Perceiving and Using Structures When Determining the Cardinality of Sets: A Child’s Learning Story

  • Priska SprengerEmail author
  • Christiane Benz


Research claims that structures play an important role in numerous models for number and arithmetic concept development. This constitutes one reason to think about possibilities to support the perception and use of structures in early childhood education. In this study, one child’s learning story in perceiving and using structures to determine the cardinality of a set of objects will be described. The child took part in a study with a pre-, post-, and follow-up design and was part of an interventional group where games focusing on structures were played. After analyzing the learning story, it must be stated that the child changed his way of perceiving structures in sets and using structures to determine the cardinality.


Structural perception Structural determination Eye-tracking Numerical development Fostering arithmetic competences 


  1. Australian Curriculum, Assessment and Reporting Authority [ACARA] (2014). Foundation to year 10 curriculum: Language for interaction (ACELA1428). Retrieved April 26, 2018, 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 (pp. 187–221). Mahwah, NJ: Lawrence Erlbaum Associates Publishers.Google Scholar
  3. Benz, C. (2010). Minis entdecken Mathematik. Braunschweig: Westermann.Google Scholar
  4. Brownell, J. O., Chen, J.-Q., Ginet, L., Hynes-Berry, M., Itzkowich, R., Johnson, D., et al. (2014). Big ideas of early mathematics. What teachers of young children need to know. Boston: Pearson.Google Scholar
  5. Department for Education (2013). The National Curriculum in England: Key stages 1 and 2 framework document. Retrieved April 26, 2018, from
  6. Gasteiger, H. (2015). Early mathematics in play situations: Continuity of learning. In B. Perry, A. Gervasoni, & A. MacDonald (Eds.), Mathematics and transition to school: International perspectives (pp. 255–272). Singapore: Springer.CrossRefGoogle Scholar
  7. Gasteiger, H., & Benz, C. (2018). Enhancing and analyzing kindergarten teachers’ professional knowledge for early mathematics education. The Journal of Mathematical Behavior, 51, 109–117. Scholar
  8. Hunting, R. (2003). Part–whole number knowledge in preschool children. Journal of Mathematical Behavior, 22(3), 217–235.CrossRefGoogle Scholar
  9. Jang, Y.-M., Mallipeddi, R., & Lee, M. (2014). Identification of human implicit visual search intention based on eye movement and pupillary analysis. User Modeling and User-Adapted Interaction, 24(4), 315–344. Scholar
  10. Lüken, M. (2012). Young children’s structure sense. Special issue “Early childhood mathematics teaching and learning”. Journal für Mathematik-Didaktik, 33(2), 263–285.CrossRefGoogle Scholar
  11. Mulligan, J., & Mitchelmore, M. (2013). Early awareness of mathematical pattern and structure. In L. D. English & J. T. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 29–45). Dordrecht: Springer. Scholar
  12. Mulligan, J., & Mitchelmore, M. (2018). Promoting early mathematical structural development through an integrated assessment and pedagogical program. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 17–33). New York: Springer.CrossRefGoogle Scholar
  13. Mulligan, J. T., Mitchelmore, M. C., English, L. D., & Crevensten, N. (2013). Reconceptualizing early mathematics learning: the fundamental role of pattern and structure. In L. D. English & J. T. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 47–66). Dordrecht: Springer. Scholar
  14. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  15. Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44, 162–169.CrossRefGoogle Scholar
  16. Schöner, P., & Benz, C. (2018). Visual structuring processes of children when determining the cardinality of sets—The contribution of eye-tracking. In C. Benz, H. Gasteiger, A. S. Steinweg, P. Schöner, H. Vollmuth, & J. Zöllner (Eds.), Early Mathematics Learning—Selected Papers of the POEM Conference 2016 (pp. 123–144). New York: Springer.Google Scholar
  17. Schöner, P., & Benz, C. (2017). “Two, three and two more equals seven”—Preschoolers’ perception and use of structures in sets. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1.5, 2017) (pp. 1893–1900). DCU Institute of Education and ERME: Dublin.Google Scholar
  18. van Oers, H. J. M. (2004). Mathematisches Denken bei Vorschulkindern. In W. E. Fthenakis & P. Oberhuemer (Eds.), Frühpädagogik international. Bildungsqualität im Blickpunkt (pp. 313–330). Wiesbaden: VS Verlag für Sozialwissenschaften.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of Education KarlsruheKarlsruheGermany

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