Number Stories

  • Judith A. MousleyEmail author
Part of the Early Mathematics Learning and Development book series (EMLD)


True personal stories are used to introduce some of the research into pre-school children’s development of number knowledge and skills. A range of conversations and stimulating environments illustrate how parents, grandparents, peers, and early childhood professionals support the mastery of new number words and concepts as well as mathematical actions, in everyday contexts and play situations. The stories discuss the learning of real children developing knowledge and skills in the pre-school years. They tell about early quantity identification along with some young children’s growth of interest in and skills with cardinal and ordinal number and counting; learning about more and less, then very simple addition and subtraction; early recognition and naming of multiplication “arrays”; written numeral identification; and one child’s earliest abstract understanding of the idea of infinity. For each of these topics, some research on pre-school learning is outlined. The growth of children’s self-concepts as they handle mathematics and the situatedness of learning in varied and everyday, informal learning contexts are supplementary themes of this chapter.


Pre-school Number Counting Number operations Abstraction 


  1. Aaker, J. (2013). Lean in today: Harnessing the power of stories. Stanford Graduate Business School, Palo Alto, CA. Retrieved March 8, 2014 from
  2. 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 the education of young children (2nd ed., pp. 187–221). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  3. Baroody, A. J., & Rosu, L. (2006, April). Adaptive expertise with basic addition and subtraction combinations: The number sense view. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA, April 7–11, 2004.Google Scholar
  4. Becker, J. (1993). Young children’s numerical use of number words: Counting in many-to-one situations. Developmental Psychology, 29, 458–465.CrossRefGoogle Scholar
  5. Benson, A. P., & Baroody, A. J. (2003, April). Where does non-verbal production fit in the emergence of children’s mental models? Paper presented to the annual meeting of the Society for Research in Child Development, held at the University of Tampa, Tampa, FL.Google Scholar
  6. Bjorkland, C. (2008). Toddlers’ opportunities to learn mathematics. International Journal of Early Childhood, 40, 81–95.CrossRefGoogle Scholar
  7. Carpenter, T. P., Fennema, E. T., Fuson, K., Hiebert, J., Murray, H., & Wearne, D. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.Google Scholar
  8. Clarke, B. A., Clarke, D. M., & Cheeseman, J. (2006). The mathematical knowledge and understanding young children bring to school. Journal of Australian Research in Early Childhood Education, 11(2), 110–127.Google Scholar
  9. Clements, D. H., & Samara, J. (2007). Effects of a pre-school mathematics curriculum: Summative research on the Building Blocks program. Journal for Research in Mathematics Education, 38, 136–163.Google Scholar
  10. Cooper, R. G. (1984). Early number development: Discovering number space with addition and subtraction. In C. Sophian (Ed.), Origins of cognitive skills (pp. 157–192). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  11. Douglass, H. R. (1925). The development of number concepts in children of pre-school and kindergarten ages. Journal of Experimental Psychology, 8, 443–470.CrossRefGoogle Scholar
  12. Durkin, D. (1968). A two-year language arts program for pre-first grade children: First year report (Report No. PS 001 700). Urbana, IL: University of IL.Google Scholar
  13. Fischer, F. E. (1990). A part-part-whole curriculum for teaching number in the kindergarten. Journal for Research in Mathematics Education, 21(3), 207–215.CrossRefGoogle Scholar
  14. Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). New York, NY: Macmillan.Google Scholar
  15. Fuson, K. C., Clements, D. H., & Sarama, J. (2015). Making early math education work for all children. Phi Delta Kappan, 97(3), 63–68.CrossRefGoogle Scholar
  16. Fuson, K. C., Grandau, L., & Sugiyama, P. A. (2001). Early childhood corner: Achievable numerical understandings for all young children. Teaching Children Mathematics, 7, 522–526.Google Scholar
  17. Fuson, K. C., Secada, W. G., & Hall, J. W. (1983). Matching, counting, and conservation of numerical equivalence. Child Development, 54, 91–97.CrossRefGoogle Scholar
  18. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 48–74.CrossRefGoogle Scholar
  19. Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
  20. Gifford, S. (1995). Number in early childhood. Early Child Development and Care, 109, 95–119.CrossRefGoogle Scholar
  21. Ginsburg, H. P. (1977). Children’s arithmetic. New York: D. Van Nostrand Co.Google Scholar
  22. Hannula, M., Räsänen, P., & Lehtinen, E. (2007). Development of counting skills: Role of spontaneous focusing on numerosity and subitizing-based enumeration. Mathematical Thinking and Learning, 9(1), 51–57.CrossRefGoogle Scholar
  23. Holmqvist, M., Tullgren, C., & Brante, G. (2012). Variation theory—A tool to achieve preschool curricula learning goals in mathematics. Curriculum Perspectives, 32(1), 1–9.Google Scholar
  24. Hughes, M. (1981). Can pre-school children add and subtract? Educational Psychology, 1, 207–219.CrossRefGoogle Scholar
  25. Huttenlocher, J., Jordan, N. C., & Levine, S. C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology, 123, 284–296.CrossRefGoogle Scholar
  26. 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.CrossRefGoogle Scholar
  27. Jung, M. (2011). Number relationships in preschool. Teaching Children Mathematics, 17, 550–557.Google Scholar
  28. Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. American Journal of Psychology, 62, 498–525.CrossRefGoogle Scholar
  29. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding up: Helping children learn mathematics. Washington, DC: National Academy Press.Google Scholar
  30. Koechlin, E., Dehaene, S., & Mehler, J. (1997). Numerical transformations in five-month-old human infants. Mathematical Cognition, 3, 89–104.CrossRefGoogle Scholar
  31. Kouba, V. L., & Franklin, K. (1995). Multiplication and division: Sense making and meaning. Teaching Children Mathematics, 1, 574–577.Google Scholar
  32. Labinowicz, E. (1985). Learning from children: New beginnings for teaching numerical thinking, a Piagetian approach. Menlo Park, CA: Addison-Wesley.Google Scholar
  33. Lave, J., & Wenger, E. (1991). Legitimate peripheral participation: Situated learning. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  34. Lee, S. (2012). Toddlers as mathematicians. Australasian Journal of Early Childhood, 37, 30–37.Google Scholar
  35. Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002). Quantitative development in infancy and early childhood. New York, NY: Oxford University Press.CrossRefGoogle Scholar
  36. Mousley, J. (1999, May). Teaching mathematics for understanding: Some reflections. Paper presented to the conference of the Queensland Association of Mathematics Teachers, May 10–14, 1999, held at the University of Queensland, St. Lucia, QLD.Google Scholar
  37. Neumann, M. M., Hood, M., Ford, R. M., & Neumann, D. L. (2013). Letter and numeral identification: Their relationship with early literacy and numeracy skills. European Early Childhood Education Research Journal, 21, 489–501.CrossRefGoogle Scholar
  38. Nunes, T., & Bryant, P. (1996). Children doing mathematics. Oxford: Blackwell.Google Scholar
  39. Piaget, J. (1928). La causalité chez l’enfant. British Journal of Psychology, 18, 276–301.Google Scholar
  40. Patel, P., & Canobi, K. H. (2010). The role of number words in preschoolers’ addition concepts and problem-solving procedures. Educational Psychology, 30, 107–124.CrossRefGoogle Scholar
  41. Resnick, L. B. (1992). From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge. In G. Leinhardt, R. Putnam, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 373–425). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  42. Rouselle, L., & Noël, M. P. (2008). The development of automatic numerosity processes in preschoolers: Evidence for numerosity-perceptual interference. Developmental Psychology, 44, 544–560.CrossRefGoogle Scholar
  43. Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.Google Scholar
  44. Schoenfeld, A. H. (1986). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. Grows (Ed.), Handbook for research in mathematics teaching and learning. New York, NY: Macmillan.Google Scholar
  45. Spelke, E. (2003). What makes us smart? Core knowledge and natural language. In D. Genter & S. Goldin-Meadow (Eds.), Language in mind (pp. 277–311). Cambridge, MA: MIT Press.Google Scholar
  46. Starkey, P. (1992a). The early development of numerical reasoning. Cognition, 43, 93–126.CrossRefGoogle Scholar
  47. Starkey, P. (1992b). Informal addition. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 359–383). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  48. Steffe, L., Thompson, P., & Richards, J. (1982). Children’s counting and arithmetic problem solving. In T. Romberg, T. Carpenter, & J. Moser (Eds.), Addition and subtraction: A cognitive perspective (pp. 83–97). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  49. Tall, D. O. (2001). A child thinking about infinity. The Journal of Mathematical Behavior, 20, 7–19.CrossRefGoogle Scholar
  50. Tolchinsky, L. (2003). The cradle of culture and what children know about writing and numbers before being taught. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  51. Willis, S. (2000, October). Strengthening numeracy: Reducing risk. Paper presented to the ACER research conference Improving numeracy learning: What does the research tell us? October 15–17, 2000, Brisbane.Google Scholar
  52. Wynn, K. (1990). Children’s understanding of counting. Cognition, 36, 144–193.CrossRefGoogle Scholar
  53. Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Deakin UniversityWaurn PondsAustralia

Personalised recommendations