The Materialisation of Children’s Mathematical Thinking Through Organisation of Turn-Taking in Small Group Interactions in Kindergarten

  • Svanhild BreiveEmail author


This chapter reports from a case study which focuses on the coordination of turn-taking within two small groups of kindergarten children (age 5–6) working on addition problems. The two segments of small group interaction were analysed from a multimodal, interpretative perspective. Drawing on Radford’s (J Res Math Educ, 2:7–44, 2013) theory of knowledge objectification, the study explores the characteristics of children’s turn-taking and what role children’s organisation of turn-taking plays in the movement of the joint activity, and thus for the materialisation of their mathematical thinking. The findings suggest that children’s various ways of organising turn-taking give rise to different ways in which their mathematical thinking is materialised and illustrates in particular how multiplicative structures emerge from their turn-taking. The chapter also illustrates how children’s turn-taking, and thus their mathematical thinking, seem dependent on contextual features like the formulation of the problem, available artefacts and children’s positional location in space. Implications that can be drawn from this study is that children’s early multiplicative thinking can be promoted by organising them in small groups and asking them to solve various equal groups addition problems with their hands and fingers.


Additive thinking Materialisation of mathematical thinking Multiplicative thinking Rhythm Small group interaction Turn-taking 


  1. Anghileri, J. (1989). An investigation of young children’s understanding of multiplication. Educational Studies in Mathematics, 20(4), 367–385.CrossRefGoogle Scholar
  2. Baroody, A. J., & Purpura, D. J. (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
  3. Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–296). New York: Macmillan.Google Scholar
  4. Lerner, G. H. (2003). Selecting next speaker: The context-sensitive operation of a context-free organization. Language in Society, 32(2), 177–201.CrossRefGoogle Scholar
  5. Lu, L., & Richardson, K. (2018). Understanding children’s reasoning in multiplication problem-solving. Investigations in Mathematics Learning, 10(4), 240–250.CrossRefGoogle Scholar
  6. Mondada, L. (2007). Multimodal resources for turn-taking: Pointing and the emergence of possible next speakers. Discourse Studies, 9(2), 194–225.CrossRefGoogle Scholar
  7. Mulligan, J. T., & Mitchelmore, M. C. (1997). Young children’s intuitive models of multiplication and division. Journal for Research in Mathematics Education, 28(3), 309–330.CrossRefGoogle Scholar
  8. Mulligan, J. T., & Mitchelmore, M. C. (2013). Early awareness of mathematical pattern and structure. In L. D. English & J. T. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 29–45). New York: Springer.CrossRefGoogle Scholar
  9. Radford, L. (2010). Layers of generality and types of generalization in pattern activities. PNA, 4(2), 37–62.Google Scholar
  10. Radford, L. (2013). Three key concepts of the theory of objectification: Knowledge, knowing, and learning. Journal of Research in Mathematics Education, 2(1), 7–44.Google Scholar
  11. Radford, L. (2015). Rhythm as an integral part of mathematical thinking. In M. Bockarova, M. Danesi, D. Martinovic, & R. Núñez (Eds.), Mind in mathematics: Essays on mathematical cognition and mathematical method (pp. 68–85). München, Germany: LINCOM GmbH.Google Scholar
  12. Radford, L., & Roth, W.-M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2-3), 227–245.CrossRefGoogle Scholar
  13. Roth, W.-M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam, The Netherlands: Sense.CrossRefGoogle Scholar
  14. Sacks, H., Schlegoff, I., & Jefferson, G. (1974). A simplest systematics for the organization of turn-taking in conversation. Language, 50(4), 696–735.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of AgderKristiansandNorway

Personalised recommendations