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

Abstract

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.

Identifying Qualitative Between-Subject and Within-Subject Variability: A Method for Clustering Regime-Switching Dynamics

“…Note that to keep the same ratio as the hands move up, the one hand has to move twice as fast as the other hand, which proves to be a challenging bodily coordination exercise for participants even though they have figured out the proportion rule. Further analysis of the participants' verbalization during the interview using natural language processing techniques confirmed our interpretation of the different regimes to some extent [see Ou et al (2020) for more details]. Additionally, Figure 7 illustrates the estimated expected logistic curves of the probabilities of an individual being in a regime during the interview.…”

Learning analytics of embodied design: Enhancing synergy

“…For example, educational designers of movement-based learning have shared their data with learning-analytics experts who applied machine-learning algorithms and statistical methods to detect and classify microprocesses of skill development (e.g., Pardos et al, 2018). Also, data-driven quantitative and qualitative insights about students' behavior have been drawn to inform the development of new ED applications for personalized learning (Ou et al, 2020). Still, it is our reading of the field that ED and LA communities mostly operate from distinct, often non-overlapping intellectual bases, secluded in their own associations, special interest groups, conferences, journals, and online activities.…”