Korean Journal of Child Studies (아동학회지)

Korean Association of Child Studies (한국아동학회)
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An Investigation Into 3-, 4-, and 5-Year-Old Children's Nonsymbolic Magnitude Comparison Ability According to Ratio Limit and Task Condition

비율제한 및 과제제시방법에 따른 3, 4, 5세 유아의 비상징 수 비교능력

  • Cho, Woomi (Department of Child Development and Family Studies, Seoul National University) ;
  • Yi, Soon-Hyung (Department of Child Development and Family Studies, Seoul National University)
  • 조우미 (서울대학교 아동가족학과) ;
  • 이순형 (서울대학교 아동가족학과)
  • Received : 2016.11.04
  • Accepted : 2016.12.14
  • Published : 2017.02.28
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Abstract

Objective: The purpose of this study was to investigate young children's nonsymbolic magnitude comparison ability according to ratio limit and task condition. Methods: The participants included 40 3-year-old children, 42 4-year-old children, and 41 5-year-old children recruited from 4 childcare centers located in Seoul, Korea. All magnitude comparison tasks were composed of image material tasks and concrete material tasks. In addition, each magnitude comparison task varied with the ratio of the two quantities; 0.5 ratio, 0.67 ratio, 0.75 ratio. Results and Conclusion: The results revealed that 3-, 4-, and 5-year-old children could perform nonsymbolic magnitude comparison tasks without learning experiences. Also, 3-, 4-, and 5-year-old children could perform concrete material tasks better than image material tasks in nonsymbolic magnitude comparison tasks. Furthermore, children's performance on nonsymbolic magnitude comparison tasks indicated the ratio signature of the approximate number system. Children have a degree of numerical capacity prior to formal mathematics instruction. Also, children were influenced by task conditions or sense stimulus when they processed numerical information. Furthermore, the approximate number system can be used in understanding the ordinality of number.

Keywords

References

  1. Antell, S. E., & Keating, D. P. (1983). Perception of numerical invariance in neonates. Child Development, 54(3), 695-701. doi:10.2307/1130057
  2. Barth, H., Beckmann, L., & Spelke, E. S. (2008). Nonsymbolic approximate arithmetic in children: Abstract addition prior to instruction. Developmental Psychology, 44(5), 1466-1477. doi:10.1037/a0013046
  3. Barth, H., la Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences of the United States of America, 102(39), 14116-14121. doi:10.1073/pnas.0505512102
  4. Barth, H., la Mont, K., Lipton, J., Dehaene, S., Kanwisher, N., & Spelke, E. (2006). Non-symbolic arithmetic in adults and young children. Cognition, 98(3), 199-222. doi:10.1016/j.cognition.2004.09.011
  5. Brannon, E. M., Abbott, S., & Lutz, D. J. (2004). Number bias for the discrimination of large visual sets in infancy. Cognition, 93(2), B59-B68. doi:10.1016/j.cognition.2004.01.004
  6. Bruner, J. (1966). The culture of education. Cambridge, MA: Harvard University Press.
  7. Bryant, P., Christie, C., & Rendu, A. (1999). Children's understanding of the relation between addition and subtraction: Inversion, identity, and decomposition. Journal of Experimental Child Psycholog y, 74(3), 194-212. doi:10.1006/jecp.1999.2517
  8. Carey, S. (2009). The origins of concepts. New York: Oxford University Press.
  9. Case, R., Kurland, D. M., & Goldberg, J. (1982). Operational efficiency and the growth of short-term memory span. Journal of Experimental Child Psychology, 33(3), 386-404. doi:10.1016/0022-0965(82)90054-6
  10. Cooper, R. G. (1984). Early number development: Discovering number space with addition and subtraction. In C. Sophian (Ed.), The origins of cognitive skill: The eighteenth annual Carnegie symposium on cognition (pp. 157-192). Hillsdale, NJ: Erlbaum.
  11. Cordes, S., & Brannon, E. M. (2008). Quantitative competencies in infancy. Developmental Science, 11(6), 803-808. doi:10.1111/j.1467-7687.2008.00770.x
  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. doi:10.1111/1467-9280.00427
  13. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307-314. doi:10.1016/j.tics.2004.05.002
  14. Flavell, J. H. (1986). The development of children's knowledge about the appearance-reality distinction. American Psychologist, 41(4), 418-425. doi:10.1037/0003-066X.41.4.418
  15. Flavell, J. H., Green, F. L., & Flavell, E. R. (1989). Young children's ability to differentiate appearance-reality and level 2 perspectives in the tactile modality. Child Development, 60(1), 201-213. doi:10.2307/1131085
  16. Gopnik, A., & Meltzoff, A. N. (1997). Words, thoughts, and theories. Cambridge, MA: MIT Press.
  17. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665-668. doi:10.1038/nature07246
  18. Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23-31. doi:10.1207/S15326985EP3801_4
  19. Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students' mathematics learning. Educational Psychology Review, 22, 215-243. doi:10.1007/s10648-010-9125-8
  20. Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense large-number discrimination in human infants. Psychological Science, 14(5), 396-401. doi:10.1111/1467-9280.01453
  21. McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception & Psychophysics, 69(8), 1324-1333. doi:10.3758/BF03192949
  22. McCrink, K., & Wynn, K. (2007). Ratio abstraction by 6-monthold infants. Psychological Science, 18(8), 740-745. Retrieved from http://www.jstor.org/stable/40064768 https://doi.org/10.1111/j.1467-9280.2007.01969.x
  23. McNeil, N. M., Fyfe, E. R., Petersen, L. A., Dunwiddie, A. E., & Brletic‐Shipley, H. (2011). Benefits of practicing 4 = 2 + 2: Nontraditional problem formats facilitate children's understanding of mathematical equivalence. Child Development, 82(5), 1620-1633. doi:10.1111/j.1467-8624.2011.01622.x
  24. Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002). Quantitative development in infancy and early childhood. New York: Oxford University Press.
  25. Mussen, P. H., & Carmichael, L. (1983). Handbook of child psychology. New York: Wiley.
  26. Pezzulo, G., Barsalou, L. W., Cangelosi, A., Fischer, M. H., McRae, K., & Spivey, M. J. (2011). The mechanics of embodiment: A dialog on embodiment and computational modeling. Frontiers in Psychology 2(5), 1-21. doi:10.3389/fpsyg.2011.00005
  27. Piaget, J. (1965). The child's conception of number. New York: W. W. Norton & Company.
  28. Rakes, C. R., Valentine J. C., McGatha, M. B., & Ronau, R. N. (2010). Methods of instructional improvement in algebra: A systematic review and meta-analysis. Review of Educational Research, 80(3), 372-400. doi:10.3102/0034654310374880
  29. Resnick, L. B. (1992). From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge. Analysis of Arithmetic for Mathematics Teaching, 19, 275-323. Retrieved from http://eric.ed.gov/ED342648.pdf
  30. Schliemann, A. D., & Carraher, D. W. (2002). The evolution of mathematical reasoning: Everyday versus idealized understandings. Developmental Review, 22(2), 242-266. doi:10.1006/drev.2002.0547
  31. Siegler, R. S. (1991). Children's thinking. Upper Saddle River, NJ: Prentice-Hall.
  32. Starkey, P., Spelke, E. S., & Gelman, R. (1990). Numerical abstraction by human infants. Cognition, 36, 97-127. doi:10.1016/0010-0277(90)90001-Z
  33. Shuman, M., & Spelke, E. (2006). Area and element size bias numerosity perception [Abstract]. Journal of Vision, 6, 777. doi:10.1167/6.6.777
  34. Wood, J. N., & Spelke, E. S. (2005). Infants' enumeration of actions: Numerical discrimination and its signature limits. Developmental Science, 8(2), 173-181. doi:10.1111/j.1467-7687.2005.00404.x