Korean Journal of Child Studies (아동학회지)

Korean Association of Child Studies (한국아동학회)
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An Investigation into 2, 4 Year Old Children's Nonsymbolic Arithmetic Ability According to Task Difficulty

과제 난이도에 따른 2, 4세 유아의 비상징적 연산능력

  • 조우미 (서울대학교 아동가족학과) ;
  • 이순형 (서울대학교 아동가족학과)
  • Received : 2015.07.31
  • Accepted : 2015.08.23
  • Published : 2015.08.31
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Abstract

The purpose of this study was to investigate young children's nonsymbolic arithmetic ability according to task difficulty. The participants in this study comprised 43 2-year-old children and 48 4-year-old children recruited from 5 childcare centers located in Seoul, Korea. All tasks were composed of comparison, addition, subtraction, multiplication and division tasks. In addition, each arithmetic task varied with the ratio of the two quantities; low level(1:2), middle level(2:3), high level(4:5). The results revealed that 2 & 4-year-old children could perform a large numerical range of nonsymbolic arithmetic tasks without influences from previously learned mathematics. This finding suggests that children have a degree of numerical capacity prior to symbolic mathematics instruction. Furthermore, children's performance on nonsymbolic arithmetic tasks indicated the ratio signature of large approximate numerical representation. This result implies that large approximate numerical representation can be used in arithmetical manipulations.

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References

  1. Antell, S. E., & Keating, D. P. (1983). Perception of numerical invariance in neonates. Child Depression, 54, 695-701.
  2. Barrouillet, P., Mignon, M., & Thevenot, C. (2008). Strategies in subtraction problem solving in children. Journal of Experimental Child Psychology, 99(4), 233-251. https://doi.org/10.1016/j.jecp.2007.12.001
  3. Barth, H., Beckmann, L., & Spelke, E. S. (2008). Nonsymbolic, approximate arithmetic in children: Abstract addition prior to instruction. Developmental Psychology, 44(5), 1466-1477. https://doi.org/10.1037/a0013046
  4. Barth, H., Kanwisher, N., & Spelke, E. S. (2003). The construction of large number representation in adults. Cognition. 86, 201-221. https://doi.org/10.1016/S0010-0277(02)00178-6
  5. Barth, H., La Mont, K., Lipton, J., & Spelke, E. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences, 102, 14116-14121. https://doi.org/10.1073/pnas.0505512102
  6. Barth, H., Dehaene, S., Kanwisher, N., & Spelke, E. (2006). Non-Symbolic arithmetic in adults and young children. Cognition, 98, 199-222. https://doi.org/10.1016/j.cognition.2004.09.011
  7. Brannon, E., Abbott, S., & Lutz, D. (2004). Number bias for the discrimination of large visual sets in infancy. Cognition, 93, B59-B68. https://doi.org/10.1016/j.cognition.2004.01.004
  8. Clearfield, M. W., & Mix, K. S. (1999). Number versus contour length in infant's discrimination of small visual sets. Psychological Science, 10, 408-411. https://doi.org/10.1111/1467-9280.00177
  9. Cooper, R. G., Jr. (1984). Early number development: Discovering number space with addition and subtraction. In C. Sopian (Ed.), Origins of cognitive skills: The eighteenth annual Carnegie simposium on cognition. Hillsdale, NJ: Erlbaum.
  10. Cordes, S., Gelman, R., Gallistel, C. R., & Whalen, J. (2001) Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin and Review, 8, 698-707. https://doi.org/10.3758/BF03196206
  11. Crollen, V., Castronovo, J., & Seron, X. (2011). Under- and over-Estimation. Experimental Psychology, 58(1), 39-49. https://doi.org/10.1027/1618-3169/a000064
  12. Feigenson, L., Carey, S., & Hauser, M. (2002). The Representations Underlying Infants' Choice of More: Object Files Versus Analog Magnitudes. Psychological Science, 13(2), 150-156. https://doi.org/10.1111/1467-9280.00427
  13. Geary, D. C. (1994). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
  14. Gelman, R. (2000). Domain specificity and variability in cognitive development. Child Development, 71, 854-856. https://doi.org/10.1111/1467-8624.00193
  15. Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
  16. Ginsburg, H. P. (1982). The development of addition in the contexts of culture, social class, and race. In T. P. Carpenter, J. M. Moser, & T. A. Rpmberg (Eds.), Addtion and subtraction; A cognitive perspective (pp. 191-210). Hillsdale. NJ: Erlbaum.
  17. Jordan, N.C., Huttenlocher, J., & Levine, S. C. (1994) Assessing early arithmetic abilities: Effects of verbal and nonverbal response types on the calculation performance of middle-and low-income children. Learning and Individual Differences, 6, 413-432. https://doi.org/10.1016/1041-6080(94)90003-5
  18. Lipton, J. S., & Spelke, E. S. (2003). Origins number sense: large number discrimination in human infants. Psychological Science. 15, 396-401.
  19. Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271-290. https://doi.org/10.1207/s15327078in0503_2
  20. Mix, K. S., Huttenlocher, J., & Levine, S. C. (1996). Do preschool children recognize auditoryvisual numerical correspondences? Child Development, 67, 1592-1608. https://doi.org/10.2307/1131720
  21. Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002). Quantitative development in infancy and early childhood. New York: Oxford University Press.
  22. Piaget, J. (1965). The child's conception of number. New York: Norton.
  23. Starkey, P. (1992). The early development of numerical reasoning. Cognition, 43, 93-126. https://doi.org/10.1016/0010-0277(92)90034-F
  24. Starkey, P. & Cooper, R. G., Jr. (1980). Perception of numbers by human infants. Science, 210, 1033-1035. https://doi.org/10.1126/science.7434014
  25. Starkey, P., Spelke, E. S., & Gelman, R. (1990). Numerical abstraction by human infants. Cognition, 36, 97-127. https://doi.org/10.1016/0010-0277(90)90001-Z
  26. Strauss, M. S., & Curtis, L. E. (1981). Infant perception of numerosity. Child development, 52, 1146-1152. https://doi.org/10.2307/1129500
  27. Strauss, M. S., & Curtis, L. E. (1984). Development of numerical concepts in infancy. In C. Sopian (Ed.), Origins of cognitive skills. Hillsdale, NJ: Erlbaum.
  28. Wood, J. N., & Spelke, E. S. (2005). Infants' enumeration of actions: numerical discrimination and its signature limits. Developmental science, 173-181.
  29. Wynn, K. (1992a) Addition and subtraction by human infants. Nature, 358. 749-750. https://doi.org/10.1038/358749a0
  30. Xu, F. (2003). Numerosity discrimination in infants: evidence for two systems of representations. Cognition, 89, B15-B25. https://doi.org/10.1016/S0010-0277(03)00050-7