Abrahamson, D. (2006). The three M’s: Imagination, embodiment, and mathematics.

Paper presented at the annual conference of the Jean Piaget Society, June 1-3, Baltimore, MD.

The objective of this paper is to call for research into the mechanisms and potential agency of imagination in mathematical reasoning and to propose an agenda for such research. Drawing on a broad spectrum of resources in philosophy, the cognitive sciences, embodiment theory, and mathematics-education research, I conjecture that by learning mathematics in environments that support engagement of imagination, students
could tap this powerful cognitive tool to support the construction and effective application of concepts. The research objectives are to: (a) investigate the roles of imagination in mathematical creativity, learning, and problem solving, e.g. exploring whether mathematicians’ images are idiosyncratic, culturally mediated, or some combination thereof; (b) ground an understanding of the roles of imagination in current cognitive-science theories and pedagogical perspectives; (c) develop methodology for evaluating students’ access to imagination as a cognitive resource and their imaginative engagement in learning activities; (d) outline principles for the design of objects and activities that encourage students both to engage in imaginative mathematical reasoning and, inter alia, to embrace imagination as an accessible cognitive resource; (e) design and build mathematical objects and create activities that encourage and guide utilization of imagination; and (f) research students’ learning in these designed activities.