Simulation and Analysis of Controlled Multi-Representational Reasoning Processes

Multi-representational reasoning processes often show a variety of reasoning paths that can be followed. To analyze such reasoning processes with special attention for differences between individuals, it is required (1) to obtain an overview of the variety of different possibilities and (2) to address navigation and control within the reasoning process. This paper presents a simulation model and a formal analysis method for the dynamics of a controlled reasoning process in which multiple representations play a role. Reasoning strategies to navigate through the space of possible reasoning states are modeled explicitly, and simulated. Simulation results are analyzed by software tools on the basis of formalized dynamic properties. The variety of dynamic properties specified and the variety of traces simulated provides an overview for the individual differences between subjects that have been observed while solving multiplication problems.