Abstract
In this commentary, I reflect from a neurocognitive perspective on the four chapters on natural number development included in this section. These chapters show that the development of seemingly basic number processing is much more complex than is often portrayed in neurocognitive research. The chapters collectively illustrate that children’s development of natural number cannot be reduced to one basic neurocognitive factor, but instead requires a multitude of skills with different developmental trajectories. Specifically, these contributions highlight that there is much more than the processing of magnitude, or the so-called Approximate Number System, and they elaborate on the roles of subitizing, place value understanding, and children’s spontaneous attention to number and relations. They also point out that number is something that needs to be constructed and that number processing is in essence a symbolic activity, which requires the integration of multiple symbolic representations, a focus that has been increasingly emphasized in more recent neurocognitive research. The contributions in this volume provide fresh perspectives that will help to further our understanding of children’s natural number development and how it should be fostered. They also offer novel avenues for investigating the origins of atypical mathematical development or dyscalculia.
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American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: American Psychiatric Association.
Ansari, D. (2016). Number symbols in the brain. In D. B. Berch, D. C. Geary, & K. Mann-Koepke (Eds.), Development of mathematical cognition: Neural substrates and genetic influences (pp. 27–50). San Diego, CA: Elsevier.
Arsalidou, M., Pawliw-Levac, M., Sadeghi, M., & Pascual-Leone, J. (2018). Brain areas associated with numbers and calculations in children: Meta-analyses of fMRI studies. Developmental Cognitive Neuroscience, 30, 239–250. https://doi.org/10.1016/j.dcn.2017.08.002
Berch, D. B., Geary, D. C., & Mann-Koepke, K. M. (2016). Development of mathematical cognition: Neural substrates and genetic influences. San Diego, CA: Elsevier.
Clements, D. C., Sarama, J., & MacDonald, B. L. (this volume). Subitizing the neglected quantifier. In A. Norton & M. W. Alibali (Eds.), Constructing number: Merging perspectives from psychology and mathematics education. Berlin: Springer.
De Smedt, B., Noel, M. P., Gilmore, C., & Ansari, D. (2013). The relationship between symbolic and non-symbolic numerical magnitude processing and the typical and atypical development of mathematics: A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2, 48–55. https://doi.org/10.1016/j.tine.2013.06.001
De Smedt, B., Peters, L., & Ghesquiere, P. (in press). Neurobiological origins of mathematical learning disabilities or dyscalculia: A review of brain imaging data. In A. Fritz-Stratmann, V. Haase, & P. Räsänen (Eds.), The international handbook of mathematical learning difficulties. New York: Springer. https://www.springer.com/us/book/9783319971476
Dehaene, S. (1997). The number sense. Oxford: Oxford University Press.
Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience, and education. Hove: Psychology Press.
Evans, T. M., & Ullman, M. T. (2016). An extension of the procedural deficit hypothesis from developmental language disorders to mathematical disability. Frontiers in Psychology, 7, 1318. https://doi.org/10.3389/fpsyg.2016.01318
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. https://doi.org/10.1016/j.tics.2004.05.002
Fias, W. (2016). Neurocognitive components of mathematical skills and dyscalculia. In D. B. Berch, D. C. Geary, & K. M. Koepke (Eds.), Development of mathematical cognition: Neural substrates and genetic influences (pp. 195–218). San Diego, CA: Elsevier.
Gebuis, T., Kadosh, R. C., & 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
Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–U662. https://doi.org/10.1038/nature07246
Hulme, C., & Snowling, M. J. (2009). Developmental disorders of language learning and cognition. Malden, MA: Wiley-Blackwell.
LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 1753–1767. https://doi.org/10.1111/j.1467-8624.2010.01508.x
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-Revue Canadienne De Psychologie Experimentale, 70(1), 12–23. https://doi.org/10.1037/cep0000070
Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, 1–16. https://doi.org/10.1017/s0140525x16000960
Lyons, I. M., Bugden, S., Zheng, S., De Jesus, S., & Ansari, D. (2018). Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners. Developmental Psychology, 54(3), 440–457.
McMullen, J., Chan, J. Y., Mazzocco, M. M. M., & Hannula-Sormunen, M. M. (this volume). Spontaneous mathematical focusing tendencies in mathematical development and education. In A. Norton & M. W. Alibali (Eds.), Constructing number: Merging perspectives from psychology and mathematics education. Berlin: Springer.
Merkley, R., & Ansari, D. (2016). Why numerical symbols count in the development of mathematical skills: Evidence from brain and behavior. Current Opinion in Behavioral Sciences, 10, 14–20. https://doi.org/10.1016/j.cobeha.2016.04.006
Mix, K. S., Smith, L. B., & Crespo, S. (this volume). Leveraging relational learning mechanisms to improve the understanding of place value. In A. Norton & M. W. Alibali (Eds.), Constructing number: Merging perspectives from psychology and mathematics education. Berlin: Springer.
Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208.
Peng, P., Namkung, J., Barnes, M., & Sun, C. Y. (2016). A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 108(4), 455–473. https://doi.org/10.1037/edu0000079
Peters, L., & De Smedt, B. (2018). Arithmetic in the developing brain: A review of brain imaging studies. Developmental Cognitive Neuroscience, 30, 265–279. https://doi.org/10.1016/j.dcn.2017.05.002
Peterson, R. L., & Pennington, B. F. (2015). Developmental dyslexia. In T. D. Cannon & T. Widiger (Eds.), Annual review of clinical psychology (Vol. 11, pp. 283–307).
Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542–551. https://doi.org/10.1016/j.tics.2010.09.008
Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., … Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41. https://doi.org/10.1016/j.cognition.2010.03.012
Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20, e12372. https://doi.org/10.1111/desc.12372
Ullman, M. T. (2004). Contributions of memory circuits to language: The declarative/procedural model. Cognition, 92(1–2), 231–270. https://doi.org/10.1016/j.cognition.2003.10.008
Ulrich, C., & Norton, A. (this volume). Discerning a progression of magnitude in children’s construction of number. In A. Norton & M. W. Alibali (Eds.), Constructing number: Merging perspectives from psychology and mathematics education. Berlin: Springer.
Vanbinst, K., & De Smedt, B. (2016). Individual differences in children’s mathematics achievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions. In M. Cappelletti & W. Fias (Eds.), Mathematical brain across the lifespan (Vol. 227, pp. 105–130).
Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson, & K. W. Fischer (Eds.), Human behavior, learning, and the developing brain: Atypical development (pp. 212–238). New York: Guilford Press.
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De Smedt, B. (2019). The Complexity of Basic Number Processing: A Commentary from a Neurocognitive Perspective. In: Norton, A., Alibali, M.W. (eds) Constructing Number. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-00491-0_6
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