The number track as an artefact when teaching ordinality to 6-year-olds

Authors

  • Maria Alkhede University of Gothenburg
  • Camilla Björklund University of Gothenburg
  • Angelika Kullberg University of Gothenburg

DOI:

https://doi.org/10.7146/nomad.v31i3.159231

Keywords:

ordinality, number track, teaching, variation theory

Abstract

This study examined the use of the number track as a teaching artefact with ordinality as the learning object. The framework of variation theory was used to analyse observations from enacted teaching when numbers were taught to 6-year-olds. In the analysis, we identified several aspects of ordinality and could draw conclusions of what was made possible to learn. The result indicated that the number track is primarily and almost exclusively used to arrange various number representations (number words, number symbols, pictures and objects) in numerical order. The study further shows a broad range of teachable aspects of ordinality rather than mere sequential placement of numbers.

 

Author Biographies

Maria Alkhede, University of Gothenburg

Maria Alkhede

Maria Alkhede is a Ph.D. candidate in Child and Youth Science at the Department of Education, Communication and Learning at the University of Gothenburg, Sweden. Her research in mathematics education addresses learning and teaching of arithmetic in preschool and early school years.

Camilla Björklund , University of Gothenburg

Camilla Björklund

Camilla Björklund is Professor in Education at the Department of Education, Communication and Learning at the University of Gothenburg, Sweden. Her research interest revolves around children's mathematical learning and teaching in preschool and early school years.

Angelika Kullberg, University of Gothenburg

Angelika Kullberg

Angelika Kullberg is a professor in mathematics education at the department of pedagogical, curricular, professional studies at the university of Gothenburg. Her research interests are foremost on early arithmetic learning and the relationship between teaching and learning in the mathematics classroom

References

Ahlberg, A. (1997). Children’s ways of handling and experiencing numbers (Gothenburg studies in educational sciences, 113). University of Gothenburg.

Askew, M. (2019). Mediating primary mathematics: measuring the extent of teaching for connections and generality in the context of whole number arithmetic. ZDM Mathematics Education, 51(1), 213–226. http://doi.org/10.1007/s11858-018-1010-9

Askew, M., & Venkat, H. (2020). Deconstructing South African Grade 1 learners’ awareness of number in terms of cardinality, ordinality and relational understandings. ZDM Mathematics Education, 52(4), 793–804. https://doi.org/10.1007/s1185 8-020-01132-2

Baccaglini‑Frank, A., Carotenuto, G., & Sinclair, N. (2020). Eliciting preschoolers’ number abilities using open, multi‑touch environments. ZDM Mathematics Education, 52(4), 779–791. https://doi.org/10.1007/s11858-020-01144-y

Björklund, C., Marton, F., & Kullberg, A. (2021). What is to be learnt? Critical aspects of elementary arithmetic skills. Educational Studies in Mathematics, 107, 261–284. https://doi.org/10.1007/s10649-021-10045-0

Coles, A. (2014). Ordinality, neuroscience and the early learning of number. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, 2, 329–336. PME.

Coles, A., & Sinclair, N. (2018). Re-thinking ’normal’ development in the early learning of number. Journal of Numerical Cognition, 4(1), 136–158. https://doi.org/10.5964/jnc.v4i1.101

Doritou, M. (2006). Understanding the number line: conception and practice. [Doctoral thesis] University of Warwick. http://go.warwick.ac.uk/wrap/2622

Ekdahl, A-L., Nord, M., & Kullberg, A. (2025). What matters in teaching for students’ learning opportunities of subtraction in the 1–20 number range? Scandinavian Journal of Educational Research, 69(6), 1288–1303. https://doi.org/10.1080/00313831.2024.2419064

Elofsson, J., Runesson Kempe, U., Ekdal, A-L., & Björklund, C. (2024). Kartläggning av förskoleklassens matematikundervisning om tal – kvalitativa skillnader och lärandemöjligheter. Forskning om undervisning och lärande, 12(1), 47–68. https://doi.org/10.61998/forskul.v12i1.22918

Fuson, K. C. (1988a). Children’s Counting and Concept of Numbers. Springer.

Fuson, K. C. (1988b). Some further clarifications of numerical terminology using results from young children. Behavioral and Brain Science, 11(4), 583–585.

Fuson, K. C., & Hall, J. W. (1983). The acquisition of early number word meanings: A conceptual analysis and review. In H.P. Ginsburg (Ed.), The development of mathematical thinking (pp. 49–107). Academic Press, Inc.

Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Harvard University Press.

Harju, H., & Van Hoof, J. (2025). Putting things in order! A systematic literature review on the ambiguity in descriptions, measurement, and terminology of ordinality [Preprint]. PsyArXiv. https://doi.org/10.31234/osf.io/s62jg_v1

Jungic, V., & Yan, X. (2020). Cardinals versus ordinals: Which come first? For the Learning of Mathematics, 40(1), 38–41. https://www.jstor.org/stable/10.2307/27091138

Kullberg, A., Runesson Kempe, U., & Marton, F. (2017). What is made possible to learn when using the variation theory of learning in teaching mathematics? ZDM Mathematics Education, 49, 559–569. https://doi.org/10.1007/s11858-017-0858-4

Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.

Lesh, R. (1981). Applied mathematical problem solving. Educational Studies in Mathematics, 12(2), 235–264. https://doi.org/10.1007/BF00305624.

Lo, M. L. (2012). Variation theory and the improvement of teaching and learning. Acta Universitatis Gothoburgensis.

Lyons, I. M., & Beilock. S., L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256–261. https://doi.org/10.1016/j.cognition.2011.07.009

MacDonald, B. L., & Shumway, J. F. (2016). Subitizing games: Assessing preschoolers’ understanding of number. Teaching Children Mathematics, 22(6), 340–348. https://doi.org/10.5951/teacchilmath.22.6.0340

Marton, F. (1981). Phenomenography – Describing conceptions of the world around us. Instructional Science, 10, 177–200.

Marton, F. (2015). Necessary conditions of learning. Routledge.

Nesher, P. (2018). Whole number thinking, learning and development: A commentary on chapter 7. In M. G. Bartolini Bussi & X. H. Sun (Eds.), Building the foundation: Whole numbers in the primary grades. New ICMI study series (pp. 169–179). Springer.

Paliwal, V., & Baroody, A. J. (2020). Cardinality principle understanding: the role of focusing on subitizing ability. ZDM Mathematics Education, 52(4), 659–661. https://doi.org/10.1007/s11858-020-01150-0.

Pasnak, R., Schmerold, K. L., Fetterer Robinson, M., Gadzichowski, K. M., Bock, A. M., O’Brien, S. E., Kidd, J. K., & Gallington, D. A. (2016). Understanding number sequences leads to understanding mathematics concepts. The Journal of Educational Research, 109(6), 640–646. https://doi.org/10.1080/00220671.2015.1020911

Piaget, J. (1965). The child’s conception of number. Norton Company.

Sarnecka, B. W., & Wright, C. E. (2013). The idea of an exact number: Children’s understanding of cardinality and equinumerosity. Cognitive Science, 37(8), 1493–1506. https://doi.org/10.1111/cogs.12043

Sasanguie, D., & Vos, H. (2018). About why there is a shift from cardinal to ordinal processing in the association with arithmetic between first and second grade. Developmental Science, 21(5), 12653–e12653. https://doi.org/10.1111/desc.12653

Sinclair, N., & Coles, A. (2017). Returning to ordinality in early numbers sense: neurological, technological and pedagogical considerations. In E. Faggiano, F. Ferrara & A. Montone (Eds.), Innovations and technology enhancing mathematics education Perspectives in the digital era (pp. 39–58). Springer.

Venkat, H., & Askew, M. (2018). Mediating primary mathematics: Theory, concepts, and a framework for studying practice. Educational Studies in Mathematics, 97(2), 71–92. https://doi.org/10.1007/s10649-017-9776-1

Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive psychology, 24(2), 220–251. https://doi.org/10.1016/0010-0285(92)90008-P

Downloads

Published

2026-08-26

How to Cite

Alkhede, M., Björklund , C., & Kullberg, A. (2026). The number track as an artefact when teaching ordinality to 6-year-olds. NOMAD Nordic Studies in Mathematics Education, 31(3), 23–42. https://doi.org/10.7146/nomad.v31i3.159231

Issue

Section

Articles