In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) (Ch. 12, “Theory and research methods: Research reports,” pp. 1261-1268). East Lansing, MI: Michigan State University.

ABSTRACT: Whereas Natural User Interface technological devices, such as tablets, are bringing physical interaction back into mathematics learning activities, existing educational theory is not geared to inform or interpret such learning. In particular, educational researchers investigating instructional interactions still need intellectual and methodological frameworks for conceptualizing, designing, facilitating, and analyzing how students’ immersive hands-on dynamical experiences become formulated within semiotic registers typical of mathematical discourse. We present paradigmatic empirical examples of tutor–student behaviors in an embodied-interaction learning environment, the Mathematical Imagery Trainer for Proportion. Drawing on ecological dynamics—a blend of dynamical-systems theory and ecological psychology—we describe the emergence of mathematical concepts from the guided discovery of sensorimotor schemes.