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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Krutetskii, V. A. (1976). The structure of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
Otte, M. (2001). Mathematical epistemology from a semiotic point of view. Paper presented in the Discussion Group, Semiotics in Mathematics Education, at the 25th Annual Meeting of the International Group for the Psychology of Mathematics Education, Utrecht, The Netherlands, 12–17 July 2001.
Peirce, C. S. (1998). The essential Peirce. Volume 2, edited by the Peirce Edition Project. Bloomington: Indiana University Press.
Presmeg, N. C. (1998). Metaphoric and metonymic signification in mathematics. Journal of Mathematical Behavior 17.1, 25–32.
Presmeg, N. C. (2002). A triadic nested lens for viewing teachers’ representations of semiotic chaining. In F. Hitt (Ed.), Representations and mathematical visualization. Mexico City: Cinvestav University, 263–276.
Russell, B. (1959). The problems of philosophy. London: Oxford University Press.
Saussure, F. de (1959). Course in general linguistics. New York: McGraw-Hill.
Sfard, A. (1991). On the dual nature of mathematical conceptions. Educational Studies in Mathematics 22, 1–36.
Whitson, J. A. (1994). Elements of a semiotic framework for understanding situated and conceptual learning. In D. Kirshner (Ed.), Proceedings of the 16th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Baton Rouge, Nov. 5–8, 1994, Vol. 1, 35–50.
Whitson, J. A. (1997). Cognition as a semiosic process: From situated mediation to critical reflective transcendance. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition: Social, semiotic, and psychological perspectives. Mahwah, New Jersey: Lawrence Erlbaum Associates, 97–149.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Presmeg, N. (2005). Metaphor and Metonymy in Processes of Semiosis in Mathematics Education. In: Hoffmann, M.H., Lenhard, J., Seeger, F. (eds) Activity and Sign. Springer, Boston, MA. https://doi.org/10.1007/0-387-24270-8_10
Download citation
DOI: https://doi.org/10.1007/0-387-24270-8_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24269-9
Online ISBN: 978-0-387-24270-5
eBook Packages: Humanities, Social Sciences and LawEducation (R0)