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Development of Number Understanding: Different Theoretical Perspectives

  • Daniel AnsariEmail author
Chapter

Abstract

In this discussion section, I provide a commentary on the five preceding chapters in this volume. I discuss what is, from my own perspective, the state of the art of our understanding of the development of numerical understanding and mathematical disabilities. I raise a number of questions regarding the evidence and theories that are being presented in this volume and discuss future directions. By doing so, I highlight what are, in my view, pressing outstanding issues and pathways to progress in both our understanding of the development of numerical and mathematical abilities and the interaction between research and educational practice.

Keywords

Numerical cognition Mathematical cognition Brain imaging Mathematics education Number sense 

References

  1. Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291.  https://doi.org/10.1038/nrn2334 CrossRefGoogle Scholar
  2. Beller, S., & Bender, A. (2008). The limits of counting: Numerical cognition between evolution and culture. Science, 319(5860), 213–215.  https://doi.org/10.1126/science.1148345 CrossRefGoogle Scholar
  3. Bender, A., & Beller, S. (2013). Cognition is … fundamentally cultural. Behavioral Sciences, 3(1), 42–54.  https://doi.org/10.3390/bs3010042 CrossRefGoogle Scholar
  4. Button, K. S., Ioannidis, J. P. A., Mokrysz, C., Nosek, B. A., Flint, J., Robinson, E. S. J., & Munafò, M. R. (2013). Power failure: Why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience, 14(5), 365–376.  https://doi.org/10.1038/nrn3475 CrossRefGoogle Scholar
  5. Cantlon, J. F. (2012). Math, monkeys, and the developing brain. Proceedings of the National Academy of Sciences of the United States of America, 109(Suppl), 10725–10732.  https://doi.org/10.1073/pnas.1201893109 CrossRefGoogle Scholar
  6. Corbetta, M., & Shulman, G. L. (2002). Control of goal-directed and stimulus-driven attention in the brain. Nature Reviews Neuroscience, 3(3), 201–215.CrossRefGoogle Scholar
  7. Cragg, L., & Gilmore, C. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education.  https://doi.org/10.1016/j.tine.2013.12.001 CrossRefGoogle Scholar
  8. Dehaene, S. (1997). The number sense. New York: Oxford University Press.Google Scholar
  9. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3–6), 487–506.CrossRefGoogle Scholar
  10. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. Retrieved from http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=15242690 CrossRefGoogle Scholar
  11. Fias, W., Menon, V., & Szucs, D. (2013). Multiple components of developmental dyscalculia. Trends in Neuroscience and Education, 2(2), 43–47. Retrieved from http://www.sciencedirect.com/science/article/pii/S2211949313000203 CrossRefGoogle Scholar
  12. Gebuis, T., Cohen Kadosh, R., & Gevers, W. (2016). Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. Acta Psychologica, 171, 17–35.  https://doi.org/10.1016/j.actpsy.2016.09.003 CrossRefGoogle Scholar
  13. Gunderson, E. A., & Levine, S. C. (2011). Some types of parent number talk count more than others: Relations between parents’ input and children’s cardinal-number knowledge. Developmental Science, 14(5), 1021–1032.  https://doi.org/10.1111/j.1467-7687.2011.01050.x CrossRefGoogle Scholar
  14. Kaufmann, L., Mazzocco, M. M., Dowker, A., von Aster, M., Göbel, S. M., Grabner, R. H., et al. (2013). Dyscalculia from a developmental and differential perspective. Frontiers in Psychology, 4.  https://doi.org/10.3389/fpsyg.2013.00516
  15. Kovas, Y., & Plomin, R. (2007). Learning abilities and disabilities: Generalist genes, specialist environments. Current Directions in Psychological Science, 16(5), 284–288.  https://doi.org/10.1111/j.1467-8721.2007.00521.x CrossRefGoogle Scholar
  16. Leibovich, T., & Ansari, D. (2016). The symbol-grounding problem in numerical cognition: A review of theory, evidence, and outstanding questions. Canadian Journal of Experimental Psychology, 70(1).  https://doi.org/10.1037/cep0000070 CrossRefGoogle Scholar
  17. Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2016). From ‘sense of number’ to ‘sense of magnitude’ – The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 1–62.  https://doi.org/10.1017/S0140525X16000960
  18. Libertus, M. E., & Brannon, E. M. (2009). Behavioral and neural basis of number sense in infancy. Current Directions in Psychological Science, 18(6), 346–351.  https://doi.org/10.1111/j.1467-8721.2009.01665.x CrossRefGoogle Scholar
  19. Maloney, E. A., Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2015). Intergenerational effects of parents’ math anxiety on children’s math achievement and anxiety. Psychological Science, 26(9), 1480–1488.  https://doi.org/10.1177/0956797615592630 CrossRefGoogle Scholar
  20. Munafò, M. R., Nosek, B. A., Bishop, D. V. M., Button, K. S., Chambers, C. D., Percie Du Sert, N., et al. (2017). A manifesto for reproducible science. Nature Human Behaviour.  https://doi.org/10.1038/s41562-016-0021 CrossRefGoogle Scholar
  21. Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208.  https://doi.org/10.1146/annurev.neuro.051508.135550 CrossRefGoogle Scholar
  22. Núñez, R. E. (2017). Is there really an evolved capacity for number? Trends in Cognitive Sciences.  https://doi.org/10.1016/j.tics.2017.03.005 CrossRefGoogle Scholar
  23. Open Science Collaboration. (2015). Estimating the reproducibility of psychological science. Science, 349(6251), aac4716-aac4716.  https://doi.org/10.1126/science.aac4716 CrossRefGoogle Scholar
  24. Peters, L., & De Smedt, B. (2017). Arithmetic in the developing brain: A review of brain imaging studies. Developmental Cognitive Neuroscience.  https://doi.org/10.1016/j.dcn.2017.05.002 CrossRefGoogle Scholar
  25. Price, G., Holloway, I., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dsycalculia. Current Biology, 17(24), R1042.CrossRefGoogle Scholar
  26. Reynvoet, B., & Sasanguie, D. (2016). The symbol grounding problem revisited: A thorough evaluation of the ANS mapping account and the proposal of an alternative account based on symbol-symbol associations. Frontiers in Psychology.  https://doi.org/10.3389/fpsyg.2016.01581
  27. Szűcs, D. (2016). Subtypes and comorbidity in mathematical learning disabilities: Multidimensional study of verbal and visual memory processes is key to understanding. In Progress in brain research (Vol. 227, pp. 277–304).  https://doi.org/10.1016/bs.pbr.2016.04.027 CrossRefGoogle Scholar
  28. van Bergen, E., van Zuijen, T., Bishop, D., & de Jong, P. F. (2017). Why are home literacy environment and children’s reading skills associated? What parental skills reveal. Reading Research Quarterly, 52(2), 147–160.  https://doi.org/10.1002/rrq.160 CrossRefGoogle Scholar
  29. Zamarian, L., Ischebeck, A., & Delazer, M. (2009). Neuroscience of learning arithmetic – Evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews.  https://doi.org/10.1016/j.neubiorev.2009.03.005 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PsychologyBrain and Mind Institute, University of Western OntarioLondonCanada

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