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Frederic Mishkin, who's been a professor at Columbia Business School for almost 30 years, is good at solving problems and expressing ideas．Whether he's standing in front of a lecture hall or engaged in a casual conversation, his hands are always waving and pointing．When he was in graduate school, one of his professors was so annoyed by this constant gesturing that he made the young economist sit on his hands whenever he visited the professor's office．
It turns out, however, that Mishkin's professor had it exactly wrong．Gesture doesn't prevent but promotes clear thought and speech．Research demonstrates that the movements we make with our hands when we talk form a kind of second language, adding information that's absent from our words．It's learning's secret code：Gesture reveals what we know．It reveals what we don't know．What's more, the agreement(or lack of agreement)between what our voices say and how our hands move offers a clue to our readiness to learn．
Manyof the studies establishing the importance of gesture to learning have been conducted by Susan Goldin-Meadow, a professor of psychology at the University of Chicago．"We change our minds by moving our hands," writes Goldin-Meadow in a review of this work．Particularly significant are what she calls "mismatches" between oral expression and physical gestures．A student might say that a heavier ball falls faster than a light one, for example, but make a gesture indicating that they fall at the same rate, which is correct．Such differences indicate that we're moving from one level of understanding to another．The thoughts expressed by hand motions are often our newest and most advanced ideas about the problem we're working on; we can't yet absorb these concepts into language, but we can capture them in movement．
Goldin-Meadow's more recent work strews not only that gesture shows our readiness to learn, but that it actually helps to bring learning about．It does so in two ways．First, it elicits(引出)helpful behavior from others around us．Goldin-Meadow has found that adults respond to children's speech-gesture mismatches by adjusting their way of instruction．Parents and teachers apparently receive the signal that children are ready to learn, and they act on it by offering a greater variety of problem-solving techniques．The act of gesturing itself also seems to quicken learning, bringing new knowledge into consciousness and aiding the understanding of new concepts．A 2007 study by Susan Wagner Cook, an assistant professor of psychology at the University of Iowa, reported that third-graders who were asked to gesture while learning algebra(代數(shù))were nearly three times more likely to remember what they'd learned than classmates who did not gesture．
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