Abrahamson, D., Sánchez-García, R., & Trninic, D. (2016). Praxes proxies: Revisiting educational manipulatives from an ecological dynamics perspective. 

In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Sin fronteras: Questioning borders with(in) mathematics education – Proceedings of the 38th annual meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) (Vol. 13, “Theory and research methods,” pp. 1565-1572). Tucson, AZ: University of Arizona.

The recent proliferation of technological devices with natural user interfaces (e.g., touchscreen tablets) is regenerating scholarship on the role of sensorimotor interaction in conceptual learning. Some researchers of mathematical education have adopted views from constructivism, phenomenology, enactivism, and ecological dynamics to interpret implicit sensorimotor schemes as both forming and manifesting disciplinary competence. Drawing on these views, this theoretical paper returns to the enduring question of what it means to develop a new skill by way of task-oriented interaction with objects. Beginning with sports then moving to mathematics, we focus on a subcategory of pedagogical artifacts that serve students only during training activities yet constitute proxies for developing target schemes toward normative application. We argue for the contribution of these views to conceptualizing the design of effective mathematics instruction.