We report a subset of results from an exploratory study that modeled mathematics learning using a dynamical systems lens. This study applied Recurrence Quantification Analysis to model participants’ interactions with a touchscreen-based embodied-design learning environment for proportionality, conducting both qualitative (case study) and quantitative (linear regression) analyses. Findings indicate an abrupt change in the RQA meanline metric associated with increased fluency, suggesting a phase transition into a new mode of interaction. These findings suggest theoretical and methodological traction for modeling embodied math learning as phase transitions in a human–technology dynamical system.