# Hands-on Math Insights: Teachers’ mismatched gestures boost learning

By Bruce Bower

As teachers instruct a child, they typically use their hands as well as their voices, but only certain gestures pack a powerful educational punch, a new study suggests. Grade-schoolers best learn how to solve a particular mathematics problem when a teacher’s gestures convey different information than his or her words do, say Melissa A. Singer and Susan Goldin-Meadow, both psychologists at the University of Chicago.

The combination of hearing one problem-solving strategy in speech and seeing another in gesture fosters more math insight than speech and gestures describing the same strategy do, the researchers propose in the February *Psychological Science*.

Results are worst when the teacher verbally describes two problem-solving strategies, with or without accompanying gestures. Youngsters in these situations may be encountering too much verbal information presented too quickly, Singer and Goldin-Meadow theorize.

“Gesture has an active hand in learning,” Goldin-Meadow says. “Teachers may need to pay more attention to how they use gestures.”

The researchers studied 160 third and fourth graders, ages 8 to 10. Each child initially failed to solve mathematical-equivalence problems, such as

6 + 4 + 3 = ___ + 3.

The children were then verbally taught either one or two problem-solving strategies in roughly half-hour sessions. One approach, the equalizer strategy, adds the numbers on the left side of an equation and then determines how much to add to the number on the right side to get the same total. This strategy highlights the problem’s underlying principle.

In the other tactic, dubbed the add-subtract strategy, a child adds up the numbers on the left side of an equation and then subtracts the number on the right from the left-side total.

Each form of verbal instruction was presented in one of three situations: no accompanying gestures, gestures that matched the tactic being described, or gestures that matched the alternative tactic. For the equalizer strategy, matching gestures consisted of a hand sweep under the left side of a written equation, a drop of the hand, and then a hand sweep under the right side. For the add-subtract strategy, matching gestures included pointing consecutively to each number on the left side, followed by a flick-away gesture near the right-side number.

On a test administered after instruction, kids performed best and provided the most thorough explanations of their reasoning after the teacher had explained one strategy verbally and used mismatching gestures. The combination of equalizer delivered verbally and add-subtract shown in gestures yielded the highest average scores.

Related studies indicate that children on the verge of understanding mathematical equivalence exhibit flawed verbal reasoning combined with gestures that depict valid strategies (SN: 3/17/01, p. 172: Available to subscribers at Learning in Waves).

The new finding that gestures not matched to speech promote learning demands closer study, remarks psychologist Martha W. Alibali of the University of Wisconsin–Madison. It’s not clear why the mismatch of gestures and speech is effective or whether it yields similar benefits in teaching other math concepts, Alibali says.