Using a cluster-based regime-switching dynamic model to understand embodied mathematical learning

Embodied learning and the design of embodied learning platforms have gained popularity in recent years due to the increasing availability of sensing technologies. In our study, we made use of the Mathematical Imagery Trainer for Proportion (MIT-P) that uses a touchscreen tablet to help students explore the concept of mathematical proportion. The use of sensing technologies provides an unprecedented amount of high-frequency data on students' behaviors. We investigated a statistical model called mixture Regime-Switching Hidden Logistic Transition Process (mixRHLP) and fit it to the students' hand motion data. Simultaneously, the model finds characteristic regimes and assigns students to clusters of regime transitions. To understand the nature of these regimes and clusters, we explore some properties in students' and tutor's verbalization associated with these different phases.