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. 1612-1615). Tucson, AZ: University of Arizona.
In a pilot study of an experimental calculus activity centered on the CalcMachine—a concrete manipulative—subjects visually “projected” the anticipated results of their actions before executing them. From these empirical findings, we tentatively argue for integrating two theoretical models: distributed cognition (Kirsh, 2009) and instrumental genesis (Vérillon & Rabardel, 1995). Emerging from a study in the concrete domain, this theoretical development may bear implications also for digital interactive educational technologies.