Children's creation of algorithms: simulations and gestures

Abstract

for advice.Experiments showed that ten-year old children are able to create algorithms, i.e., 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 kinematic mental simulations. Gestures are outward signs of moves and they help the process. We tested ten-year children, because they can make mental simulations, and because they gesture more than adults. They readily rearranged the order of six 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 unable to gesture as they formulated algorithms, the accuracy of their algorithms declined by13% (Experiment 3). We discuss the implications of these results for accounts of reasoning and theories of gestures.

Simulation in children’s conscious recursive reasoning

“…To the best of our knowledge, no previous study has obtained such a result. The results also corroborated our earlier finding that children could abduce algorithms for trains of six cars (Bucciarelli et al, 2016). In sum, the results corroborated the three predictions of the model theory.…”

“…Likewise, in a previous study of fifth-grade children, we examined two of the three tasks. We showed that children can solve problems of rearranging five cars, and that they can abduce informal algorithms for rearranging trains of six cars (Bucciarelli, Mackiewicz, Khemlani, & Johnson-Laird, 2016). We also showed that gestures helped them abduce algorithms when they were not allowed to move the cars.…”

“…Children and adults have no difficulty understanding the environment and its rules, and in solving problems that call for rearranging cars in a train (Bucciarelli et al, 2016;Khemlani, Goodwin, & Johnson-Laird, 2015;. One potential worry is that the environment is idiosyncratic and not representative of recursive domains.…”

“…This partial means-ends analysis can solve any rearrangement, but to guarantee a minimal solution-one with the fewest possible moves-takes some exploration in certain cases. The process could be carried out in actual moves on the railway track, but children do have some ability to simulate moves if they are prohibited from touching the actual cars (Bucciarelli et al, 2016). Instead of performing physical moves, children construct mental models of what cars are where on the railway track.…”

“…Our previous study of children had shown that they could abduce algorithms for rearranging trains of six cars (Bucciarelli et al, 2016). An open question was whether they could abduce recursive algorithms to rearrange trains of an indefinite length.…”