Abstract
Motion-based metaphors help explain a single, often a static, concept (e.g., number, mathematical function, limit of function, continuity of function) in terms of a human motion. In mathematics, many mathematical concepts, such as function and continuity, are described in terms of graphical representations. Although these graphical representations are static, they can be transformed into motion events and understood as motions by motion-based metaphors. This can be done by either using a hand gesture to depict the graphical representation of the target concept or by mentally simulating hand movements that depict the graphical representation. By employing these mechanisms, the motor system becomes engaged in the process of aiding the learner to understand static mathematical concepts (concepts that are defined in terms of non-moving mathematical objects), acting as a cognitive resource to ground and understand non-motion mathematical concepts. In this paper, we theorize that visual representations of mathematical concepts have varying degrees of what we term to be “motor strength” whereby, for example, curves of functions may be either strongly or weakly motoric depending on the degree to which they aid in the development of associated deep mathematical thinking.
Similar content being viewed by others
Data Availability
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
Code Availability
Not applicable.
References
Abrahamson, D., Nathan, M. J., Williams-Pierce, C., Walkington, C., Ottmar, E. R., Soto, H., & Alibali, M. W. (2020). The future of embodied design for mathematics teaching and learning. Frontiers in Education, 5, 147. https://doi.org/10.3389/feduc.2020.00147
Al-Azary, H., & Katz, A. N. (2021). Do metaphorical sharks bite? Simulation and abstraction in metaphor processing. Memory & Cognition, 49(3), 557–570. https://doi.org/10.3758/s13421-020-01109-2
Alibali, M. W., & Nathan, M. J. (2012). Embodiment in mathematics teaching and learning: Evidence from learners’ and teachers’ gestures. Journal of the Learning Sciences, 21(2), 247–286. https://doi.org/10.1080/10508406.2011.611446
Binder, J. R., & Desai, R. H. (2011). The neurobiology of semantic memory. Trends in Cognitive Science, 15(11), 527–536.
Chen, I. H., Zhao, Q., Long, Y., Lu, Q., & Huang, C. R. (2019). Mandarin Chinese modality exclusivity norms. PLoS ONE, 14(2), 1–18. https://doi.org/10.1371/journal.pone.0211336
Connell, L., & Lynott, D. (2012). Strength of perceptual experience predicts word processing performance better than concreteness or imageability. Cognition, 125(3), 452–456.
Edwards, L. D., Moore-Russo, D., & Ferrara, F. (2014). Emerging perspectives on gesture and embodiment in mathematics. Charlotte: Information Age Information Age Publishing.
Edwards, L. D. (2019). The body of/in proof: An embodied analysis of mathematical reasoning. In: Danesi M. (eds), Interdisciplinary Perspectives on Math Cognition: Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-22537-7_6
Feldman, J., & Narayanan, S. (2004). Embodied meaning in a neural theory of language. Brain and Language, 89(2), 385–392.
Filipović Đurđević, D. F., Popović Stijačić, M., & Karapandžić, J. (2016). A quest for sources of perceptual richness: Several candidates. In S.Halupka-Rešetar & S. Martínez-Ferreiro (Eds.), Studies in language and mind (pp. 187–238). Novi Sad, Serbia: Filozofski fakultet uNovom Sadu.
Gallese, V. (2003). The manifold nature of interpersonal relations: The quest for a common mechanism. Philosophical Transactions of the Royal Society of London, B, 358, 517–528.
Gallese, G., & Lakoff, G. (2005). The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22(3), 455–479.
Gibbs, R. W. (2006). Embodiment and cognitive science. New York: Cambridge University Press.
Gibbs, R. W. (2013). Walking the walk while thinking about the talk: Embodied interpretation of metaphorical narratives. Journal of Psycholinguistic Research, 42(4), 363–378. https://doi.org/10.1007/s10936-012-9222-6
Gibson, J. J. (1979). The ecological approach to visual perception. Houghton Mifflin.
Glenberg, A. M., & Kaschak, M. P. (2002). Grounding language in action. Psychonomic Bulletin & Review, 9(3), 558–565.
Glenberg, A. M., Satao, M., Cattaneo, L., Riggio, L., Palumbo, D., & Buccino, G. (2008). Processing abstract language modulates motor system activity. Quarterly Journal of Experimental Psychology, 61(6), 905–919.
Goldin-Meadow, S., Cook, S. W., & Mitchell, Z. A. (2008). Gesturing gives children new ideas about math. Psychological Science, 20(3), 267–272.
Hall, R., & Nemirovsky, R. (2012). Introduction to the special issue: Modalities of body engagement in mathematical activity and learning. Journal of the Learning Sciences, 21(2), 207–215.
Hauk, O., & Tschentscher, N. (2013). The body of evidence: What can neuroscience tell us about embodied semantics? Frontiers in Psychology, 4, 1–14.
Johnson-Glenberg, M. C., & Megowan-Romanowicz, C. (2017). Embodied science and mixed reality: How gesture and motion capture affect physics education. Cognitive Research: Principles and Implications, 2, 24. https://doi.org/10.1186/s41235-017-0060-9
Khatin-Zadeh, O. (2021a). How does representational transformation enhance mathematical thinking? Axiomathes. https://doi.org/10.1007/s10516-021-09602-2
Khatin-Zadeh, O. (2021b). Psychological processes of perceiving implied motion in static images. Polish Psychological Bulletin, 52(4), 334–340. https://doi.org/10.24425/ppb.2021.139167
Khatin-Zadeh, O., Eskandari, Z., Cervera-Torres, S., Ruiz Fernández, S., Farzi, R., & Marmolejo-Ramos, F. (2021). The strong versions of embodied cognition: Three challenges faced. Psychology & Neuroscience, 14(1), 16–33.
Khatin-Zadeh, O., Yazdani-Fazlabadi, B., & Eskandari, Z. (2021). The grounding of mathematical concepts through fictive motion, gesture and the motor system. For the Learning of Mathematics, 41(3), 19–21.
Khatin-Zadeh, O., Eskandari, Z. & Marmolejo-Ramos, F. (2022). Gestures enhance executive functions for the understating of mathematical concepts. Integrative Psychological and Behavioral Science, 56(1). https://doi.org/10.1007/s12124-022-09694-4.
Kiefer, M., & Pulvermüller, F. (2011). Conceptual representations in mind and brain: Theoretical developments, current evidence and future directions. Cortex, 48, 805–825.
Kim, C. Y., & Blake, R. (2007). Brain activity accompanying perception of implied motion in abstract paintings. Spatial Vision, 20(6), 545–560. https://doi.org/10.1163/156856807782758395
Kourtzi, Z., & Kanwisher, N. (2000). Activation in human MT/MST by static images with implied motion. Journal of Cognitive Neuroscience, 12(1), 48–55. https://doi.org/10.1162/08989290051137594
Lakoff, G. (2014). Mapping the brain’s metaphor circuitry: Metaphorical thought in everyday reason. Frontiers in Human Neuroscience, 8, 958. https://doi.org/10.3389/fnhum.2014.00958
Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
Lakoff, G. (2008). The neural theory of metaphor. In Gibbs, R. W. Jr. (Ed.). The Cambridge handbook of metaphor and thought (pp. 17–38). Oxford: Oxford University Press. https://doi.org/10.1017/cbo9780511816802.003
Lambon-Ralph, M. A. (2013). Neurocognitive insights on conceptual knowledge and its breakdown. Philosophical Transactions of the Royal Society, 369(1634), 1–11. 20120392–20120392. https://doi.org/10.1098/rstb.2012.0392
Langacker, R. W. (1999). Grammar and conceptualization. Berlin: Mouton de Gruyter.
Longcamp, M., Anton, J. L., Roth, M., & Velay, J. L. (2003). Visual presentation of single letters activates a premotor area involved in writing. NeuroImage, 19(4), 1492–1500.
Longcamp, M., Hlushchuk, Y., & Hari, R. (2011). What differs in visual recognition of handwritten vs. printed letters? An fMRI study. Human Brain Mapping, 32(8), 1250–1259.
Lorteije, J. A. M., Barraclough, N. E., Jellema, T., Raemaekers, M., Duijnhouwer, J., Xiao, D., Oram, M. W., Lankheet, M. J. M., Perrett, D. I., & van Wezel, R. J. A. (2011). Implied motion activation in cortical area MT can be explained by visual low-level features. Journal of Cognitive Neuroscience, 23(6), 1533–1548. https://doi.org/10.1162/jocn.2010.21533
Lynott, D., Connell, L., Brysbaert, M., Brand, J., & Carney, J. (2019). The Lancaster Sensorimotor Norms: Multidimensional measures of perceptual and action strength for 40,000 English words. Behavior Research Method, 52(3), 1271–1291. https://doi.org/10.3758/s13428-019-01316-z
Marghetis, T., & Núñez, R. (2013). The motion behind the symbols: A vital role for dynamism in the conceptualization of limits and continuity in expert mathematics. Topics in Cognitive Science, 5(2), 299–316.
Masson, M. E., Bub, D. N., & Warren, C. M. (2008). Kicking calculators: Contribution of embodied representations to sentence comprehension. Journal of Memory and Language, 59(3), 256–265.
Matlock, T. (2004). The conceptual motivation of fictive motion. In G. Radden & R. Dirven (Eds.), Motivation in Grammar (pp. 221–248). John Benjamins.
Matlock, T. (2010). Abstract motion is no longer abstract. Language and Cognition, 2(2), 243–260.
Matsumoto, Y. (1996). Subjective motion and English and Japanese verbs. Cognitive Linguistics, 7(2), 183–226.
Miklashevsky, A. (2018). Perceptual experience norms for 506 Russian nouns: Modality rating, spatial localization, manipulability, imageability and other variables. Journal of Psycholinguistic Research, 47(3), 641–661.
Mishra, R. (2009). Interaction of language and visual attention: Evidence from production and comprehension. Progress in Brain Research, 176, 277–292.
Nathan, M. J., & Walkington, C. (2017). Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language. Cognitive Research: Principles and Implications, 2, 9. https://doi.org/10.1186/s41235-016-0040-5
Núñez, R., & Lakoff, G. (1998). What did Weierstrass really define? The cognitive structure of natural and δ-ε continuity. Mathematical Cognition, 4(2), 85–101.
Núñez, R. (2008). A fresh look at the foundations of mathematics. In A. Cienki & C. Müller (Eds.), Metaphor and Gesture (pp. 93–114). Amsterdam, The Netherlands: John Benjamins.
Osaka, N., Matsuyoshi, D., Ikeda, T., & Osaka, M. (2010). Implied motion because of instability in Hokusai Manga activates the human motion-sensitive extrastriate visual cortex: An fMRI study of the impact of visual art. NeuroReport, 21(4), 264–267. https://doi.org/10.1097/wnr.0b013e328335b371
Pulvermüller, F. (2005). Brain mechanisms linking language and action. Nature Reviews Neuroscience, 6(7), 576–582.
Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70, 111–126.
Reed, E. S. (1996). Encountering the world. New York: Oxford University Press.
Reys, R. E. (1972). Mathematics, multiple embodiment, and elementary teachers. The Arithmetic Teacher, 19(6), 489–493.
Rizzolatti, G., & Sinigaglia, C. (2008). Mirrors in the brain: How our minds share actions, emotions, and experience. Oxford: Oxford University Press.
Rojo, A., & Valenzuela, J. (2003). Fictive motion in English and Spanish. International Journal of English Studies, 3(2), 123–150.
Saygin, A. P., McCullough, S., Alac, M., & Emmorey, K. (2010). Modulation of BOLD response in motion sensitive lateral temporal cortex by real and fictive motion sentences. Journal of Cognitive Neuroscience, 22(11), 2480–2490.
Sbriscia-Fioretti, B., Berchio, C., Freedberg, D., Gallese, V., & Umiltà, M. A. (2013). ERP modulation during observation of abstract paintings by Franz Kline. PLoS One, 8(10), e75241. https://doi.org/10.1371/journal.pone.0075241
Schaefer, S. (2019). Embodiment helps children solve a spatial working memory task: Interactions with age and gender. Journal of Cognitive Enhancement, 3(2), 233–244. https://doi.org/10.1007/s41465-018-0081-4
Senior, C., Barnes, J., Giampietroc, V., Simmons, A., Bullmore, E. T., Brammer, M., & David, A. S. (2000). The functional neuroanatomy of implicit-motion perception or representational momentum. Current Biology, 10(1), 16–22.
Shapiro, L. (2019). Embodied Cognition. Oxford: Routledge.
Shvarts, A., Alberto, R., Bakker, A., Doorman, M., & Drijvers, P. (2021). Embodied instrumentation in learning mathematics as the genesis of a body-artifact functional system. Educational Studies in Mathematics, 107(3), 447–469. https://doi.org/10.1007/s10649-021-10053-0
Singer, M. A., Radinsky, J., & Goldman, S. R. (2008). The role of gesture in meaning construction. Discourse Processes, 45(4–5), 365–386.
Speed, L. J., & Majid, A. (2017). Dutch modality exclusivity norms: Simulating perceptual modality in space. Behavior Research Methods, 49, 2204–2218.
Tall, D. (2011). Crystalline concepts in long-term mathematical invention and discovery. For the Learning of Mathematics, 31(1), 3–8.
Talmy, L. (1996). Fictive motion in language and “ception.” In P. Bloom, M. A. Peterson, L. Nadel, & M. F. Garrett (Eds.), Language and Space (pp. 211–276). MIT Press.
Umilta’, M. A., Berchio, C., Sestito, M., Freedberg, D., & Gallese, V. (2012). Abstract art and cortical motor activation: An EEG study. Frontiers in Human Neuroscience, 6, 311. https://doi.org/10.3389/fnhum.2012.00311
Wallentin, M., Lund, T. E., Østergaard, S., Østergaard, L., & Roepstorff, A. (2005). Motion verb sentences activate left posterior middle temporal cortex despite static context. NeuroReport, 16(6), 649–652.
Wamain, Y., Tallet, J., Zanone, P. G., & Longcamp, M. (2012). Brain responses to handwritten and printed letters differentially depend on the activation state of the primary motor cortex. NeuroImage, 63(3), 1766–1773.
Williams, A. L., & Wright, M. J. (2009). Static representations of speed and their neural correlates in human area MT/V5. NeuroReport, 20(16), 1466–1470. https://doi.org/10.1097/wnr.0b013e32833203c1
Yang, J., & Shu, H. (2016). Involvement of the motor system in comprehension of non-literal action language: A meta-analysis study. Brain Topography, 29(1), 94–107. https://doi.org/10.1007/s10548-015-0427-5
Yeo, A., Ledesma, I., Nathan, M. J., Alibali, M. W., & Breckinridge Church, R. (2017). Teachers’ gestures and students’ learning: Sometimes “hands off” is better. Cognitive. Research: Principles and Implications, 2, 41. https://doi.org/10.1186/s41235-017-0077-0
Zona, C. I., Raab, M., & Fischer, M. H. (2019). Embodied perspectives on behavioral cognitive enhancement. Journal of Cognitive Enhancement, 3(2), 144–160. https://doi.org/10.1007/s41465-018-0102-3
Zwaan, R. (2014). Embodiment and language comprehension: Reframing the discussion. Trends in Cognitive Sciences, 18(5), 229–234.
Acknowledgements
We thank Prof. Arthur Glenberg for his insightful comments on an earlier draft of this paper.
Author information
Authors and Affiliations
Contributions
Omid Khatin-Zadeh wrote the first draft of the paper. Fernando Marmolejo-Ramos and Sven Trenholm commented on it and revised it.
Corresponding author
Ethics declarations
Ethics Approval
This is a theoretical paper. Therefore, ethics approval is not applicable.
Consent to Participate
Not applicable.
Consent for Publication
Not applicable.
Conflict of Interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khatin-Zadeh, O., Marmolejo-Ramos, F. & Trenholm, S. The Role of Motion-Based Metaphors in Enhancing Mathematical Thought: a Perspective from Embodiment Theories of Cognition. J Cogn Enhanc 6, 455–462 (2022). https://doi.org/10.1007/s41465-022-00247-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41465-022-00247-6