Mathematical Signs and Their Cultural Transmission in Pretend Play

  • Maulfry WorthingtonEmail author


Mathematics is a critical aspect of early childhood curricula and integral to competency in all STEM subjects. Developed historically, the abstract symbolic language of mathematics is a powerful cultural phenomenon. Using a genetic approach to research the beginning mathematical inscriptions of 3–4-year-olds has highlighted their meaning-based symbol use as children move towards the formal, “higher psychological functions” (Vygotsky, 1978, p. 46). Underpinned by Vygotsky’s socio-cultural and social-semiotic theories, this chapter considers from whom and how young children learn the mathematical signs of the established cultural system of mathematics. It investigates intertextuality and modes of cultural transmission, the social learning mechanisms of imitation and emulation whereby teachers, other adults and children transmit cultural knowledge. The findings show the potential of rich pretend play for learning including peer-to-peer natural pedagogy, highlighting the importance of an effective early learning culture and underscoring the extent to which social learning is paramount for mathematics.


  1. Aubrey, C. (1997). Mathematics teaching in the early years. London: Falmer Press.Google Scholar
  2. Bakhtin, M. M. (1981). The dialogic imagination: Four essays. (M. Holquist, Ed.). Austin, TX: University of Texas Press.Google Scholar
  3. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh & D. Tirosh (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  4. Bonawitz, E., Shafto, P., Gweon, H., Goodman, N. D., Spelke, E., & Schulz, E. (2011). The double-edged sword of pedagogy: Instruction limits spontaneous exploration and discovery. Cognition, 120(3), 322–330. Scholar
  5. Boyette, A. H. (2016). Children’s play and the integration of social and individual learning: A cultural niche construction perspective. In H. Terashima & B. S. Hewlett (Eds.), Social learning and innovation in contemporary hunter-gatherers: Evolutionary and ethnographic perspectives (pp. 159–169). Japan: Springer.CrossRefGoogle Scholar
  6. Boylan, M. (2019). Remastering mathematics: Mastery, remixes and mash ups. Mathematics Teaching 266. May 2019, 14–17.
  7. Brooker, L. (2011). Taking play seriously. In S. Rogers (Ed.), Rethinking play and pedagogy in early childhood education (pp. 152–164). Maidenhead: Open University Press.Google Scholar
  8. Carpay, J., & van Oers, B. (1999). Didactic models and the problem of intertextuality and polyphony. In Y. Engeström, R. Meittinen & R-L. Punamäki (Eds.), Perspectives on activity theory (pp. 298–313). Cambridge: Cambridge University Press.Google Scholar
  9. Carruthers, E. (1997). Number: A developmental theory: A case study of a child from 20 to 44 months. Unpublished Masters (M.Ed.) Dissertation, University of Plymouth.Google Scholar
  10. Carruthers, E. (2015). Listening to children’s mathematics in school. In B. Perry, A. MacDonald & A. Gervasoni (Eds.), Mathematics and transition to school: International perspectives (pp. 313–330). Singapore: Springer.Google Scholar
  11. Carruthers, E., & Worthington, M. (2005). Making sense of mathematical graphics: The development of understanding abstract symbolism. European Early Childhood Education Research Journal, 13(1), 57–79. Scholar
  12. Carruthers, E., & Worthington, M. (2006). Children’s mathematics: Making marks, making meaning (2nd ed.). London: Sage Publications.Google Scholar
  13. Carruthers, E., & Worthington, M. (2011). Understanding children’s mathematical graphics: Beginnings in play. Maidenhead: Open University Press.Google Scholar
  14. Clements, D. H., & Sarama, J. (2014). Play, mathematics, and false dichotomies [Web blog post].
  15. Clements, D. H., & Sarama, J. (2016). Math, science, and technology in the early grades. The Future of Children, 26 (2), 75–94.
  16. Cavalli-Sforza, L. L., & Feldman, M. W. (1981). Cultural transmission and evolution: A quantitative approach. Princetown: Princetown University Press.Google Scholar
  17. Csibra, G. & Gergely, G. (2006). Social learning and social cognition: The case for pedagogy. In Y. Munakata & M. H. Johnson (Eds.), Processes of change in brain and cognitive development. Attention and performance, XXI, (pp. 249–274). Oxford: Oxford University Press.Google Scholar
  18. Csibra, G., & Gergely, G. (2009). Natural pedagogy. Trends in Cognitive Science, 13(4), 148–153. Scholar
  19. Csibra, G., & Gergely, G. (2011). Natural pedagogy as evolutionary adaptation. Philosophical Transactions of the Royal Society, B, 366, 1149–1157. Scholar
  20. van Dijk, E. F., Oers, B., & Terwel, J. (2004). Schematising in early childhood mathematics education: Why, when and how? European Early Childhood Education Research Journal, 12(1), 71–83. Scholar
  21. Ernest, P. (2005). Activity and creativity in the semiotics of learning mathematics. In M. Hoffmann, J. Lenhard & F. Seeger (Eds.), Activity and sign: Grounding mathematics education (pp. 23–34). London: Springer.Google Scholar
  22. Ewers-Rogers, J. (2002). Very young children’s use and understanding of numbers and number symbols. Doctoral thesis, Institute of Education, University of London.Google Scholar
  23. Ferrari, P. L. (2003). Abstraction in mathematics. Philosophical Transactions of the Royal Society London B, 358(1435), 1225–1230. Scholar
  24. Fleer, M. (2010). Conceptual and contextual intersubjectivity for affording concept formation in children’s play. In L. Brooker & S. Edwards (Eds.), Engaging play (pp. 67–79). Maidenhead: Open University Press.Google Scholar
  25. Gasteiger, H. (2015). Early mathematics in play situations: Continuity of learning. In B. Perry, A. MacDonald, & A. Gervasoni (Eds.), Mathematics and transitions to school; International perspectives. Singapore: Springer.Google Scholar
  26. Gergely, G. & Csibra, G. (2007). The social construction of the cultural mind. Imitative learning as a mechanism of human pedagogy. In P. Hauf & F. Förstetlling (Eds.), Making minds: The shaping of human minds through social context (pp. 241–258). Amsterdam: John Benjamins Publishing Company.Google Scholar
  27. Gifford, S. (2005). Teaching mathematics 3–5. Maidenhead: Open University Press.Google Scholar
  28. Ginsburg, H. (1977). Children’s arithmetic. New York: van Nostrand.Google Scholar
  29. Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177. Scholar
  30. Harris, P. (2007). Hard work for the imagination. In A. Goncu & S. Gaskins (Eds.), Play and development: Evolutionary, sociocultural and functional perspectives (pp. 205–225). London: Psychology Press.Google Scholar
  31. Hedges, H., Cullen, J., & Jordan, B. (2011). Early years curriculum: Funds of knowledge as a conceptual framework for children’s interests. Journal of Curriculum Studies, 43(2), 185–205. Scholar
  32. Hiebert, J. (1984). Children’s mathematics learning: The struggle to link form and understanding. The Elementary School Journal, 84(5), 497–513. Scholar
  33. Hewes, J. (2014). Seeking balance in motion: the role of spontaneous free play in promoting social and emotional health in early child care and education. Children, 1, 280–301. Scholar
  34. Hewlett, B. S. (2016). Social learning and innovation in hunter gatherers. In H. Terashima & B. S. Hewlett (Eds.), Social learning and innovation in contemporary hunter-gatherers: Evolutionary and ethnographic perspectives (pp. 1–15). Japan: Springer.Google Scholar
  35. Hoyles, C., Reiss, M. & Tough, S. (2011). Supporting STEM in schools and colleges in England: The role of research. Report (London, Universities UK).
  36. Hughes, M. (1986). Children and number. Difficulties in learning Mathematics. Oxford: Blackwell.Google Scholar
  37. Kristeva, J. (1980). Desire in language: A semiotic approach to literature and art. USA: Columbia University Press.Google Scholar
  38. Legare, C. & Harris, P. L. (2016). The ontogeny of cultural learning. Child Development, 87(3), 633–642. Scholar
  39. McClure, E. R., Guernsey, L., Clements, D. H., Bales, S. N., Nichols, J., Kendall-Taylor, N., et al. (2017). STEM starts early: Grounding in science, technology, engineering, and math education in early childhood. New York: The Joan Ganz Cooney Centre at Sesame Workshop.Google Scholar
  40. Moll, L., Amanti, C., Neff, D., & Gonzales, N. (1992). Funds of knowledge for teaching. Theory into Practice, 31(2), 132–141.CrossRefGoogle Scholar
  41. Munn, P., & Kleinberg, S. (2003). Describing good practice in the early years—A response to the “third way”. Education, 3–13, 3(2), 50–53.Google Scholar
  42. Nielsen, M., Cucchiaro, J. & Mohamedally, J. (2012). When the transmission of culture is child’s play. PLoS One, 7(3), e34066, 1–6. Scholar
  43. Poland, M. (2007). The treasures of schematizing. PhD Diss.: VU University, Amsterdam.Google Scholar
  44. Poland, M., van Oers, B. & Terwel, J. (2009). Schematising activities in early childhood education. Educational Research and Evaluation, 15(3), 305–321. Scholar
  45. Riojas-Cortéz, M. (2000). Mexican American pre-schoolers create stories: Sociodramatic play in a dual language classroom. Bilingual Research Journal, 24(3), 295–307. Scholar
  46. Rogers, S. (2010). Powerful pedagogies and playful resistance. In L. Brooker & S. Edwards (Eds.), Engaging play (pp. 152–165). Maidenhead: Open University Press.Google Scholar
  47. Rogers, S., & Evans, J. (2008). Inside role-play in early childhood education. London: Routledge.CrossRefGoogle Scholar
  48. Sarama, J., & Clements, D. H. (2008). Mathematics in early childhood. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 67–94). Charlotte, NC: Information Age Publishing.Google Scholar
  49. Seo, K-H. & Ginsburg, H. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. Clements, J. Sarama & A. M. DiBase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 91–104). Mahwah: Lawrence Erlbaum.Google Scholar
  50. Tomasello, M. (1999). The cultural origins of human cognition. Cambridge, Massachusetts: Harvard University Press.Google Scholar
  51. Tomasello, M. (2005). Constructing a language: A usage-based theory of language acquisition. Cambridge, MA: Harvard University Press.Google Scholar
  52. Tomasello, M. (2010). Origins of human communication. Cambridge, Massachusetts: The MIT Press.Google Scholar
  53. Tomasello, M. (2016). The ontogeny of cultural learning. Current Opinion in Psychology, 8(1), 1–4. Scholar
  54. van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: an example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9–35. Scholar
  55. van Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46(1), 59–85.CrossRefGoogle Scholar
  56. van Oers, B. (2005) The potentials of imagination. Inquiry: Critical Thinking across the Disciplines, 24(4), 5–17. Scholar
  57. van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in Mathematics, 74(1), 23–37. Scholar
  58. van Oers, B. (2012). Meaningful cultural learning by imitative participation: The case of abstract thinking in primary school. Human Development, 55(1), 136–158. Scholar
  59. van Oers, B. (2013). Challenges in the innovation of mathematics education for young children. Educational Studies in Mathematics, 84(2), 267–272. Scholar
  60. van Schaik, C. P., & Burkart, J. M. (2011). Social learning and evolution: The cultural intelligence hypothesis. Philosophical Transactions of the Royal Society, B, 2011(366), 1008–1016. Scholar
  61. Vygotsky, L. S. (1967). Play and Its role in the mental development of the child. Soviet Psychology, 5(3), 1–18. Scholar
  62. Vygotsky, L. S. (1978). Mind in society. The development of higher psychological processes. Cambridge, Massachusetts: Harvard University Press.Google Scholar
  63. Vygotsky, L. S. (1981). The genesis of higher mental functions. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 144–188). Abingdon: Routledge.Google Scholar
  64. Want, S. C., & Harris, P. (2002). How do children ape? Applying concepts from the study of non-human primates to the developmental study of “imitation” in children. Developmental Science, 5(1), 1–41. Scholar
  65. Wertsch, J. V. (1991). Voices of the mind: A sociocultural approach to mediated action. Cambridge, MA: Harvard University Press.Google Scholar
  66. Whiten, A. (2013). Social cognition: Making us smart or sometimes making us dumb? In M. R. Banaji & S. A. Gelman (Eds.), Navigating the social world: What infants, children and other species can teach us (pp. 150–154). Oxford: Oxford University Press.CrossRefGoogle Scholar
  67. Williams, S. P. (2008). Final report of the Independent review of mathematics teaching in early years settings and primary schools. London, UK: Department for Children, Schools and Families, (DCSF).
  68. Williams, J. (2016). Alienation in mathematics education: Critique and development of neo-Vygotskian perspectives. Educational Studies in Mathematics, 92(1), 59–73. Scholar
  69. Wood, E. (2010). Developing integrated pedagogical approaches to play and learning. In P. Broadhead, J. Howard, & E. Wood (Eds.), Play and learning in the early years. London: Sage Publications Ltd.Google Scholar
  70. Worthington, M. (2005). Issues of collaboration and co-construction within an online discussion forum: Information ecology for continuing professional development. Reflecting Education, 1(1–2), 76–98.
  71. Worthington, M. (2009). Fish in the water of culture: Signs and symbols in young children’s drawing. Psychology of Education Review, 33(1), 37–46.Google Scholar
  72. Worthington, M. (2010). Play is a complex landscape: Imagination and symbolic meanings. In P. Broadhead, L. Wood & J. Howard (Eds.), Play and learning in educational settings. London: Sage Publications.Google Scholar
  73. Worthington, M., & van Oers, B. (2016). Pretend play and the cultural foundations of Mathematics. European Early Childhood Education Research Journal, 24(1), 51–66. Scholar
  74. Worthington, M. & van Oers, B. (2017). Children’s social literacies: Meaning making and the emergence of graphic symbols in pretence. International Journal of Early Childhood Literacy, 24(1), 147–175. doi: 10.1177%2F1468798415618534.CrossRefGoogle Scholar
  75. Worthington, M. (2018). Funds of knowledge: Children’s cultural ways of knowing mathematics. In M-Y. Lai, T. Muir & V. Kinnear (Eds.), Forging connections in early mathematics teaching and learning (pp. 239–258). Singapore: Springer.Google Scholar
  76. Worthington, M., Dobber, M. & van Oers, B. (2019). The development of mathematical abstraction in the nursery. Educational Studies in Mathematics, 102(1), 91–110. Scholar
  77. Worthington, M., Dobber., M. & van Oers, B. (submitted). Intertextuality and mathematisation in early childhood education.Google Scholar
  78. Worthington, M., Carruthers, E., & Hattingh, L. (2020) “This is the safe: It has a number and no one else knows it”: Playing and mathematics. In O. Thiel, E. Severina, & B. Perry (Eds.), Mathematics in early childhood: Research, practice and innovative pedagogy. London: Routledge.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Vrije UniversiteitAmsterdamThe Netherlands

Personalised recommendations