, Volume 48, Issue 3, pp 385–391 | Cite as

Neuroscientific studies of mathematical thinking and learning: a critical look from a mathematics education viewpoint

  • Lieven Verschaffel
  • Erno Lehtinen
  • Wim Van Dooren
Commentary Paper


In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories—namely neuroscientific studies of (a) children’s numerical magnitude representation, (b) arithmetical thinking, and (c) more advanced mathematical thinking—and which nicely document the scientific progression being made within the domain of educational neuroscience applied to the domain of mathematics education during the last 5 years, we point to some general caveats that should be considered in future research.


Neuroscience Numerical magnitude representation Arithmetic Advanced mathematical thinking 


  1. Acevedo Nistal, A., Van Dooren, W., Clarebout, G., Elen, J., & Verschaffel, L. (2009). Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: a critical review. ZDM - The International Journal on Mathematics Education, 41, 627–636.CrossRefGoogle Scholar
  2. Babai, R., Nattiv, L., & Stavy, R. (2016). Comparison of perimeters: Improving students’ performance by increasing the salience of the relevant variable. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  3. Carey, S. (2004). Bootstrapping & the origin of concepts. Daedalus, 133, 59–68.CrossRefGoogle Scholar
  4. Christou, K. P., Vosniadou, S., & Vamvakoussi, X. (2007). Students’ interpretations of literal symbols in algebra. In S. Vosniadou, A. Baltas, & X. Vamvakoussi (Eds.), Re-framing the conceptual change approach in learning and instruction (pp. 283–297). Oxford: Elsevier.Google Scholar
  5. De Corte, E., Mason, L., Depaepe, F., & Verschaffel, L. (2011). Self-regulated learning of mathematical knowledge and skills. In B. Zimmerman & D. Schunk (Eds.), Handbook of self-regulation of learning and performance (pp. 155–172). Oxford: Routledge.Google Scholar
  6. De Corte, E., Verschaffel, L., & Lowyck, J. (1994). Computers and learning. In T. Husen & T. N. Postlethwaite (Eds.), The international encyclopedia of education (2nd ed., pp. 1002–1007). Oxford: Pergamon.Google Scholar
  7. De Smedt, B, & Grabner, R. (2015). Applications of neuroscience to mathematics education. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 612–632). Oxford, UK: Oxford University Press.Google Scholar
  8. De Smedt, B., Noël, M., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2, 48–55.CrossRefGoogle Scholar
  9. De Smedt, B., & Verschaffel, L. (2010). Traveling down the road: from cognitive neuroscience to mathematics education … and back. ZDM - The International Journal on Mathematics Education, 42, 649–652.CrossRefGoogle Scholar
  10. Elia, I., Panaoura, A., Eracleous, A., & Gagatsis, A. (2007). Relations between secondary pupils’ conceptions about functions and problem solving in different representations. International Journal of Science and Mathematics Education, 5, 533–556.CrossRefGoogle Scholar
  11. English, L. D., & Mulligan, J. T. (Eds.). (2013). Reconceptualising early mathematics learning. (Series Advances in Mathematics Education). New York: Springer.Google Scholar
  12. Fischbein, E. (1987). Intuition in Science and Mathematics: An educational approach. Dordrecht: Reidel.Google Scholar
  13. Gillard, E., Van Dooren, W., Schaeken, W., & Verschaffel, L. (2009). Dual-processes in the psychology of mathematics education and cognitive psychology. Human Development, 52, 95–108.CrossRefGoogle Scholar
  14. 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 (Special Section on Numerical Cognition, edited by Jamie Campbell), 70, 12–23.Google Scholar
  15. Leikin, R., Waisman, I., & Leikin, M. (2016). Does solving insight-based problems differ from solving learning-based problems? Some evidence from an ERP study. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  16. Leron, U., & Hazzan, O. (2006). The rationality debate: Application of cognitive psychology to mathematics education. Educational Studies in Mathematics, 62, 105–126.CrossRefGoogle Scholar
  17. Leron, U., & Hazzan, O. (2009). Intuitive vs. analytical thinking: Four perspectives. Educational Studies in Mathematics, 71, 263–278.CrossRefGoogle Scholar
  18. Merenluoto, K., & Lehtinen, E. (2004). Number concept and conceptual change: towards a systemic model of the processes of change. Learning and Instruction, 14, 519–534.CrossRefGoogle Scholar
  19. Merkley, R., Shimi, A., & Scerif, G. (2016). Electrophysiological markers of newly acquired symbolic numerical representations: the role of magnitude and ordinal information. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  20. Müller, G., Selter, C., & Wittmann, E. C. (2012). Zahlen, Muster und Strukturen - Spielräume für aktives Lernen und Üben. Stuttgart: Klett.Google Scholar
  21. Obersteiner, A., & Tumpek, C. (2016). Measuring fraction comparison strategies with eye‑tracking. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  22. Pollack, C., Guerrero, S. L., & Star, J. R. (2016). Exploring mental representations for literal symbols using priming and comparison distance effects. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  23. Schillinger, F. L., De Smedt, B., & Grabner, R. H. (2016). When errors count: an EEG study on numerical error monitoring under performance pressure. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  24. Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2016). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science (in press).Google Scholar
  25. Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101, 359–372.CrossRefGoogle Scholar
  26. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428–444.CrossRefGoogle Scholar
  27. Spüler, M., Walter, C., Rosenstiel, W., Gerjets, P., Moeller, K., & Klein, E. (2016). EEG‑based prediction of cognitive workload induced by arithmetic: a step towards online adaptation in numerical learning. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  28. Stern, E., & Schneider, M. (2010). A digital road map analogy of the relationship between neuroscience and educational research. ZDM - The International Journal on Mathematics Education, 42(6), 511–514.CrossRefGoogle Scholar
  29. Thomas, H. B. G. (1963). Communication theory and the constellation hypothesis of calculation. Querterly Journal of Experimental Psychology, 15, 173–191.CrossRefGoogle Scholar
  30. Torbeyns, J., Obersteiner, A., & Verschaffel, L. (2012). Number sense in early and elementary mathematics education. Yearbook of the Department of Early Childhood Studies (Vol. 5, pp. 60–75). Ioannina: University of Ioannina.Google Scholar
  31. Verschaffel, L. (2014, April). “It’s all about strategies, stupid”. Invited Introduction to the theme “Arithmetic strategies” at the “Sixth Expert Meeting on Mathematical Thinking and Learning”, Leiden, The Netherlands.Google Scholar
  32. Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Greenwich: Information Age Publishing.Google Scholar
  33. Vogel, S. E., Keller, C., Koschutnig, K., Reishofer, G., Ebner, F., Dohle, S., Siegrist, M., & Grabner, R. H. (2016). The neural correlates of health risk perception in individuals with low and high numeracy. ZDM Mathematics Education, 48(3), this issue.Google Scholar
  34. Waisman, I., Leikin, M., & Leikin, R. (2016). Brain activity associated with logical inferences in geometry: Focusing on students with different levels of ability. ZDM Mathematics Education, 48(3), this issue.Google Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  • Lieven Verschaffel
    • 1
  • Erno Lehtinen
    • 2
  • Wim Van Dooren
    • 1
  1. 1.University of LeuvenLeuvenBelgium
  2. 2.University of TurkuTurkuFinland

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