Markov solution processes: Modeling human problem solving with procedural knowledge space theory

Abstract

Stefanutti (2019) recently developed procedures and a related theory for deriving learning spaces from problem spaces. The approach provides a deterministic model for partially ordering individuals, on the basis of their performances in problem-solving tasks. This deterministic model accounts for both the accuracy of the responses and, especially, the sequence of ”moves” (observable solution process) made by the problem solver. A Markov model of the solution process of a problem-solving task is proposed, that provides a stochastic framework for the empirical test of the deterministic model and the related problem-space-derived learning space. This type of model allows for making predictions with respect to both the observable solution process, and the unobservable knowledge state on which the solution process is assumed to be based. The Tower of London test has been chosen as the problem-solving task for the empirical validation of the model. The results of a simulation study and of two different empirical studies are presented and discussed.