This software is used in the "Kinemathics" research project at the Embodied Design Research Laboratory, Graduate School of Education, UC Berkeley. It enables students to act out "proportional progressions" in which they raise their hands from a flat surface such that they maintain a fixed ratio (say 2:3) between the height of their hands. A Nintendo Wii remote can track infrared LED dots placed on the students' hands, and the software provides feedback on the accuracy of the hand motion.

Theoretical Premise

Current instructional practices in mathematics education can by-and-large be said to focus on students' development of competencies involving the production of textual, symbolical, and diagrammatic semiotic artifacts through activities such as computation, problem-solving, and logical argument. Research into the embodied nature of mathematical cognition, however, points to the central role of body-based experience in grounding mathematical concepts and enabling problem-solving. We are interested in how students recruit their body-based pre-articulated experiences as a basis for the reflective abstraction of embodied schemata that come to underlie their production of normative mathematical semiotic artifacts. A pilot study conducted by Abrahamson and Fuson (2005) demonstrated that students' cognitive difficulties in understanding proportional progression (e.g., the sequence of equivalent proportions 2:3, 4:6, 6:9, etc.) coincided with their physical difficulty of acting out such progressions with their hands (e.g., one hand grows by 2 units while the other hand simultaneously grows by 3). Our bold conjecture is that a lack of physical coordination might delimit the mental simulation of a concept, and therefore impede its mental construction. If we physically support the students in enacting the ambidexterity of proportional progression, they may be able to draw on their physical experience in developing a dynamic image of proportion, a potential prerequisite for conceptual understanding. Building on this conjecture, we plan to examine whether kinesthetically-induced experiences of proportional progression help students learn the mathematical concept.

Further Reading

Abrahamson, D., & Howison, M. L. (2008, December). Kinemathics: Kinetically induced mathematical learning. Presentation and workshop at the UC Berkeley Gesture Group (E. Sweetser, Director), December 5, 2008. PDF