The emergence of proportional reasoning from embodied interaction with a tablet application: an eyetracking study

Embodied cognition is emerging as a promising approach in educational technology. This study is based on the conjecture that a potentially powerful methodology for researching embodied mathematics design would be to gather empirical data on children’s shifting visual attention as they learn to operate the technological devices so as to solve the situated problems. The aim of the study is to gain insight into the role of visual attention in the emergence of new sensorimotor schemes underlying mathematical concepts, especially proportion tasks. The research question is: How does visual attention change in the emergence of sensorimotor schemes during proportional reasoning tasks? An exploratory study was conducted amongst eight 5th- and 6th-grade students (age 10-12 years). Based on the original Mathematical Imagery Trainer for Proportion (MIT-P) designs for Wii and iPad (Abrahamson), a new tablet app has been developed. While students completed the hands-on proportion tasks, a Tobii x2-30 and an external camera were used for real-time processing and storage of both video and gaze data, resulting in integrated videos of hand- and eye movements. Data analysis revealed cross-participant variation in exploration path, progress rate, and inferences. Yet across all participants insight coincided with a shift from: (a) random finger movements accompanied by gazing at salient figural contour; to (b) new bimanual coordinations accompanied by gazing at new non-salient figural features. The study thus supports classical constructivist claims that mathematical concepts are grounded in operatory schemes. In particular, the data literally show the dynamical emergence of attentional anchors for situated problem solving as mediating the development of mathematical concepts. Thus new research methodologies stand to validate claims from embodiment.