*Embodied spatial articulation* is an individual's design-facilitated negotiation between personal and cultural resources pertaining to the visuo–spatiality of mathematical situations and representations. The personal resources are proto-mathematical action-based images, and the cultural resources are the appropriate seeing-in-using of classroom spatial–numerical artifacts. Embodied spatial articulation, I conjecture, underpins human interacting with epistemic artifacts historically, developmentally, in the designer's workshop, and in classroom space–time.

Abrahamson, D. (2004). Embodied spatial articulation: A gesture perspective on student negotiation between kinesthetic schemas and epistemic forms in learning mathematics. In D. E. McDougall & J. A. Ross (Eds.), *Proceedings of the Twenty Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (Vol. 2, pp. 791 – 797). Toronto, Ontario: Preney.

ABSTRACT: Two parallel strands in mathematics-education research—one that delineates students’ embodied schemas supporting their mathematical cognition and the other that focuses on the mediation of cultural knowledge through mathematical tools—could converge through examining reciprocities between schemas and tools. Using a gesture-based methodology that attends to students’ hand movements as they communicate their understanding, data examples from design research in two domains illustrate students’ spontaneous spatial articulation of embodied cognition. Such embodied spatial articulation could be essential for deep understanding of content, because in performing these articulations, students may be negotiating between their dynamic image-based intuitive understanding of a concept and the static formal mathematical formats of representing the concept. Implications for mathematics education are drawn.