wanted to see if gestures might help with learning new ideas—and if so, what kinds of gestures. Most important, they wanted to find out how gestures might enhance learning. What’s going on in the gesticulator's mind?

They studied third and fourth graders, and selected only kids who had not yet learned this specific math operation: 6 + 3 + 4 = __ + 4. This seems simple enough to us, but it actually requires that kids master the concept of “grouping.” That is, they have to learn to group 6 and 3 (and not 3 and 4) to get the correct answer to the equation.

All the kids were told that the challenge was to make the two sides of the equation equal. But some kids were also taught to gesture as they solved the problem: Specifically, they formed a “V” with two fingers (like a peace sign) and pointed to the numbers that needed to be grouped. Then they pointed to the answer with a single finger, the index finger. So the gesture aped the mental operation: Two numbers became one.

Other kids also gestured, but inaccurately, pointing to the wrong two numbers with their two fingers. Still others used no gestures at all. After some practice sessions, the teacher taught a traditional math lesson, explaining in words the meaning of equivalence. Importantly, the teacher never used the word “grouping” in the lesson. The idea was to see if the kids who gestured meaningfully actually learned better—and also if they added the word “grouping” to their spoken repertoire on their own.

And they did. They not only solved more problems correctly later on, they did so only if they had verbalized to themselves what the gesture symbolized—its meaning. This is quite remarkable, since at no time was “grouping” mentioned. The kids had to extract that abstract idea from their own hand movements.

These findings, reported in the March issue of the journal Psychological Science, leave one important question. Were the kids movements—the peace signs and pointing fingers—really gestures? After all, they acquired them through rote learning, at a teacher’s request—not spontaneously. But the researchers point out that kids who do know this mathematical concept actually use these same gestures on their own. This raises the intriguing possibility that kids start off making meaningless gestures, which then take on meaning in the context of learning. In other words, it may be a general intellectual progression, common to all childhood learning.

If gestures are indeed an essential part of learning new ideas, then it may be possible to recruit the body as a tool in learning—and not just rudimentary arithmetic. Why not calculus, or chemistry—or for that matter, chess?

For more insights into the quirks of human nature, visit “We’re Only Human” at Excerpts from the blog also appear regularly in the magazine Scientific American Mind and at

posted by Wray Herbert @ 4:05 PM


At 10:55 AM , Blogger replicatorinc said...

how is it possible to use only one discipline, like psychology, to explain things. Don't you just want to use everything you've got in your toolbag? it's like a man with a hammer, all problems look lie a nail. do you apply psychology to all of your problems?


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