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

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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 motor-action 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.

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Notes

  1. See Clancey (2008) for a survey of complementary intellectual antecedents to the situated/embodied/enactive paradigm, such as the cybernetics research of Gregory Bateson and the robotics work of Andy Clark.

  2. We acknowledge that Feldenkrais scholarship is unconventional as an academic perspective. Notwithstanding, we value its conjectures regarding the roles of embodiment and awareness with respect to learning. These conjectures are original and grounded in a practice that is empirically shown to be effective. Moreover, the conjectures parallel many of our own findings, some of which we arrived at prior to our exposure to Feldenkrais practice.

  3. For a brief video demonstration of the MIT-P, see https://www.youtube.com/watch?v=n9xVC76PlWc.

  4. Interestingly, dynamical-systems research into coordination of bimanual action (Kelso and Engstrøm 2006, p. 208) has demonstrated a dichotomy between “smooth” and “abrupt” transitions in the development of motor skill, analogous to our findings.

  5. For further empirical results from this line of work, see Abrahamson et al. (2014).

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Abrahamson, D., Trninic, D. Bringing forth mathematical concepts: signifying sensorimotor enactment in fields of promoted action. ZDM Mathematics Education 47, 295–306 (2015). https://doi.org/10.1007/s11858-014-0620-0

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