Mathematical Metaphors Presuppose Common Logico-Mathematical Structures

Norton, Anderson; Kokushkin, Vladislav

Volume 16 · Number 3 · Pages 285–287

< Previous Paper · Next Paper >

Mathematical Metaphors Presuppose Common Logico-Mathematical Structures

Anderson Norton & Vladislav Kokushkin

Abstract

Open peer commentary on the article “Enactive Metaphorizing in the Mathematical Experience” by Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes. Abstract: Constructivist and embodied theories of learning each focus on action as the basis for cognition. However, in restricting action to sensorimotor activity, some embodied perspectives eschew abstraction and replace it with metaphor. Here, we argue that metaphors, and mathematical development itself, depend upon coordinations of actions, within structures that we call abstract.

Citation

Norton A. & Kokushkin V. (2021) Mathematical metaphors presuppose common logico-mathematical structures. Constructivist Foundations 16(3): 285–287. https://constructivist.info/16/3/285

Export article citation data: Plain Text · BibTex · EndNote · Reference Manager (RIS)

References

Alibali M. W. & DiRusso A. A. (1999) The function of gesture in learning to count: More than keeping track. Cognitive Development 14(1): 37–56. ▸︎ Google︎ Scholar

Ansari D. & Dhital B. (2006) Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: An event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience 18(11): 1820–1828. ▸︎ Google︎ Scholar

Fischer M. H. & Brugger P. (2011) When digits help digits: Spatial–numerical associations point to finger counting as prime example of embodied cognition. Frontiers in psychology 2: 260. https://doi.org/10.3389/fpsyg.2011.00260

Gallagher S. & Lindgren R. (2015) Enactive metaphors: Learning through full-body engagement. Educational Psychology Review 27(3): 391–404. https://cepa.info/6847

Gallese V. & Lakoff G. (2005) The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology 22(3–4): 455–479. ▸︎ Google︎ Scholar

Hostetter A. B. & Alibali M. W. (2008) Visible embodiment: Gestures as simulated action. Psychonomic Bulletin & Review 15(3): 495–514. https://cepa.info/7132

Kant I. (1998) Critique of pure reason. Translated and edited by Paul Guyer and Allen Wood. Cambridge University Press, Cambridge. German original published in 1781. ▸︎ Google︎ Scholar

Lakoff G. & Núñez R. (2000) Where mathematics comes from. Basic Books, New York. ▸︎ Google︎ Scholar

Lakoff G., Johnson M. (1999) Philosophy in the Flesh: The embodied mind and its challenge to western thought. Basic Books, New York. ▸︎ Google︎ Scholar

McCulloch W. S. (1965) Embodiments of mind. MIT Press, Cambridge MA. ▸︎ Google︎ Scholar

Nemirovsky R. & Ferrara F. (2009) Mathematical imagination and embodied cognition. Educational Studies in Mathematics 70: 159–174. https://cepa.info/7133

Nemirovsky R., Tierney C. & Wright T. (1998) Body motion and graphing. Cognition and Instruction 16(2): 119–172. ▸︎ Google︎ Scholar

Piaget J. & Inhelder B. (1967) The child’s conception of space. Translated by F. J. Langdon & J. L. Lunzer. Norton, New York. French original published in 1948. ▸︎ Google︎ Scholar

Rivera S. M., Reiss A. L., Eckert M. A. & Menon V. (2005) Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex 15(11): 1779–1790. ▸︎ Google︎ Scholar

Rizzolatti G. & Craighero L. (2004) The mirror neuron system. Annual Review of Neuroscience 27: 169–192. ▸︎ Google︎ Scholar

Roth W. M. & Thom J. S. (2009) Bodily experience and mathematical conceptions: From classical views to a phenomenological reconceptualization. Educational Studies in Mathematics 70(2): 175–189. ▸︎ Google︎ Scholar

Steffe L. P. (1992) Schemes of action and operation involving composite units. Learning and Individual Differences 4(3): 259–309. ▸︎ Google︎ Scholar

Varela F. J., Thompson E. & Rosch E. (1991) The embodied mind. MIT Press, Cambridge MA. ▸︎ Google︎ Scholar

Wilson M. (2002) Six views of embodied cognition. Psychological Bulletin and Review 9(4): 625–636. https://cepa.info/4970

Comments: 0

To stay informed about comments to this publication and post comments yourself, please log in first.

LATEST ISSUES

FOLLOW US

Abstract

Citation

References

Comments: 0