Handing Down Mathematics: The Roles of Gesture in the Design, Teaching, and Learning of Ratio and Proportion

Analyzing videotaped classroom interactions to understand the roles of gesture in the design, teaching, and learning of mathematics.


Abrahamson, D. (2007). Handling problems: Embodied reasoning in situated mathematics. In T. Lamberg & L. Wiest (Eds.), Proceedings of the Twenty Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 219 – 226). Stateline (Lake Tahoe), NV: University of Nevada, Reno.

ABSTRACT: Fifty 4th -17th -grade students participated in individual interviews oriented toward probabilistic intuition. Participants were given a boxful of equal numbers of green and blue marbles, mixed, and a device for scooping 4 ordered marbles and asked to predict the most common sample. Students replied that the outcome with the highest relative frequency would have 2 green and 2 blue marbles. Their verbal reasoning was accompanied by a deictic–metaphoric gesture to the left then right, as if they were separating the colors in the box. Gesture, I argue, bridges direct intuitive grasps of situations to conscious reflection, thus concretizing the prereflective, possibly grounding it in material form such that it emerges as conducive to further elaboration in mimetic symbolic form. Situated mathematical reasoning transpires largely as embodied negotiation among kinesthetic image schemas afforded by available material resources and epistemic forms.

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Fuson, K. C., & Abrahamson, D. (2005). Understanding ratio and proportion as an example of the Apprehending Zone and Conceptual-Phase problem-solving models. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 213-234). New York: Psychology Press.

5th-grade student discussing relation between mathematical operation (multiplication) and representation (multiplication table): “Every time you times 5 times one of the other number, it goes up five”

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.