In D. L. Holton (Chair) & J. P. Gee (Discussant), Embodied and enactive approaches to instruction: implications and innovations. Paper presented at the annual meeting of the American Educational Research Association, April 30 – May 4.

Abrahamson-Howison-AERA2010-ReinholzTrninic.pdf

Building on growing evidence that human reasoning simulates multi-modal dynamical imagery drawn from lived experience (e.g., Barsalou, 2008), we conjectured that some mathematical concepts may be difficult to learn precisely because our everyday experience fails to provide adequate opportunities to develop the requisite body-based imagery underlying those specific concepts. To evaluate this conjecture, we are conducting a study in which we first provide students with a “ready-made” visual–kinesthetic basis for developing imagery pertaining to a difficult mathematical concept and then measure the effects of such provision on their emergent understanding of the targeted mathematical concept. This initially “meaningless” yet embodied experience (aka the “Karate Kid effect” http://www.youtube.com/watch?v=3PycZtfns_U) is to play a pedagogical role analogous to concrete artifacts, such as an abacus, pendulum, or dice, in terms of creating opportunities for guided reflection, mathematization, and reinvention of culturally knowledge.

Our study is thus geared to comment on theoretical models that argue for an embodied basis of mathematical learning and reasoning. Prior arguments build either on theoretical analyses of human reasoning (Barsalou, 1999; Goldin, 1987; Lakoff & Núñez, 2000), empirical studies of human activity in general (Clark, 1999; Hatano, Miyake, & Binks, 1977), interpretations of mathematics students’ behaviors (Abrahamson, 2004, 2009; Fuson & Abrahamson, 2005; Nemirovsky, Tierney, & Wright, 1998), or specifically evidence of gestures accompanying speech utterances produced during the solution of mathematical problems (Alibali et al., 1999; Edwards, Radford, & Arzarello, 2009). Whereas these studies furnish strong support for the potential viability of the embodied conjecture, and whereas they have demonstrated the plausibility of an embodied substrate for working memory, they have not established conclusively a *sine qua non*role of multi-modal dynamical imagery in the ontological development of mathematical concepts. Namely, it has yet to be shown compellingly that imagery plays more than a supportive or epiphenomenal role in the instruction of essentially abstract concepts (cf., Schwartz & Black, 1999).

We chose the mathematical content domain of proportionality because rational numbers are fraught with conceptual challenges (e.g., Lamon, 2007). We conjecture that students’ difficulties with proportionality, and in particular their “additive” or “same difference” errors, stem from their lack of a suitable dynamic image in which to ground their understanding of proportionality. We have developed a device that trains the user to perform arm motions describing proportional growth.

Clearly, this is pioneering work in progress, and assessment tools are still under development. Yet, we feel confident that there is already sufficient *theoretical *material for sparking useful scholarly discourse. Notwithstanding, by AERA we will have collected and analyzed *empirical *data from a study we are conducting this fall with thirty 4^{th}-grade students. During the symposium, we will also demonstrate the technology.