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.

Some forms of movement, such as rocking, are common means of sensory self-regulation yet are discouraged in classroom contexts. We analyze the ableist underpinnings of this approach, and ask instead: could sensory-attractive activities such as rocking instead be solicited to serve content learning? Our design-based research project, Balance Board Math, fosters sensory-cognitive opportunities for the regulatory movement of rocking to serve as an intrinsic interaction resource for exploring mathematical graphical representations, with a focus on properties of sinusoidal functions such as frequency and amplitude. We analyze the role of balance/vestibular activation in pilot participants' exploration of graphing before, during, and after Balance Board Math activities.