Pre-fraction Concepts of Preschoolers

  • Robert P. Hunting
  • Christopher F. Sharpley
Part of the Recent Research in Psychology book series (PSYCHOLOGY)

Abstract

Much school mathematics is devoted to teaching concepts and procedures based on those units that form the core of whole number arithmetic, such as ones, tens, and hundreds. Other topics such as fractions and decimals demand new and extended understanding of units and their relationships. Researchers have noted how children’s whole number ideas interfere with their efforts to learn fractions (Behr, Wachsmuth, Post, & Lesh, 1984; Hunting, 1986; Streefland, 1984). Hunting (1986) suggested that a reason why children seem to have difficulty learning stable and appropriate meanings for fractions is because instruction on fractions, if delayed too long, allows whole number knowledge to become the predominant scheme to which fraction language and symbolism is then related. There is some evidence which suggests that children can successfully complete fraction-related tasks earlier than when these procedures are taught in school. Polkinghome (1935) concluded from a study of 266 kindergarten, first, second, and third grade children that considerable knowledge of fractions is held prior to formal instruction in this topic, and Gunderson and Gunderson (1957) demonstrated that second graders had concepts and ideas about fractions that could be developed subsequently.

Keywords

Clay Alan Candy 

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References

  1. Behr, M. J., Wachsmuth, I., Post, T., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15, 323–341.CrossRefGoogle Scholar
  2. Brush, L.R. (1978). Preschool children’s knowledge of addition and subtraction. Journal for Research in Mathematics Education, 9, 44–54.CrossRefGoogle Scholar
  3. Davis, G. & Pitkethly, A. (1990). Cognitive aspects of sharing. Journal for Research in Mathematics Education, 21 (2), 145–153.CrossRefGoogle Scholar
  4. Gelman, R., & Gallistel, C.R. (1978). The child’s understanding of number. Cambridge: Harvard University Press.Google Scholar
  5. Ginsburg, H.P. (1977). Children’s arithmetic: The learning process. New York: D. Van Nostrand Co.Google Scholar
  6. Gunderson, A.G., & Gunderson, E. (1957). Fraction concepts held by young children. Arithmetic Teacher, 4 (4), 168–174.Google Scholar
  7. Hendrickson, A.D.(1979). An ibventory of mathematical done by incoming first-grade childeen. Journal for Research in Mathematics Education, 10, 7–23.CrossRefGoogle Scholar
  8. Hiebert, J., & Tonnessen, L. H. (1978). Development of the fraction concept in two physical concepts: An exploratory investigation. Journal for Research in Mathematics Education, 9, 374–378.CrossRefGoogle Scholar
  9. Hunting, R. P. (1981). The role of discrete quantity partition knowledge in the child’s construction of fractional number. (Doctoral dissertation, University of Georgia, 1980.) Dissertation Abstracts International, 41, 4308A–4390A. (University Microfilms No. 8107919 ).Google Scholar
  10. Hunting, R.P. (1982). Qualitative compensation thought in children’s solutions to fraction comparison problems. In C.J. Irons (Ed.), Research in Mathematics Education in Australia 1981 (Vol. 2 ). Kelvin Grove: Brisbane College of Advanced Education, Mathematics Education Research Group of Australasia.Google Scholar
  11. Hunting, R.P. (1983a). Emerging methodologies for understanding internal processes governing children’s mathematical behavior. Australian Journal of Education, 27, 45–61.Google Scholar
  12. Hunting, R. P. (1983b). Alan: A case study of knowledge of units and performance with fractions. Journal for Research in Mathematics Education, 14, 182–197.CrossRefGoogle Scholar
  13. Hunting, R. P. (1986). Rachel’s schemes for constructing fraction knowledge. Educational Studies in Mathematics, 17, 49–66.CrossRefGoogle Scholar
  14. Kieren, T.E. (1983). Partitioning, equivalence, and the construction of rational number ideas. In M. Zweng (Ed.), Proceedings of the 4th International Congress on Mathematical Education (pp. 506–508 ), Boston: Birkhauser.Google Scholar
  15. Korbosky, R. K. (1984). Partitioning continuous quantities. Collected papers of the National Conference of the Australian Association for Research in Education (pp. 441–449 ). Perth, Western Australia: Research Branch, Education Department of W.A.Google Scholar
  16. Miller, K. (1984). Child as the measurer of all things: Measurement procedures and the development of quantitative concepts. In C. Sophian (Ed.), Origins of cognitive skills.(pp. 193–228 ). Hillsdale, NJ: Erlbaum.Google Scholar
  17. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of Geometry. New York: Basic Books.Google Scholar
  18. Polkinghorne, A. R. (1935). Young children and fractions. Childhood Education, 11, 354–358.Google Scholar
  19. Pothier, Y., & Sawada, D. (1983). Partitioning: The emergence of rational number ideas in young children. Journal for Research in Mathematics Education, 14, 307–317.CrossRefGoogle Scholar
  20. Rea, R.E. & Reys, R.E. (1970). Mathematical competencies of entering kindergartners. The Arithmetic Teacher, 17, 65–74.Google Scholar
  21. Smith, J. ( 1985, April). Children’s conceptual abilities in the partitioning task. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, Illinois.Google Scholar
  22. Streefland, L. (1984). Unmasking N-Distractors as a source of failures in learning fractions. In B. Southwell (Ed.), Proceedings of the Eighth International Conference for the Psychology of Mathematics Education (pp. 142–152 ). Sydney, Australia: Mathematical Association of New South Wales.Google Scholar
  23. Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127–174 ). New York: Academic Press.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Robert P. Hunting
  • Christopher F. Sharpley

There are no affiliations available

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