Another article was just published (in the Journal of Experimental Psychology: Learning, Memory, and Cognition) providing more evidence about the link between embodiment/actions/gestures and mathematics understanding. From “What do the hands externalize in simple arithmetic?”:
In 4 experiments, the authors examined the use of the hands in simple arithmetic tasks. Experiments 1 and 2 demonstrated that pointing increases both accuracy and speed in counting arrays of items, whether those items are identical or distinctive. Experiment 3 demonstrated that individuals tend to nod their heads when not allowed to point and that nodding is associated with greater accuracy, suggesting that pointing is functional for reasons other than simply providing additional visual information. Experiment 4 examined changes in speech when adding arrays of digits, depending on whether participants were allowed to use their hands to manipulate the tokens on which the digits were presented. Taken together, the results of these experiments are consistent with recent research suggesting that gesture can serve cognitive functions and that the hands can support the binding of representational elements to their functional roles by providing phase markers for cyclic cognitive processes.
This is reminiscent of a story Seymour Papert told about a classroom student he observed who was not allowed to use his hands while working on math problems. Papert followed up on this story in 1998:
In The Children’s Machine I told a learning story about how I helped a student in the “resource room” — which is where they send the kids who are supposed to have learning disabilities– of a public school in one of our big cities.. I was able to guess why this kid was looking all around him with an unhappy expression on his face. He had been assigned a list of little “math problems” in the form of numbers to add together but knew that he was not allowed to use his fingers as he liked to do. I guessed that he was unsuccessfully looking for some external support he could use in the place of fingers. I thought for a moment about whether to intervene and how. I did not want to offend the teacher. I certainly did not want to get the kid into any trouble. On the other hand I was firmly convinced that allowing him to use external aids was the best way to encourage real learning and denying the use of fingers the best way to make sure that he hated doing these sums. So I thought for a while and then said in a loud enough voice for the teacher and the kid to hear: “What about your teeth?”
The result was exactly what I hoped. The teacher saw no connection with the assignment but I saw from his face that the kid did: first a puzzled expression, then a lighting up that expressed “aha, I get it” and then a little moving bulge in his cheek and lips. “Learning disability indeed” I thought to myself “this is one smart kid.”
This incident happened ten years ago. Since then I have asked a lot of people about using teeth as a support system for mental work. Most people need some explanation to know what I am talking about: obviously they had never done it. But quite a few kids admitted to using teeth in such ways and quite a few adults — including one of the leading theorists of computer science–remembered doing so in the past.
For more research and theory in this vein, see work by people such as David Tall, Susan Goldin-Meadow (her book Hearing Gesture), Ricardo Nemirovsky, and the book Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, by George Lakoff & Rafael Nunez.