In L. D. Edwards & C. M. Krause (Eds.), The body in mathematics: Theoretical and methodological lenses (pp. 126–173). Brill.
ABSTRACT: We evaluate the viability of modeling the phenomenon of mathematics teaching/learning from the combined theoretical perspectives of radical embodied cognition and the cultural–historical approach. In particular, we illuminate an apparent deep affinity
between two notions, respectively: (1) a complex dynamic system is a self-organizing coordination of distributed processes within a set of constraints; and (2) a functional system is a spontaneous organization of cognitive processes oriented on a subjective
task. Our thesis is grounded empirically in detailed analyses of several student–tutor dyads working on an action-based embodied design for parabolas. Micro-analysis of audio–video and dual-eye-tracking data reveals the dyad operating tacitly in intercor-
poreal sensory–motor coupling, giving rise to joint visual attention to the manipulated material. In so doing, tutor and student form an intercorporeal dynamic functional system. Contingent scaffolding within the system steers the student to coordinate the
learning material with cultural ways of referring. Later, the tutor’s scaffolding operations are transformed into the student’s self-regulation of her attention as extended by co-thought gestures. Learning is thus the transformation of an intercorporeal system
into new intracorporeal dynamics generating the student’s new functional capacity.
KEYWORDS: functional dynamic system – cultural-historical approach – embodied design – eye-tracking – forward model – intentionality – intercorporeal (coupling) – joint attention – micro-zone of proximal development – mathematics education.