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Preschoolers’ Ways of Using Fingers in Numerical Reasoning

  • Camilla BjörklundEmail author
  • Maria Reis
Chapter
  • 26 Downloads

Abstract

This is a study of preschoolers’ ways of using fingers in numerical reasoning, before formal education. Research advocates finger use in early mathematics as it is found to be related to number sense and arithmetic skills, but whether children should be encouraged to use fingers or not in solving arithmetic problems remains debated. Our study contributes with an analysis of finger use as expressions of ways to experience numbers and thus related to arithmetic problem-solving proficiency. We analyzed 133 observations of 4- to 5-year-olds’ ways of using fingers when solving arithmetic tasks. The analysis revealed that preschoolers may use their fingers in three distinctly different ways. Two of these ways are expressions of number knowledge that do not enable the child to solve the arithmetic tasks and one seems to be more prosperous. Based on the results, we suggest that it is not finger use per se that facilitates arithmetic problem-solving but how fingers are used.

Keywords

Arithmetic skills Counting single units Fingers Numerical reasoning Part-part-whole structure Iconic representation of numbers Variation theory of learning 

References

  1. Baroody, A. (1987). Children’s mathematical thinking. A developmental framework for preschool, primary, and special education teachers. New York: Teachers College Columbia University.Google Scholar
  2. Baroody, A. J. (2016). Curricular approaches to connecting subtraction to addition and fostering fluency with basic differences in grade 1. PNA, 10(3), 161–190.Google Scholar
  3. Baroody, A. J., Lai, M.-l., & Mix, K. S. (2006). The development of young children’s early number and operation sense and its implications for early childhood education. In B. Spodek & O. N. Saracho (Eds.), Handbook of research on education of young children. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  4. Baroody, A., & Purpura, D. (2017). Early number and operations: Whole numbers. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 308–354). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  5. Bender, A., & Beller, S. (2012). Nature and culture of finger counting: Diversity and representational effects of an embodied cognitive tool. Cognition, 124(2), 156–182.CrossRefGoogle Scholar
  6. Berteletti, I., & Booth, J. R. (2015). Perceiving fingers in single-digit arithmetic problems. Frontiers in Psychology, 6(226), 1–10.Google Scholar
  7. Björklund, C., Kullberg, A., & Runesson Kempe, U. (2019). Structuring versus counting—critical ways of using fingers in subtraction. ZDM Mathematics Education, 51, 13–24.  https://doi.org/10.1007/s11858-018-0962-0CrossRefGoogle Scholar
  8. Boaler, J., Chen, L., Williams, C., & Cordero, M. (2016). Seeing as understanding: The importance of visual mathematics for our brain and learning. Journal of Applied and Computational Mathematics, 5(325).  https://doi.org/10.4172/2168-9679.1000325
  9. Brissiaud, R., (1992). A tool for number construction: Finger symbol sets. (Trans.) In J. Bideaud, C. Meljac, & J.-P. Fischer (Eds.), Pathways to number: Children’s developing numerical abilities. (pp. 41–65). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  10. Carpenter, T. P., Moser, J. M., & Romberg, T. A. (Eds.). (1982). Addition and subtraction: A cognitive perspective. Hillsdale, NY: Lawrence Erlbaum.Google Scholar
  11. Davydov, V. V. (1982). The psychological characteristics of the formation of elementary mathematical operations in children. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 224–238). Hillsdale, NY: Lawrence Erlbaum.Google Scholar
  12. Fuson, K. (1982). An analysis of the counting-on solution procedure in addition. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 67–81). Hillsdale, NY: Lawrence Erlbaum.Google Scholar
  13. Fuson, K. (1988). Children’s counting and concepts of number. New York, NY: Springer-Verlag.CrossRefGoogle Scholar
  14. Gattegno, C. (1974). The common sense of teaching mathematics. New York, NY: Educational Solutions.Google Scholar
  15. Geary, D., Hoard, M., Byrd-Craven, J., & DeSoto, C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121–151.CrossRefGoogle Scholar
  16. Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
  17. Ifrah, G. (1985). From one to zero: A universal history of numbers. New York: Viking Penguin.Google Scholar
  18. Marton, F. (2015). Necessary conditions of learning. New York: Routledge.Google Scholar
  19. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, N.J: Lawrence Erlbaum.Google Scholar
  20. Moeller, K., Martignon, L., Wessolowski, S., Engel, J., & Nuerk, H.-C. (2011). Effects of finger counting on numerical development—the opposing views of neurocognition and mathematics education. Frontiers in Psychology, 2, 328.  https://doi.org/10.3389/fpsyg.2011.00328CrossRefGoogle Scholar
  21. Neuman, D. (1987). The origin of arithmetic skills: A phenomenographic approach. Göteborg: Acta Universitatis Gothoburgensis.Google Scholar
  22. Ostad, S. (1998). Developmental differences in solving simple arithmetic word problems and simple number-fact problems: A comparison of mathematically normal and mathematically disabled children. Mathematical Cognition, 4(1), 1–19.CrossRefGoogle Scholar
  23. Reeve, R., & Humberstone, J. (2011). Five- to 7-year-olds’ finger gnosia and calculation abilities. Frontiers in Psychology, 2, 359.  https://doi.org/10.3389/fpsyg.2011.00359CrossRefGoogle Scholar
  24. Rusconi, E., Walsh, V., & Butterworth, B. (2005). Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing. Neuropsychologia, 43, 1609–1624.CrossRefGoogle Scholar
  25. Sarnecka, B. W., & Gelman, S. A. (2004). Six does not just mean a lot: Preschoolers see number words as specific. Cognition, 92(3), 329–352.  https://doi.org/10.1016/j.cognition.2003.10.001CrossRefGoogle Scholar
  26. Schmittau, J. (2004). Vygotskian theory and mathematics education: Resolving the conceptual-procedural dichotomy. European Journal of Psychology of Education, 19(1), 19–43.CrossRefGoogle Scholar
  27. Steffe, L., Thompson, P. W., & Richards, J. (1982). Children’s counting in arithmetical problem solving. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 83–89). Hillsdale, NY: Lawrence Erlbaum.Google Scholar
  28. Vergnaud, G. (1979). The acquisition of arithmetical concepts. Educational Studies in Mathematics, 10(2), 263–274.CrossRefGoogle Scholar
  29. Wynn, K. (1990). Children’s understanding of counting. Cognition, 36, 155–193.CrossRefGoogle Scholar
  30. Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220–251.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of GothenburgGothenburgSweden

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