An analysis on the process from "play" to "learning"

It has been recognized especially in preschool that "play" is very useful for educating children since early times. Infants play just for enjoyment and learn many things such as scientific concept, communication and physical function through play. Many schoolteachers and educators had tried to make great efforts to apply "play" to schooling. To date many educational practices have been reported. But the mechanism of the transition process from "play" to "learning" as well as important factors for it has not been made apparent yet. We introduce an agent-model with several parameters, based on the probabilistic game theory and obtain analytic solution. The result shows that our model exhibits the existence of the mode transition from play-mode to learning-mode in a certain parameter regime.