Bringing forth mathematical concepts: signifying sensorimotor enactment in fields of promoted action

Abstract

Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an ''instrumented field of promoted action''. Children operating in this field first develop environmentally coupled motoraction coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4-6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners' operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics education research. All doing is knowing, and all knowing is doing. (Maturana and Varela 1992, p. 26).

Enactive Metaphorising in the Learning of Mathematics

“…So in fact negative emotions may foster creativity! We noticed a remarkable convergence of our claims and experimental findings regarding the positive incidence of enacting in the arising of new insights in problem-solving situations with very recent research in cognitive science (e.g., Glenberg 2015;Vallée-Tourangeau et al 2016;Abrahamson and Trninic 2015).…”

Invited Lectures from the 13th International Congress on Mathematical Education

“…We noticed a remarkable convergence of our claims and experimental findings regarding the positive incidence of enacting in the arising of new insights in problem-solving situations with very recent research in cognitive science (e.g., Glenberg 2015;Vallée-Tourangeau et al 2016;Abrahamson and Trninic 2015).…”

“…Each way of enacting-determined primarily by the solvers' structures and histories-suggests various different ideas and insights that do not emerge so easily when they just think about a problem. Our learners working on the challenges in Cases 34.4.1 and 34.4.2 indeed discovered unforeseen mathematical relations or facts in their bodily actions (see Abrahamson and Trninic 2015).…”

Designing Affordances for Health-Enhancing Physical Activity and Exercise in Sedentary Individuals

“…These ideas suggest how schools could be designed to take into account how classrooms, gymnasia, playgrounds and open spaces could facilitate PA in children with different abilities and effectivities. For example, interacting with grass, ledges, surfaces and trees can help children become and remain active whilst they are engaged in learning, even in subjects like mathematics which have been traditionally associated with static, classroombased learning environments [17,18].…”