Metaphor and metonymy in processes of semiosis in mathematics education

Abstract

Building on Michael Otte's insights regarding the roles of icon, index, and symbol in mathematical signification, definitions of these categories of representation are explored in terms of metaphors and metonymies. A nested model of signs, based on Peirce's triadic formulation, is described, along with his trichotomic distinction among interpretants that are intentional, effectual, and communicational (leading to the commens). The theoretical argument and its utility is illustrated in terms of an episode of creating a proof in a college geometry class. The significance of the theoretical notions for creativity in mathematics is seen to reside in metaphorical and metonymical processes. © 2005 Springer Science+Business Media, Inc.