Symposium presented at the annual conference of the American Education Research Association, New York, March 24-28.
Examining data from a design-based research study on mathematical cognition, I analyze gestures performed by mathematically oriented undergraduate/graduate students engaged in a probability-related activity. I reveal three aspects of embodied reasoning in situated problem solving. Participants spontaneously: (a) overlaid upon physical objects manipulated images of these objects; (b) appropriated mathematical representations that had been specifically designed to accommodate their images; and (c) indicated when available media constrained their expressivity. I explain and demonstrate how new learning tools, implemented in subsequent studies, responded to students’ elicited needs by introducing interactive mathematical representations that materialize students’ spontaneous imagistic constructions. These special tools offload aspects of the expressive acts so as to free cognitive resources, thus enabling students to hone and elaborate their mathematical inquiry in accord with the design’s objectives and rationale. I conclude that mathematical reasoning is the enacted embodied negotiation and coordination of multiple multimodal resources, including material and symbolic artifacts. In the context of a situated problem-solving task, students manipulate elements of their pre-reflective apprehension, rendering the situation better conducive to the discursive practices of a professional community, that is, as modeled, encodable, and expressive in normative epistemic forms such as diagrammatic and symbolic expressions. Gesture, and especially gesture that has not yet been articulated verbally, is embodied reasoning groping for epistemic form.