# Kids ‘get’ math when they use their hands

University of Chicago *right*Original Study

Posted by Jann Ingmire-Chicago on

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Children gain a deeper understanding of math and perform better when doing a problem if they use hand gestures, new research shows.

Previous research has found that gestures can help children learn. The new study, published online in *Psychological Science,* was designed to address the questions of whether abstract gesture can support generalization beyond a particular problem and if abstract gesture is a more effective teaching tool than concrete action.

“We found that acting gave children a relatively shallow understanding of a novel math concept, whereas gesturing led to deeper and more flexible learning,” says the study’s lead author, Miriam A. Novack, a doctoral student in the University of Chicago’s department of psychology’s developmental program.

The researchers taught third-grade children a strategy for solving one type of mathematical equivalence problem—for example, 4 + 2 + 6 = ____ + 6. They then tested the students on similar mathematical equivalence problems to determine how well they understood the underlying principle.

The researchers randomly assigned 90 children to conditions in which they learned using different kinds of physical interaction with the material.

In one group, children picked up magnetic number tiles and put them in the proper place in the formula. For example, for the problem 4 + 2 + 6 = ___ + 6, they picked up the 4 and 2 and placed them on a magnetic white board. Another group mimed that action without actually touching the tiles and a third group was taught to use abstract gestures with their hands to solve the equations.

### Abstract gestures

In the abstract gesture group, children were taught to produce a V-point gesture with their fingers under two of the numbers, metaphorically grouping them, followed by pointing a finger at the blank in the equation.

The children were tested before and after solving each problem in the lesson, including problems that required children to generalize beyond what they had learned in grouping the numbers. For example, they were given problems that were similar to the original one, but had different numbers on both sides of the equation.

Children in all three groups learned the problems they had been taught during the lesson. But only children who gestured during the lesson were successful on the generalization problems.

“Abstract gesture was most effective in encouraging learners to generalize the knowledge they had gained during instruction, action least effective, and concrete gesture somewhere in between,” says senior author Susan Goldin-Meadow, professor of psychology.

“Our findings provide the first evidence that gesture not only supports learning a task at hand but, more importantly, leads to generalization beyond the task. Children appear to learn underlying principles from their actions only insofar as those actions can be interpreted symbolically.”

*Source: University of Chicago*

## 3 Comments

pencilAdd A CommentLeast surprising “study” of the year so far. Real teachers have understood this forever.

Also most useless “study” of the year so far, because American math education is completely impermeable to common sense. With a very few heroic exceptions, American math ed will continue to focus entirely on bizarre idiotic theories and rote memory.

I disagree with the previous comment. This study has potentially wide-ranging significance. I remember talking with David McNeill some years ago and he was telling me about the gestures professional (academic) mathematicians used when they were talking about abstract operations and abstract objects. I was pleased to see that the gestures used in the study were modeled on the spontaneous movements of children who already understand how to solve the problems. Performing mathematical operations is like performing any action, except that mathematical “actions” are completely “interiorised”. The gesture provides an overt sensorimotor manifestation which is equivalent in specifiable aspects of logical form to the abstract operation. (The gestures are described as “metaphorical”, and metaphors involve an equivalence relation which can again be specified.) E.g., the “2 into 1” relation is involved in all equivalence relations, since you want to say that two objects somehow have a single significance. This idea of the role of gestures in abstract thinking can be generalized to other cases, but I think further analysis would be required; for instance there is no way to distinguish, using only the gestures in this study, the operations of addition and multiplication, or of differentiation (rational numbers). Let’s look again at the mathematicians talking.

Well, I wouldn’t have said anything, but the dismissiveness of the previous comment bothered me. BTW, I noticed this article because my wife is a Montessori teacher, and we were talking recently of how encouraging kids to use gestures when learning mathematical operations would be effective, and I’m sure she will find that the original article will give her useful insights. Montessori doesn’t focus on rote memory.

How does an identification system become a problematic abstraction? Or can I abstract the hell out of everything by finger pointing?