Digital Experiences in Mathematics Education

, Volume 5, Issue 2, pp 166–177 | Cite as

“The Other Ten”: Order Irrelevance and Auden’s Sense of Number

  • Sheree RodneyEmail author


This Snapshot paper presents a case study of Auden, a student aged 5 years and 6 months, who interacted with a touchscreen App called TouchCounts. This App is designed to support children’s activity around counting. I use Sfard’s commognitive framework to examine how Auden thinks and learns about number, and show how his exploration of number helped me understand the challenges children can face when moving from identifying subsequent numbers as they appear in the natural counting sequence to identifying numbers that appear before and after each other.


Counting Ordinality Cardinality TouchCounts Touchscreen device Commognition 



  1. Bermejo, V. (1996). Cardinality development and counting. Developmental Psychology, 32(2), 263–268.CrossRefGoogle Scholar
  2. Châtelet, G. (1993/2000). Figuring space: Philosophy, mathematics and physics (R. Shore & M. Zagha, Trans.) Dordrecht: Kluwer Academic Publishers. (Original work published in French.)Google Scholar
  3. Coles, A. (2014). Ordinality, neuro-science and the early learning of number. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 1, pp. 329–337). Vancouver: PME.Google Scholar
  4. Gattegno, C. (1974). The common sense of teaching mathematics. New York: Educational Solutions.Google Scholar
  5. Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Cambridge: Harvard University Press.Google Scholar
  6. Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.CrossRefGoogle Scholar
  7. Noss, R., & Hoyles, C. (1996). Windows on mathematics meaning: Learning cultures and computers. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  8. Olive, J., & Makar, K., with V. Hoyos, L. Kor, O. Kosheleva, & R. Straesser (2010). Mathematical knowledge and practices resulting from access to digital technologies. In C. Hoyles & J. Lagrange (Eds.), Mathematics education and technology: Rethinking the terrain (pp. 133–177) New York: Springer.Google Scholar
  9. Pimm, D., & Sinclair, N. (2015). “How do you make numbers?”: Rhythm and turn-taking when co-ordinating ear, eye and hand. In K. Krainer, & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 1961–1967). Prague: Charles University/ERME.Google Scholar
  10. Sadik, A. (2008). Digital storytelling: A meaningful, technology-integrated approach for engaged student learning. Educational Technology Research and Development, 56(4), 487–506.CrossRefGoogle Scholar
  11. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, UK. Cambridge University Press.Google Scholar
  12. Sfard, A. (2009). What’s all the fuss about gestures? A commentary. Educational Studies in Mathematics, 70(2), 191–200.CrossRefGoogle Scholar
  13. Sinclair, N. & Jackiw, N. (2014). TouchCounts [iPad application software].Google Scholar
  14. Xu, F., Spelke, E., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88–101.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Simon Fraser UniversityBurnabyCanada

Personalised recommendations