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Metaphors in Mathematics Education

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Definition

Etymologically metaphor means “transfer,” from the Greek meta (trans) + pherein (to carry). Metaphor is in fact “transfer of meaning.”

Introduction

Metaphors are very likely as old as humankind. Recall Indra’s net, a 2500-year-old Buddhist metaphor of dependent origination and interconnectedness (Cook 1977; Capra 1982), consisting of an infinite network of pearls, each one reflecting all others, in a never-ending process of reflections of reflections, highly appreciated by mathematicians (Mumford et al. 2002).

It was Aristotle, however, with his taxonomic genius, who first christened and characterized metaphors c. 350 BC in his Poetics: “Metaphor consists in giving the thing a name that belongs to something else; the transference being either from genus to species, or from species to genus, or from species to species, on the grounds of analogy” (Aristotle 1984, 21:1457b). Interestingly for education, Aristotle added:

The greatest thing by far is to be a master of metaphor....

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References

  • Aristotle (1984) Poetics (trans: Bywater I). In: Barnes J (ed) The complete works of Aristotle. The revised Oxford translation. Princeton University Press, Princeton

    Google Scholar 

  • Bills C (2003) Metaphor in young children’s mental calculation. Accessed 18 Sept 2013 from http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG1/TG1_bills_cerme3.pdf

  • Black M (1962) Models and metaphors: studies in language and philosophy. Cornell University Press, Ithaca

    Google Scholar 

  • Black M (1993) More about metaphor. In: Ortony A (ed) Metaphor and thought, 2nd edn. Cambridge University Press, Cambridge, pp 19–41

    Chapter  Google Scholar 

  • Boyd R (1993) Metaphor and theory change: what is “metaphor” a metaphor for? In: Ortony A (ed) Metaphor and thought, 2nd edn. Cambridge University Press, Cambridge, pp 481–532

    Chapter  Google Scholar 

  • Bruner G (1986) Actual minds, possible worlds. Harvard University Press, Cambridge

    Google Scholar 

  • Capra F (1982) The turning point. Simon and Schuster, New York

    Google Scholar 

  • Chiu MM (1996) Exploring the origins, uses and interactions of student intuitions. J Res Math Educ 27(4):478–504

    Article  Google Scholar 

  • Chiu MM (2000) Metaphorical reasoning: origins, uses, development and interactions in mathematics. Educ J 28(1):13–46

    Google Scholar 

  • Chiu MM (2001) Using metaphors to understand and solve arithmetic problems. Math Think Learn 3(2):93–124

    Article  Google Scholar 

  • Cook FH (1977) Hua-Yen Buddhism: The jewel net of Indra. Penn State Press, University Park

    Google Scholar 

  • Coulson S (2008) Metaphor comprehension and the brain. In: Gibbs RW (ed) The Cambridge handbook of metaphor and thought. Cambridge University Press, Cambridge, pp 177–196

    Chapter  Google Scholar 

  • Dubinsky E (1999) Review of mathematical reasoning: analogies, metaphors, and images, English L (ed). Notices of the Am Math Soc 46(5):555–559. http://www.ams.org/notices/199905/rev-dubinsky.pdf

  • Dubinsky E, McDonald M (2001) APOS: a constructivist theory of learning in undergrad mathematics education research 2001. In: Holton D (ed) The teaching and learning of mathematics at University level: an ICMI study. Kluwer, Dordrecht, pp 273–280

    Google Scholar 

  • Edwards L (2005) Metaphors and gestures in fraction talk. In: Proceedings CERME 4. pp 92–101. http://ermeweb.free.fr/CERME4/CERME4_WG1.pdf

  • English L (ed) (1997) Mathematical reasoning: analogies, metaphors, and images. Lawrence Erlbaum Associates, London

    Google Scholar 

  • Ferrara F (2003) Bridging perception and theory: what role can metaphors and imagery play? In: Proceedings CERME 3. http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG1/TG1_ferrara_cerme3.pdf

  • Gentner D (1982) Are scientific analogies metaphors? In: Miall D (ed) Metaphor: problems and perspectives. Harvester, Brighton, pp 106–132

    Google Scholar 

  • Gentner D (1983) Structure mapping: a theoretical framework for analogy. Cogn Sci 7:155–170

    Article  Google Scholar 

  • Gibbs RW (ed) (2008) The Cambridge handbook of metaphor and thought. Cambridge University Press, Cambridge

    Google Scholar 

  • Gibbs RW, Mattlock T (2008) Metaphor, imagination, and simulation: psycholinguistic evidence. In: Gibbs RW (ed) The Cambridge handbook of metaphor and thought. Cambridge University Press, Cambridge, pp 161–176

    Chapter  Google Scholar 

  • Goldin GA (1998) Imagery and imagination: How minds create mathematics [A review of Mathematical Reasoning: Analogies, Metaphors, and Images. In: English L (ed) Mahwah, NJ, Erlbaum (1997)]. Contemp Psychol 43(10):677–679

    Google Scholar 

  • Goldin GA (2001) Review of where mathematics comes from: how the embodied mind brings mathematics into being by Lakoff G, Núñez R. Nature 413:18–19

    Article  Google Scholar 

  • Goldin GA (2003) Developing complex understandings: on the relation of mathematics education research to mathematics. Educ Stud Math 54:171–202

    Article  Google Scholar 

  • Indurkhya B (1992) Metaphor and cognition. Kluwer, Dordrecht

    Book  Google Scholar 

  • Indurkhya B (2006) Emergent representations, interaction theory and the cognitive force of metaphor. New Ideas Psychol 24(2):133–162

    Article  Google Scholar 

  • Johnson M, Lakoff G (2003) Metaphors we live by. The University of Chicago Press, New York

    Google Scholar 

  • Kaput JJ (1979) Mathematics and learning: roots of epistemological status. In: Clement J, Lochhead J (eds) Cognitive process instruction. Franklin Institute Press, Philadelphia, pp 289–303

    Google Scholar 

  • Knops A, Thirion B, Hubbard E, Michel V, Dehaene S (2009) Recruitment of an area involved in eye movements during mental arithmetic. Science 324(5934):1583–1585. https://doi.org/10.1126/science.1171599

    Article  Google Scholar 

  • Lakoff G, Núñez R (1997) The metaphorical structure of mathematics. In: English L (ed) Mathematical reasoning: analogies, metaphors and images. Lawrence Erlbaum Associates, London, pp 21–89

    Google Scholar 

  • Lakoff G, Nuñez R (2000) Where mathematics comes from. Basic Books, New York

    Google Scholar 

  • Low GD (2008) Metaphor and Education. In: Gibbs RW (ed) The Cambridge handbook of metaphor and thought. Cambridge University Press, Cambridge, pp 212–231

    Chapter  Google Scholar 

  • Manin YI (2007) Mathematics as metaphor. American Mathematical Society, Providence

    Google Scholar 

  • McGowen MA, Tall DO (2010) Metaphor or met-before? The effects of previouos experience on practice and theory of learning mathematics. J Math Behav 29:169–179

    Article  Google Scholar 

  • Mumford D, Series C, Wright D (2002) Indra’s pearls. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Núñez R (2007) The cognitive science of mathematics: why is it relevant for mathematics education? In: Lesh R, Hamilton E, Kaput J (eds) Foundations for the future in mathematics education. Lawrence Erlbaum Associates, Mahwah, pp 127–154

    Google Scholar 

  • Núñez R (2008) A fresh look at the foundations of mathematics: gesture and the psychological reality of conceptual metaphor. In: Cienki A, Müller C (eds) Gesture and metaphor. John Benjamins, Amsterdam, pp 93–114

    Chapter  Google Scholar 

  • Ortony A (ed) (1993) Metaphor and thought, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Parzysz B, Kadunz G, Robotti E, Rogers L (2007) The role of images and metaphors in the learning and understanding mathematics (including embodied cognition). In: Pitta-Pantazi D, Philippou J (eds) Proceedings CERME 5. University of Cyprus, Larnaca, pp 84–89. http://ermeweb.free.fr/CERME5b/WG1.pdf

    Google Scholar 

  • Pimm D (1987) Speaking mathematically. Routledge, New York

    Google Scholar 

  • Porte M (2013) Citations de René Thom. Retrieved 25 Sept 2013 from http://www.maths.ed.ac.uk/~aar/papers/thom/data/citations.pdf

  • Presmeg NC (1997) Reasoning with metaphors and metonymies in mathematics learning. In: English L (ed) Mathematical reasoning: analogies, metaphors, and images. Lawrence Erlbaum Associates, London, pp 267–279

    Google Scholar 

  • Presmeg NC (2004) Use of personal metaphors in the learning of mathematics (Plenary paper). In: Electronic proceedings of topic study group 25: language and communication in mathematics education, 10th international congress on mathematical education, Copenhagen, 4–11 July 2004, pp 1–12

    Google Scholar 

  • Reddy MJ (1993) The conduit metaphor: a case of frame conflict in our language about language. In: Ortony A (ed) Metaphor and thought, 2nd edn. Cambridge University Press, Cambridge, pp 284–324

    Google Scholar 

  • Richards IA (1936) The philosophy of rhetoric. Oxford University Press, Oxford

    Google Scholar 

  • Ricoeur P (1977) The rule of metaphor. University of Toronto Press, Toronto (In French: La Métaphore Vive. Editions du Seuil, Paris, 1975)

    Google Scholar 

  • Sapolsky R (2010) This is your brain on metaphors. Retrieved 11 Sept 2012 from http://opinionator.blogs.nytimes.com/2010/11/14/this-is-your-brain-on-metaphors/

  • Sfard A (1994) Reification as the birth of metaphor. Learn Math 14(1):44–55

    Google Scholar 

  • Sfard A (1997) Commentary: on metaphorical roots of conceptual growth. In: English L (ed) Mathematical reasoning: analogies, metaphors, and images. Erlbaum, London, pp 339–371

    Google Scholar 

  • Sfard A (1998) On two metaphors for learning and the dangers of choosing just one. Educ Res 27(2):4–13

    Article  Google Scholar 

  • Sfard A (2009) Metaphors in education. In: Daniels H, Lauder H, Porter J (eds) Educational theories, cultures and learning: a critical perspective. Routledge, New York, pp 39–50

    Google Scholar 

  • Soto-Andrade J (2006) Un monde dans un grain de sable: métaphores et analogies dans l’apprentissage des mathématiques. Ann Didact Sci Cognit 11:123–147

    Google Scholar 

  • Soto-Andrade J (2007) Metaphors and cognitive styles in the teaching-learning of mathematics. In: Pitta-Pantazi D, Philippou J (eds) Proceedings CERME 5. University of Cyprus, Larnaca, pp 191–200

    Google Scholar 

  • Thom R (1994) Spectre, bord d’un centre obscure. In: Porte M (ed) Passion des Formes. ENS Éditions, Fontenay-St Cloud, pp 13–24

    Google Scholar 

  • van Dormolen J (1991) Metaphors mediating the teaching and understanding of mathematics. In: Bell AJ, Mellin-Olsen S, van Dormolen J (eds) Mathematical knowledge: its growth through teaching. Kluwer, Dordrecht, pp 89–106

    Google Scholar 

  • Wu K (2001) On metaphoring: a cultural hermeneutic. Drill, Leiden

    Google Scholar 

  • Yoon C, Thomas MOJ, Dreyfus T (2011) Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures. Educ Stud Math 78:371–393

    Article  Google Scholar 

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Correspondence to Jorge Soto-Andrade .

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Soto-Andrade, J. (2020). Metaphors in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_113

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