When Is Young Children’s Play Mathematical?

  • Ola HeleniusEmail author
  • Maria L. Johansson
  • Troels Lange
  • Tamsin Meaney
  • Eva Riesbeck
  • Anna Wernberg


One of Bishop’s six mathematical activities is playing which includes modelling, hypothetical thinking and abstraction. These can be in young children’s play, but do they by their presence make this play mathematical? In this chapter, we explore this question by first defining play and then comparing its features with what is known about mathematicians’ academic play and how mathematics education researchers have described young children’s play. From this theoretical discussion, we discuss the features of play, which can enable it to be described as mathematical. We use these features to analyse a small episode of children playing to discuss if and how their play could be considered to be mathematical.


Mathematical Content Mathematical Process Mathematical Activity Free Play Play Situation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Alcock, S., & Haggerty, M. (2013). Recent policy developments and the “schoolification” of early childhood care and education in Aotearoa New Zealand. Early Childhood Folio, 17(2), 21–26.Google Scholar
  2. Bergen, D. (2009). Play as the learning medium for future scientists, mathematicians, and engineers. American Journal of Play, 1(4), 413–428.Google Scholar
  3. Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht: Kluwer.CrossRefGoogle Scholar
  4. Bishop, A. J. (2016). Can values awareness help teachers and parents transition preschool learners into mathematics learning? In T. Meaney, T. Lange, A. Wernberg, O. Helenius, & M. L. Johansson (Eds.), Mathematics education in the early years—Results from the POEM conference 2014. Cham: Springer.Google Scholar
  5. Brandt, R. S. (1985). On talent development: A conversation with Benjamin Bloom. Educational Leadership, 43(1), 33–35.Google Scholar
  6. Bruner, J. S. (1975). Play is serious business. Psychology Today, 8(8), 80–83.Google Scholar
  7. Carraher, D. W., & Schliemann, A. D. (2002). Is everyday mathematics truly relevant to mathematics education. In M. E. Brenner & J. N. Moschkovich (Eds.), Journal for Research in Mathematics Education Monograph: Everyday and academic mathematics in the classroom (monograph) (pp. 131–153). Reston, VI: National Council of Teachers of Mathematics.Google Scholar
  8. Ernest, P. (1991). The philosophy of mathematics education. London: Falmer Press.Google Scholar
  9. Flottorp, V. (2011, February 9–13). How and why do children classify objects in free play? A case study. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings from seventh congress of the European Society for Research in Mathematics Education, Rzeszów, Poland (pp. 1852–1862). European Society for Research in Mathematics. Available from
  10. Fromberg, D. P. (1999). A review of research on play. In C. Seefeldt (Ed.), The early childhood curriculum: Current findings in theory and practice (3rd ed., pp. 27–53). New York: Teachers College Press.Google Scholar
  11. Garfunkel, S., & Young, G. (1990). Mathematics outside of mathematics departments. Notices of the American Mathematical Society, 37, 408–411.Google Scholar
  12. Garnier, P. (2012). Preschool education in France Scholarisation of the École maternelle and Schoolification of Family Life. Pedagogy—Theory & Praxis, 5, 43–53.Google Scholar
  13. Ginsburg, H. P. (2006). Mathematical play and playful mathematics: A guide for early education. In D. G. Singer, R. M. Golinkoff, & K. Hirsh-Pased (Eds.), Play = learning: How play motivates and enhances children’s cognitive and social-emotional growth (pp. 145–165). New York: Oxford University Press.CrossRefGoogle Scholar
  14. Helenius, O., Johansson, M. L., Lange, T., Meaney, T., Riesbeck, E., & Wernberg, A. (2014, February 4–5). Preschool teachers’ awareness of mathematics. In O. Helenius, A. Engström, T. Meaney, P. Nilsson, E. Norén, J. Sayers, & M. Österholm (Eds.), Evaluation and comparison of mathematical achievement: Dimensions and perspectives: Proceedings from Madif9: Nionde forskningsseminariet med Svensk Förening för Matematikdidaktisk Forskning, Umeå. Forthcoming.Google Scholar
  15. Helenius, O., Johansson, M. L., Lange, T., Meaney, T., & Wernberg, A. (2015a, June 21–26). Beginning early: Mathematical exclusion. In S. Mukhopadhyay & B. Greer (Eds.), Proceedings of the eighth international mathematics education and society conference, Portland State University, Oregon, USA (pp. 596–609). Portland, OR: MES8.Google Scholar
  16. Helenius, O., Johansson, M. L., Lange, T., Meaney, T., & Wernberg, A. (2015b, February 4–8). Mathematical exclusion with the every day. In Proceedings of the 9th Congress of European Research in Mathematics Education, Prague. Prague: CERME9 and Charles University in Prague. Forthcoming.Google Scholar
  17. Hersh, R. (1997). What is mathematics, really? Oxford: Oxford University Press.Google Scholar
  18. Holton, D. D., Ahmed, A., Williams, H., & Hill, C. (2001). On the importance of mathematical play. International Journal of Mathematical Education in Science and Technology, 32(3), 401–415.CrossRefGoogle Scholar
  19. Huizinga, J. (1976). Nature and significance of play as a cultural phenomenon. In R. Schechner & M. Schuman (Eds.), Ritual, play, and performance: Readings in the social sciences/theatre (pp. 46–66). New York: Seabury Press.Google Scholar
  20. Johansson, M. L., Lange, T., Meaney, T., Riesbeck, E., & Wernberg, A. (2012, July 8–15). What maths do children engage with in Swedish preschools? In Proceedings from TSG1: Mathematics education at preschool level at ICME-12 the 12th International Congress on Mathematics Education, Seoul, Korea. Available from
  21. Kamii, C., Miyakawa, Y., & Kato, Y. (2004). The development of logico-mathematical knowledge in a block-building activity at ages 1-4. Journal for Research in Childhood Education, 19(1), 44–57.CrossRefGoogle Scholar
  22. Lakatos, I. (1976). Proof and refutations: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  23. Lange, T., Meaney, T., Riesbeck, E., & Wernberg, A. (2014). Mathematical teaching moments: Between instruction and construction. In U. Kortenkamp, B. Brandt, C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early mathematics learning: Selected papers of the POEM 2012 conference (pp. 37–54). New York: Springer.CrossRefGoogle Scholar
  24. Lee, J. S., & Ginsburg, H. P. (2009). Early childhood teachers’ misconceptions about mathematics education for young children in the United States. Australasian Journal of Early Childhood, 34(4), 37–45.Google Scholar
  25. Macmillan, A. (1995). Children thinking mathematically beyond authoritative identities. Mathematics Education Research Journal, 7(2), 111–131.CrossRefGoogle Scholar
  26. Macmillan, A. (1998). Pre-school children’s informal mathematical discourses. Early Child Development and Care, 140(1), 53–71.CrossRefGoogle Scholar
  27. Meaney, T. (2005). Mathematics as text. In A. Cronaki & I. M. Christiansen (Eds.), Challenging perspectives in mathematics classroom communication (pp. 109–141). Westport, CT: Information Age.Google Scholar
  28. Morsanyi, K., Devine, A., Nobes, A., & Szücs, D. (2013). The link between logic, mathematics and imagination: Evidence from children with developmental dyscalculia and mathematically gifted children. Developmental science, 16(4), 542–553.CrossRefGoogle Scholar
  29. Osgood, B. (1998). Mathematics as engineering: Notes from a foreign correspondent. Focus on Calculus. A Newsletter for the Calculus Consortium Based at Harvard University, (14).Google Scholar
  30. Perry, B., & Dockett, S. (1998). Play, argumentation and social constructivism. Early Child Development and Care, 140(1), 5–15.CrossRefGoogle Scholar
  31. Sarama, J., & Clements, D. H. (2009). Building blocks and cognitive building blocks. American Journal of Play, 1(3), 313–337.Google Scholar
  32. Skolverket. (2011). Curriculum for the preschool Lpfö 98: Revised 2010. Stockholm: Skolverket.Google Scholar
  33. Sofou, E., & Tsafos, V. (2010). Preschool teachers’ understandings of the national preschool curriculum in Greece. Early Childhood Education Journal, 37(5), 411–420.CrossRefGoogle Scholar
  34. Ugurel, I., & Morali, S. (2010). A short view on the relationship of mathematics and game from literature context and concept of the (educational) mathematics game. World Applied Sciences Journal, 9(3), 314–321.Google Scholar
  35. van Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46(1-3), 59–85.CrossRefGoogle Scholar
  36. van Oers, B. (2014). The roots of mathematising in young children’s play. In U. Kortenkamp, B. Brandt, C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early mathematics learning: Selected papers of the POEM 2012 conference (pp. 111–123). New York: Springer.CrossRefGoogle Scholar
  37. Vogel, R. (2014). Mathematical situations of play and exploration as an empirical research instrument. In U. Kortenkamp, B. Brandt, C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early mathematics learning: Selected papers of the POEM 2012 conference (pp. 223–236). New York: Springer.CrossRefGoogle Scholar
  38. Whitehead, A. N. (1959). The aims of education and other essays. London: Ernest Benn.Google Scholar
  39. Wolfgang, C. H., Stannard, L. L., & Jones, I. (2001). Block play performance among preschoolers as a predictor of later school achievement in mathematics. Journal of Research in Childhood Education, 15(2), 173–180.CrossRefGoogle Scholar
  40. Wolfgang, C. H., Stannard, L. L., & Jones, I. (2003). Advanced constructional play with LEGOs among preschoolers as a predictor of later school achievement in mathematics. Early Child Development and Care, 173(5), 467–475.CrossRefGoogle Scholar
  41. Wong, N.-Y., Marton, F., Wong, K.-M., & Lam, C.-C. (2002). The lived space of mathematics learning. Journal of Mathematical Behaviour, 21(1), 25–47.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ola Helenius
    • 1
    Email author
  • Maria L. Johansson
    • 2
  • Troels Lange
    • 3
  • Tamsin Meaney
    • 3
  • Eva Riesbeck
    • 4
  • Anna Wernberg
    • 4
  1. 1.National Centre for Mathematics, Gothenburg UniversityGothenburgSweden
  2. 2.Luleå Technical UniversityLuleåSweden
  3. 3.Bergen University CollegeBergenNorway
  4. 4.Malmö UniversityMalmöSweden

Personalised recommendations