Design and Evaluation of a Case-Based System for Modelling Exploratory Learning Behavior of Math Generalization

Exploratory learning environments (ELEs) promote a view of learning that encourages students to construct and/or explore models and observe the effects of modifying their parameters. The freedom given to learners in this exploration context leads to a variety of learner approaches for constructing models and makes modelling of learner behavior a challenging task. To address this issue, we propose a learner modelling mechanism for monitoring learners' actions when constructing/exploring models by modelling sequences of actions reflecting different strategies in solving a task. This is based on a modified version of case-based reasoning for problems with multiple solutions. In our formulation, approaches to explore the task are represented as sequences of simple cases linked by temporal and dependency relations, which are mapped to the learners' behavior in the system by means of appropriate similarity metrics. This paper presents the development and validation of the modelling mechanism. The model was validated in the context of an ELE for mathematical generalisation using data from classroom sessions and pedagogically-driven learning scenarios.