Role of mental representations in problem solving: Students’ approaches to nondirected tasks

In this paper, we report on a project concerned with the role of cognition during problem solving. We specifically explore the categories of mental representations that students work with during problem solving of different representational task formats. The sample, consisting of 19 engineering students taking a calculus-based physics course, attempted tasks from the topics of kinematics and work. Profiles were designed to capture the overall actions and reasoning of individual students across the various tasks. Two main profiles emerged from each topic under consideration. They were related to the Johnson-Laird cognitive framework to infer about the kinds of mental constructs. The results indicate that, for both topics, students work primarily at the level of propositional mental representation. When handling the kinematics tasks, a few students construct mental images and none of them can be categorized as using a mental model. In contrast, in the context of work, none of the participants generated a mental image while a minority of the sample was classified as using a mental model. Moreover, a comparison across the two topics indicates the predominance of propositional mental representation