Monica Bucciarelli, Robert Mackiewicz, Phil Johnson-Laird and I recently published a new paper in the Journal of Cognitive Psychology describing a theory of how children use mental simulations and gestures to reason about simple algorithms, such as reversing the order of items in list. Here’s a link to the paper, and here’s the abstract:
Experiments showed that children are able to create algorithms, that is, sequences of operations that solve problems, and that their gestures help them to do so. The theory of mental models, which is implemented in a computer program, postulates that the creation of algorithms depends on mental simulations that unfold in time. Gestures are outward signs of moves and they help the process. We tested 10-year-old children, because they can plan, and because they gesture more than adults. They were able to rearrange the order of 6 cars in a train (using a siding), and the difficulty of the task depended on the number of moves in minimal solutions (Experiment 1). They were also able to devise informal algorithms to rearrange the order of cars when they were not allowed to move the cars, and the difficulty of the task depended on the complexity of the algorithms (Experiment 2). When children were prevented from gesturing as they formulated algorithms, the accuracy of their algorithms declined by13% (Experiment 3). We discuss the implications of these results.