UC Berkeley

Although cognitive activity has been modeled through the lens of dynamical systems theory, the field lacks robust demonstrations in the learning of mathematical concepts. One empirical context demonstrating potential for closing this gap is embodied design, wherein students learn to enact new movement patterns that instantiate mathematical schemes. Changes in students’ perceptuomotor behavior in such contexts have been described as bearing markers of systemic phase transitions, but no research to date has characterized these dynamics quantitatively. This study applied a nonlinear analysis method, continuous cross-Recurrence Quantification Analysis (RQA), to touchscreen data excerpts from 39 study participants working with the Mathematics Imagery Trainer on the Parallel Bars problem. We then conducted linear regression analysis of a panel of five RQA metrics on learning phase (Exploration, Discovery, and Fluency) to identify how nonlinear dynamics changed as fluency developed. Results showed an increase in determinism from the Exploration to the Discovery phase, and an increase in recurrence rate, trapping time, mean line length, and normalized entropy from Discovery to Fluency phases. To put these dynamics in context, we qualitatively contrasted the RQA metric trajectories of two case study participants who developed different degrees of fluency. Our results support the hypothesized existence of phase transitions in the human–technology dynamical system during a math learning task. More broadly, this study illustrates the purchase of nonlinear methods on multimodal mathematics learning data and reveals perceptuomotor learning dynamics informative for the design and use of embodied-interaction technologies.