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Gepubliceerd in: Psychological Research 8/2022

10-11-2021 | Original Article

Grounding (fairly) complex numerical knowledge: an educational example

Auteurs: Martin H. Fischer, Arthur M. Glenberg, Korbinian Moeller, Samuel Shaki

Gepubliceerd in: Psychological Research | Uitgave 8/2022

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Abstract

In this article, we contextualize and discuss an on-line contribution to this special issue in which a video-recorded lecture demonstrates the teaching of an abstract mathematical concept, namely regression to the mean. We first motivate the pertinence of this example from the perspective of embodied cognition. Then, we identify mechanisms of teaching that reflect embodied cognitive practices, such as the concreteness fading approach. Rather than a comprehensive review of multiple extensive literatures, this article provides the interested reader with several sources or entries into those literatures.
Literatuur
go back to reference Barrocas, R., Roesch, S., Gawrilow, C., & Moeller, K. (2020a). Putting a finger on numerical development—Reviewing the contributions of kindergarten finger gnosis and fine motor skills to numerical abilities. Frontiers in Psychology, 11, 1012.PubMedPubMedCentralCrossRef Barrocas, R., Roesch, S., Gawrilow, C., & Moeller, K. (2020a). Putting a finger on numerical development—Reviewing the contributions of kindergarten finger gnosis and fine motor skills to numerical abilities. Frontiers in Psychology, 11, 1012.PubMedPubMedCentralCrossRef
go back to reference Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22(4), 577–660.PubMedCrossRef Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22(4), 577–660.PubMedCrossRef
go back to reference Bonato, M., Zorzi, M., & Umiltà, C. (2012). When time is space: Evidence for a mental time line. Neuroscience and Biobehavioral Reviews, 36, 2257–2273.PubMedCrossRef Bonato, M., Zorzi, M., & Umiltà, C. (2012). When time is space: Evidence for a mental time line. Neuroscience and Biobehavioral Reviews, 36, 2257–2273.PubMedCrossRef
go back to reference Borghi, A. M., & Binkofski, F. (2014). Words as social tools: An embodied view on abstract concepts. Springer-Verlag.CrossRef Borghi, A. M., & Binkofski, F. (2014). Words as social tools: An embodied view on abstract concepts. Springer-Verlag.CrossRef
go back to reference Borghi, A. M., Binkofski, F., Castelfranchi, C., Cimatti, F., Scorolli, C., & Tummolini, L. (2017). The challenge of abstract concepts. Psychological Bulletin, 143(3), 263–292.PubMedCrossRef Borghi, A. M., Binkofski, F., Castelfranchi, C., Cimatti, F., Scorolli, C., & Tummolini, L. (2017). The challenge of abstract concepts. Psychological Bulletin, 143(3), 263–292.PubMedCrossRef
go back to reference Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press. Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.
go back to reference Campos, J. J., Bertenthal, B. I., & Kermoian, R. (1992). Early experience and emotional development: The emergence of wariness of heights. Psychological Science, 3(1), 61.CrossRef Campos, J. J., Bertenthal, B. I., & Kermoian, R. (1992). Early experience and emotional development: The emergence of wariness of heights. Psychological Science, 3(1), 61.CrossRef
go back to reference Card, S. K., Moran, T. P., & Newell, A. (1986). The model human processor. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.), Handbook of perception and human performance (Vol. 2, Chapt. 45). Wiley. Card, S. K., Moran, T. P., & Newell, A. (1986). The model human processor. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.), Handbook of perception and human performance (Vol. 2, Chapt. 45). Wiley.
go back to reference Casasanto, D. (2009). Embodiment of abstract concepts: Good and bad in right- and left-handers. Journal of Experimental Psychology: General, 138, 351–367.CrossRef Casasanto, D. (2009). Embodiment of abstract concepts: Good and bad in right- and left-handers. Journal of Experimental Psychology: General, 138, 351–367.CrossRef
go back to reference Casasanto, D. (2011). Different bodies, different minds: The body specificity of language and thought. Current Directions in Psychological Science, 20, 378–383.CrossRef Casasanto, D. (2011). Different bodies, different minds: The body specificity of language and thought. Current Directions in Psychological Science, 20, 378–383.CrossRef
go back to reference Collins, A. M., & Quillian, M. R. (1969). Retrieval time from semantic memory. Journal of Verbal Learning and Verbal Behavior, 8, 240–247.CrossRef Collins, A. M., & Quillian, M. R. (1969). Retrieval time from semantic memory. Journal of Verbal Learning and Verbal Behavior, 8, 240–247.CrossRef
go back to reference De Bock, D., Deprez, J., Van Dooren, W., Roelens, M., & Verschaffel, L. (2011). Abstract or concrete examples in learning mathematics? A replication and elaboration of Kaminski, Sloutsky, and Heckler’s study. Journal for Research in Mathematics Education, 42(2), 109–126.CrossRef De Bock, D., Deprez, J., Van Dooren, W., Roelens, M., & Verschaffel, L. (2011). Abstract or concrete examples in learning mathematics? A replication and elaboration of Kaminski, Sloutsky, and Heckler’s study. Journal for Research in Mathematics Education, 42(2), 109–126.CrossRef
go back to reference Dijkstra, K., Kaschak, M. P., & Zwaan, R. A. (2007). Body posture facilitates retrieval of autobiographical memories. Cognition, 102, 139–149.PubMedCrossRef Dijkstra, K., Kaschak, M. P., & Zwaan, R. A. (2007). Body posture facilitates retrieval of autobiographical memories. Cognition, 102, 139–149.PubMedCrossRef
go back to reference Fayol, M., Barrouillet, P., & Marinthe, C. (1998). Predicting arithmetical achievement from neuropsychological performance: A longitudinal study. Cognition, 68(2), B63–B70.PubMedCrossRef Fayol, M., Barrouillet, P., & Marinthe, C. (1998). Predicting arithmetical achievement from neuropsychological performance: A longitudinal study. Cognition, 68(2), B63–B70.PubMedCrossRef
go back to reference Fernalt, A. (1985). Four-month-old infants prefer to listen to motherese. Infant Behavior and Development, 8, 181–195.CrossRef Fernalt, A. (1985). Four-month-old infants prefer to listen to motherese. Infant Behavior and Development, 8, 181–195.CrossRef
go back to reference Fischer, M. H. (2008). Finger counting habits modulate spatial-numerical associations. Cortex, 44, 386–392.PubMedCrossRef Fischer, M. H. (2008). Finger counting habits modulate spatial-numerical associations. Cortex, 44, 386–392.PubMedCrossRef
go back to reference Fischer, M. H., & Coello, Y. (2016). Foundations of embodied cognition—Volume 2: Conceptual and interactive embodiment. Taylor & Francis. Fischer, M. H., & Coello, Y. (2016). Foundations of embodied cognition—Volume 2: Conceptual and interactive embodiment. Taylor & Francis.
go back to reference Fischer, M. H., Dewulf, N., & Hill, R. L. (2005). Designing bar graphs: Orientation matters. Applied Cognitive Psychology, 19(7), 953–962.CrossRef Fischer, M. H., Dewulf, N., & Hill, R. L. (2005). Designing bar graphs: Orientation matters. Applied Cognitive Psychology, 19(7), 953–962.CrossRef
go back to reference Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition: from single digits to arithmetic. Quarterly Journal of Experimental Psychology, 67(8), 1461–1483.CrossRef Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition: from single digits to arithmetic. Quarterly Journal of Experimental Psychology, 67(8), 1461–1483.CrossRef
go back to reference Fischer, M. H., & Zwaan, R. A. (2008). Embodied language—A review of the role of the motor system in language comprehension. Quarterly Journal of Experimental Psychology, 61(6), 825–850.CrossRef Fischer, M. H., & Zwaan, R. A. (2008). Embodied language—A review of the role of the motor system in language comprehension. Quarterly Journal of Experimental Psychology, 61(6), 825–850.CrossRef
go back to reference Fodor, J. A. (1975). The language of thought. Harvard University Press. Fodor, J. A. (1975). The language of thought. Harvard University Press.
go back to reference Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26(1), 9–25.CrossRef Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26(1), 9–25.CrossRef
go back to reference Fyfe, E. R., & Nathan, M. J. (2019). Making “concreteness fading” more concrete as a theory of instruction for promoting transfer. Educational Review, 71(4), 403–422.CrossRef Fyfe, E. R., & Nathan, M. J. (2019). Making “concreteness fading” more concrete as a theory of instruction for promoting transfer. Educational Review, 71(4), 403–422.CrossRef
go back to reference Gentner, D. (2010). Bootstrapping the mind: Analogical processes and symbol systems. Cognitive Science, 34(5), 752–775.PubMedCrossRef Gentner, D. (2010). Bootstrapping the mind: Analogical processes and symbol systems. Cognitive Science, 34(5), 752–775.PubMedCrossRef
go back to reference Gentner, D., & Holyoak, K. J. (1997). Reasoning and learning by analogy. American Psychologist, 52, 32–34.PubMedCrossRef Gentner, D., & Holyoak, K. J. (1997). Reasoning and learning by analogy. American Psychologist, 52, 32–34.PubMedCrossRef
go back to reference Goldin-Meadow, S., & Alibali, M. (2013). Gesture’s role in speaking, learning, and creating language. Annual Review of Psychology, 64, 257–283.PubMedCrossRef Goldin-Meadow, S., & Alibali, M. (2013). Gesture’s role in speaking, learning, and creating language. Annual Review of Psychology, 64, 257–283.PubMedCrossRef
go back to reference Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientific principles using concrete and idealized simulations. The Journal of the Learning Sciences, 14(1), 69–110.CrossRef Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientific principles using concrete and idealized simulations. The Journal of the Learning Sciences, 14(1), 69–110.CrossRef
go back to reference Held, R., & Hein, A. (1963). Movement-produced stimulation in the development of visually guided behavior. Journal of Comparative and Physiological Psychology, 56(5), 872–876.PubMedCrossRef Held, R., & Hein, A. (1963). Movement-produced stimulation in the development of visually guided behavior. Journal of Comparative and Physiological Psychology, 56(5), 872–876.PubMedCrossRef
go back to reference Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2008). Development of number combination skill in the early school years: When do fingers help? Developmental Science, 11(5), 662–668.PubMedCrossRef Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2008). Development of number combination skill in the early school years: When do fingers help? Developmental Science, 11(5), 662–668.PubMedCrossRef
go back to reference Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2008). Learning theory. The advantage of abstract examples in learning math. Science, 320(5875), 454–455.PubMedCrossRef Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2008). Learning theory. The advantage of abstract examples in learning math. Science, 320(5875), 454–455.PubMedCrossRef
go back to reference Kultusminister-Konferenz. (2004). Bildungsstandards im Fach Mathematik für den Primarbereich. [Decisions of the Standing Conference of the Ministers of Education and Cultural Affairs of the Länder in the Federal Republic of Germany. Scholastic standards for mathematics for elementary schools]. Luchterhand. Kultusminister-Konferenz. (2004). Bildungsstandards im Fach Mathematik für den Primarbereich. [Decisions of the Standing Conference of the Ministers of Education and Cultural Affairs of the Länder in the Federal Republic of Germany. Scholastic standards for mathematics for elementary schools]. Luchterhand.
go back to reference Lakoff, G. (1987). Women, fire, and dangerous things. University of Chicago Press.CrossRef Lakoff, G. (1987). Women, fire, and dangerous things. University of Chicago Press.CrossRef
go back to reference Lakoff, G., & Johnson, M. (1980). Metaphors we live by. University of Chicago Press. Lakoff, G., & Johnson, M. (1980). Metaphors we live by. University of Chicago Press.
go back to reference Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from. Basic Books. Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from. Basic Books.
go back to reference Lindemann, O., Alipour, A., & Fischer, M. H. (2011). Finger counting habits in Middle-Eastern and Western individuals: an online survey. Journal of Cross-Cultural Psychology, 42, 566–578.CrossRef Lindemann, O., Alipour, A., & Fischer, M. H. (2011). Finger counting habits in Middle-Eastern and Western individuals: an online survey. Journal of Cross-Cultural Psychology, 42, 566–578.CrossRef
go back to reference McNeil, N. M., & Fyfe, E. R. (2012). “Concreteness fading” promotes transfer of mathematical knowledge. Learning and Instruction, 22(6), 440–448.CrossRef McNeil, N. M., & Fyfe, E. R. (2012). “Concreteness fading” promotes transfer of mathematical knowledge. Learning and Instruction, 22(6), 440–448.CrossRef
go back to reference Michotte, A. (1946). La perception de la causalite (The perception of causality). Vrin. Michotte, A. (1946). La perception de la causalite (The perception of causality). Vrin.
go back to reference Myachykov, S. C., Fischer, M. H., & Kessler, K. (2014). TEST: A tropic, embodied, situated theory of cognition. Topics in Cognitive Science, 6, 442–460.PubMedCrossRef Myachykov, S. C., Fischer, M. H., & Kessler, K. (2014). TEST: A tropic, embodied, situated theory of cognition. Topics in Cognitive Science, 6, 442–460.PubMedCrossRef
go back to reference Nathan, M. J. (2021). Foundations of embodied learning: A paradigm for education. Routledge. Nathan, M. J. (2021). Foundations of embodied learning: A paradigm for education. Routledge.
go back to reference Newen, A., De Bruin, L., & Gallagher, S. (2018). The Oxford handbook of 4E cognition. Oxford University Press.CrossRef Newen, A., De Bruin, L., & Gallagher, S. (2018). The Oxford handbook of 4E cognition. Oxford University Press.CrossRef
go back to reference Ojose, B. (2008). Applying Piaget’s theory of cognitive development to mathematics instruction. The Mathematics Educator, 18(1), 26–30. Ojose, B. (2008). Applying Piaget’s theory of cognitive development to mathematics instruction. The Mathematics Educator, 18(1), 26–30.
go back to reference Rizzolatti, G., & Craighero, L. (2004). The mirror-neuron system. Annual Review of Neuroscience, 27, 169–192.PubMedCrossRef Rizzolatti, G., & Craighero, L. (2004). The mirror-neuron system. Annual Review of Neuroscience, 27, 169–192.PubMedCrossRef
go back to reference Rizzolatti, G., & Sinigaglia, C. (2010). The functional role of the parieto-frontal mirror circuit: Interpretations and misinterpretations. Nature Reviews Neuroscience, 11, 264–274.PubMedCrossRef Rizzolatti, G., & Sinigaglia, C. (2010). The functional role of the parieto-frontal mirror circuit: Interpretations and misinterpretations. Nature Reviews Neuroscience, 11, 264–274.PubMedCrossRef
go back to reference Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin and Review, 16(2), 328–331.PubMedCrossRef Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin and Review, 16(2), 328–331.PubMedCrossRef
go back to reference Soylu, F., Leister, F. K., & Newman, S. D. (2018). You can count on your fingers: the role of fingers in early mathematical development. Journal of Numerical Cognition, 4(1), 107–135.CrossRef Soylu, F., Leister, F. K., & Newman, S. D. (2018). You can count on your fingers: the role of fingers in early mathematical development. Journal of Numerical Cognition, 4(1), 107–135.CrossRef
go back to reference Tall, D. (2006). A theory of mathematical growth through embodiment, symbolism and proof. Annales De Didactique Et De Sciences Cognitives, 11, 195–215. Tall, D. (2006). A theory of mathematical growth through embodiment, symbolism and proof. Annales De Didactique Et De Sciences Cognitives, 11, 195–215.
go back to reference Tall, D. (2009). Cognitive and social development of proof through embodiment, symbolism & formalism. In Proceedings of the ICMI Study 19 conference: Proof and proving in mathematics education (Vol. 2, pp. 220–225). Tall, D. (2009). Cognitive and social development of proof through embodiment, symbolism & formalism. In Proceedings of the ICMI Study 19 conference: Proof and proving in mathematics education (Vol. 2, pp. 220–225).
go back to reference Tomasello, M. (1999). The cultural origins of human cognition. Harvard University Press. Tomasello, M. (1999). The cultural origins of human cognition. Harvard University Press.
go back to reference Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4), 625–636.CrossRef Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4), 625–636.CrossRef
go back to reference Winter, B., Matlock, T., Shaki, S., & Fischer, M. H. (2015). Mental number space in three dimensions. Neuroscience and Biobehavioral Reviews, 57, 209–219.PubMedCrossRef Winter, B., Matlock, T., Shaki, S., & Fischer, M. H. (2015). Mental number space in three dimensions. Neuroscience and Biobehavioral Reviews, 57, 209–219.PubMedCrossRef
Metagegevens
Titel
Grounding (fairly) complex numerical knowledge: an educational example
Auteurs
Martin H. Fischer
Arthur M. Glenberg
Korbinian Moeller
Samuel Shaki
Publicatiedatum
10-11-2021
Uitgeverij
Springer Berlin Heidelberg
Gepubliceerd in
Psychological Research / Uitgave 8/2022
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI
https://doi.org/10.1007/s00426-021-01577-4

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