Returning to Ordinality in Early Number Sense: Neurological, Technological and Pedagogical Considerations

  • Nathalie Sinclair
  • Alf ColesEmail author
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 9)


This chapter brings together recent research in neuroscience about the processing of number ability in the brain and new pedagogical approaches to the teaching and learning of number in order to highlight the significance roles of fingers and of ordinality in the development of early number sense. We use insights from these two domains to show how TouchCounts, a multitouch app designed for exploring counting and arithmetic, enables children to develop the symbol-symbol awareness that is characteristic of ordinality. We conclude by drawing out implications for further research making use of technology and neuroscience.


  1. Barad, K. (2007). Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning. Duke University Press.Google Scholar
  2. Bateson, G. (1972). Steps to an ecology of mind. Chicago: University of Chicago Press, 2000.Google Scholar
  3. Bugden, S., & Ansari, D. (2015). How can cognitive developmental neuroscience constrain our understanding of developmental dyscalculia? In S. Chinn (Ed.), International handbook of dyscalculia and mathematical learning difficulties (pp. 18–43). London: Routledge.Google Scholar
  4. Butterworth, B. (1999). The mathematical brain. London: Macmillan.Google Scholar
  5. Clements, D. (1999). Subitising: What is it? Why teach it? Teaching Children Mathematics, 5(7), 400–405.Google Scholar
  6. Coles, A. (2014). Transitional devices. For the Learning of Mathematics, 34(2), 24–30.Google Scholar
  7. Coles, A. (submitted). A relational view of mathematical concepts. In E. de Freitas, N. Sinclair, & A. Coles (Eds.), What is a mathematical concept. Cambridge: Cambridge University Press.Google Scholar
  8. Dedekind, R. (1872/1963). Essays on the theory of numbers. New York, NY: Dover.Google Scholar
  9. de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglements in the mathematics classroom. New York: Cambridge University Press.CrossRefGoogle Scholar
  10. de Freitas, E. & Sinclair, N. (2016). The cognitive labour of mathematics dis/ability: Neurocognitive approaches to number sense. International Journal of Educational Research, 79, 222–230.Google Scholar
  11. Gattegno, C. (1957). Numbers in colour: A new method of teaching the process of arithmetic to all levels of the primary school. London: Heinemann.Google Scholar
  12. Gattegno, C. (1974). The common sense of teaching mathematics. New York, NY: Educational Solutions.Google Scholar
  13. Harvey, B., Klein, B., Petridou, N., & Dumoulin, S. (2013). Topographic representation of numerosity in the human parietal lobe. Science, 341(6150), 1123–1126.CrossRefGoogle Scholar
  14. Lyons, I., & Beilock, S. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256–261.CrossRefGoogle Scholar
  15. Maturana, H., & Varela, F. (1987). The tree of knowledge: The biological roots of human understanding. Boston: Shambala.Google Scholar
  16. Merleau-Ponty, M. (1962). The phenomenology of perception. London: Routledge & Kegan Paul.Google Scholar
  17. Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208.Google Scholar
  18. Nieder, A., & Miller, E. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37, 149–157.CrossRefGoogle Scholar
  19. Reid, D., & Mgombelo, J. (2015). Soots and key concepts in enactivist theory and methodology. ZDM, The International Journal on Mathematics Education, 47, 171–183.CrossRefGoogle Scholar
  20. Reigosa-Crespo, V., & Castro, D. (2015). Dots and digits: how do children process the numerical magnitude? Evidence from brain and behaviour. In S. Chinn (Ed.), International Handbook of Dyscalculia and Mathematical Learning Difficulties (pp. 60–77). London: Routledge.Google Scholar
  21. Rips, L. (2015). Beliefs about the nature of number. In E. Davis & P. Davis (Eds.), Mathematics, Substance and Surmise (pp. 321–345). New York: Springer.CrossRefGoogle Scholar
  22. Rubinstein, O., & Sury, D. (2011). Processing ordinality and quantity: The case of developmental dyscalculia. PLoS One, 6(9) Epub.Google Scholar
  23. Santi, G., & Baccaglini-Frank, A. (2015). Possible forms of generalization we can expect from students experiencing mathematical learning difficulties. PNA, Revista de Investigacion en Didactica de la Mathematica, 9(3), 217–243.Google Scholar
  24. Seidenberg, A. (1962). The ritual origin of counting. Archive for History of Exact Sciences, 2(1), 1–40.CrossRefGoogle Scholar
  25. Souriau, É. (2015). The different modes of existence. (E. Beranek & T. Howles, Trans.). Univocal Publishing.Google Scholar
  26. Varela, F. (1996). Neurophenomenology: A methodological remedy for the hard problem. Journal of Consciousness Studies, 3(4), 330–349.Google Scholar
  27. Varela, F. (1999). Ethical know-how: Action, wisdom and cognition. Stanford, California: Stanford University Press.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Simon Fraser UniversityBurnabyCanada
  2. 2.University of BristolBristolEngland

Personalised recommendations