Advertisement

Young Children’s Cross-Domain Mapping of Numerosity in Path Navigation

  • Morten BjørnebyeEmail author
  • Thorsteinn Sigurjonsson
Chapter
  • 23 Downloads

Abstract

This case study explores 3- and 4-year olds who do not master the use of the cardinal principle for exact enumeration (i.e. subset-knowers) in cross-domain mapping of numerosity in an outdoors navigation task from a perspective of Conceptual Metaphor Theory. Based on shared experiences in an intervention involving articulated physical tagging of 1- to 4-dotted arrays (e.g. articulate “kangaroo-two” while using the feet to tag the two elements in a 2-dotted array), the participants engaged individually in a novel task with free use of number metaphors for body-spatial mapping of numerosity and navigation across a circle with 50 dots. The child’s and the experimenter’s actions and non-verbal and verbal utterances were recorded on video. From an interpretive stance, the pattern and cross-case analysis show both a shared ability to use number metaphors (i.e. “cock-a-doodle-doo-one”, “kangaroo-two”, “monkey-three” and “frog-four”) for physical and verbal communication of additive structures that exceed their cardinal knower level, as well as quality differences in navigation and cross-domain mapping of quantities within and across knower levels. We argue that the use of a spatial structured language might cultivate subset-knowers’ subitising-based enumeration skills in a manner that integrates navigation and authentic movement patterns.

Keywords

Early learning Embodiment Metaphors Numbers Cardinality Navigation 

References

  1. Bjørnebye, M., Sigurjonsson, T., & Solbakken, T. (2017). Perception, cognition and measurement of verbal and non-verbal aspects of the cardinal concept in bodily-spatial interaction. In T. Dooley & G. Gueuder (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10) (pp. 1829–1836). Dublin, Ireland: European Society for Resarch in Mathematics Eduction.Google Scholar
  2. Clements, D. H. (1999). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5, 400–405.Google Scholar
  3. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.CrossRefGoogle Scholar
  4. Feigenson, L., Libertus, M. E., & Halberda, J. (2013). Links between the intuitive sense of number and formal mathematics ability. Child Development Perspectives, 7(2), 74–79.  https://doi.org/10.1111/cdep.12019CrossRefGoogle Scholar
  5. Flyvbjerg, B. (2001). Making social science matter: Why social inquiry fails and how it can succeed again. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  6. Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.CrossRefGoogle Scholar
  7. Gallahue, D. L., Ozmun, J., & Goodway, J. (2012). Understanding motor development: infants, children, adolescents, adults (7th ed.). New York: McGraw-Hill.Google Scholar
  8. Gallistel, C. R. (2011). Mental magnitudes. In S. Dehane & E. M. Brannon (Eds.), Space, time and number in the brain: Searching for the foundations of mathematical thought (pp. 3–12). New York: Elsevier.CrossRefGoogle Scholar
  9. Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
  10. Gerring, J. (2004). What is a case study and what is it good for? American Political Science Review, 98(2), 341–354.CrossRefGoogle Scholar
  11. Gibbs, R. W. (2009). Why do some people dislike conceptual metaphor theory? Cognitive Semiotics, 5(1–2), 14–36.Google Scholar
  12. Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.Google Scholar
  13. Gimbert, F., Gentaz, E., Camos, V., & Mazens, K. (2016). Children’s approximate number system in haptic modality. Perception, 45(1–2), 44–55.CrossRefGoogle Scholar
  14. Kaufman, E. L., Lord, M., Reese, T., & Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 498–525.Google Scholar
  15. Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86.  https://doi.org/10.1207/s15326985ep4102_1CrossRefGoogle Scholar
  16. Lakoff, G. (1993). The contemporary theory of metaphor. Metaphor and Thought, 2, 202–251.CrossRefGoogle Scholar
  17. Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago, IL: University of Chicago press.Google Scholar
  18. Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh: The embodied mind and its challenge to western thought. New York: Basic Books.Google Scholar
  19. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  20. Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105(2), 395–438.CrossRefGoogle Scholar
  21. Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52(2), 130–169.  https://doi.org/10.1016/j.cogpsych.2005.07.002CrossRefGoogle Scholar
  22. Lee, M. D., & Sarnecka, B. W. (2010). A model of knower-level behavior in number concept development. Cognitive Science, 34(1), 51–67.CrossRefGoogle Scholar
  23. Levine, S. C., Suriyakham, L. W., Rowe, M. L., Huttenlocher, J., & Gunderson, E. A. (2010). What counts in the development of young children’s number knowledge? Developmental Psychology, 46(5), 1309.CrossRefGoogle Scholar
  24. Mix, K. S., Sandhofer, C. M., Moore, J. A., & Russell, C. (2012). Acquisition of the cardinal word principle: The role of input. Early Childhood Research Quarterly, 27(2), 274–283.  https://doi.org/10.1016/j.ecresq.2011.10.003CrossRefGoogle Scholar
  25. Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542–551.CrossRefGoogle Scholar
  26. Piazza, M., Fumarola, A., Chinello, A., & Melcher, D. (2011). Subitizing reflects visuo-spatial object individuation capacity. Cognition, 121(1), 147–153.CrossRefGoogle Scholar
  27. Riggs, K. J., Ferrand, L., Lancelin, D., Fryziel, L., Dumur, G., & Simpson, A. (2006). Subitizing in tactile perception. Psychological Science, 17(4), 271–272.CrossRefGoogle Scholar
  28. Schaeffer, B., Eggleston, V. H., & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6(3), 357–379.CrossRefGoogle Scholar
  29. Spelke, E. S., & Kinzler, K. D. (2007). Core knowledge. Developmental Science, 10(1), 89–96.CrossRefGoogle Scholar
  30. Vygotsky, L. S. (1978). Mind and society: The development of higher mental processes. Cambridge, MA: Harvard University Press.Google Scholar
  31. Waxer, M., & Morton, J. B. (2012). Cognitive conflict and learning. In N. M. Seel (Ed.), Encyclopedia of the sciences of learning (pp. 585–587). Boston: Springer US.CrossRefGoogle Scholar
  32. Wynn, K. (1990). Children’s understanding of counting. Cognition, 36(2), 155–193.CrossRefGoogle Scholar
  33. Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24(2), 220–251.CrossRefGoogle Scholar
  34. Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Inland Norway University of Applied SciencesElverumNorway

Personalised recommendations