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Neurocognitive Perspective on Numerical Development

  • Karin LanderlEmail author
Chapter

Abstract

Cognitive processing of numbers is an important subcomponent of arithmetic skills, which has been found to be often deficient in children with mathematical learning disorder. This chapter summarizes current knowledge on the development of the cognitive representations of different number formats (analog magnitudes, number words, Arabic numbers). It provides an overview of experimental effects of numerical processing that are informative with respect to the neurocognitive representation of numbers (e.g., distance, size congruity, compatibility, SNARC effect) and reports recent findings on relevant neural networks in typical and atypical development. Implications for instruction and intervention are discussed.

Keywords

Approximate number system (ANS) Number words Arabic numbers Symbolic and non-symbolic numerical processing Core mechanism of numerical processing 

References

  1. Agrillo, C. (2015). Numerical and arithmetic abilities in non-primate species. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford Handbook of Numerical Cognition (pp. 214–236). Oxford, UK: Oxford University Press.Google Scholar
  2. Barouillet, P., Camos, V., Perruchet, P., & Seron, X. (2004). ADAPT: A developmental, asemantic, and procedural model for transcoding from verbal to Arabic numerals. Psychological Review, 111(2), 368–394.Google Scholar
  3. Barrouillet, P., & Fayol, M. (1998). From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults. Memory & Cognition, 26(2), 355–368.Google Scholar
  4. Benavides-Varela, S., Butterworth, B., Burgio, F., Arcara, G., Lucangeli, D., & Semenza, C. (2016). Numerical activities and information learned at home link to the exact numeracy skills in 5-6 years-old children. Frontiers in Psychology, 7, 94.Google Scholar
  5. Benoit, L., Lehalle, H., Molina, M., Tijus, C., & Jouen, F. (2013). Young children’s mapping between arrays, number words, and digits. Cognition, 129(1), 95–101.Google Scholar
  6. Beran, M. J., Perdue, B. M., & Evans, T. A. (2015). Monkey mathematical abilities. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford Handbook of Numerical Cognition (pp. 237–257). Oxford, UK: Oxford University Press.Google Scholar
  7. Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118(1), 32–44.Google Scholar
  8. Butterworth, B. (1999). The mathematical brain. London, UK: Macmillan.Google Scholar
  9. Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry and Allied Disciplines, 46(1), 3–18.Google Scholar
  10. Chan, W. W. L., & Wong, T. T. Y. (2016). The underlying number-space mapping among kindergarteners and its relation with early numerical abilities. Journal of Experimental Child Psychology, 148, 35–50.Google Scholar
  11. Chodura, S., Kuhn, J.-T., & Holling, H. (2015). Interventions for children with mathematical difficulties: A meta-analysis. Zeitschrift für Psychologie, 223(2), 129–144.Google Scholar
  12. Clark, C. A. C., Sheffield, T. D., Wiebe, S. A., & Espy, K. A. (2013). Longitudinal associations between executive control and developing mathematical competence in preschool boys and girls. Child Development, 84(2), 662–677.Google Scholar
  13. De Smedt, B., Noël, M. P., 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(2), 48–55.Google Scholar
  14. De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103(4), 469–479.Google Scholar
  15. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1-2), 1–42.Google Scholar
  16. Dehaene, S. (1997). The number sense. How the mind creates mathematics. Oxford, UK: Oxford University Press.Google Scholar
  17. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396.Google Scholar
  18. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83–120.Google Scholar
  19. Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56(2), 384–398.Google Scholar
  20. Dehaene, S., Molko, N., Cohen, L., & Wilson, A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14(2), 218–224.Google Scholar
  21. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3), 487–506.Google Scholar
  22. Donlan, C., Cowan, R., Newton, E. J., & Lloyd, D. (2007). The role of language in mathematical development: Evidence from children with specific language impairments. Cognition, 103(1), 23–33.Google Scholar
  23. Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Hove, UK: Psychology Press.Google Scholar
  24. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.Google Scholar
  25. Froyen, D., Van Atteveldt, N., Bonte, M., & Blomert, L. (2008). Cross-modal enhancement of the MMN to speech-sounds indicates early and automatic integration of letters and speech-sounds. Neuroscience Letters, 430(1), 23–28.Google Scholar
  26. Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65.Google Scholar
  27. Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
  28. Gibson, L. C., & Maurer, D. (2016). Development of SNARC and distance effects and their relation to mathematical and visuospatial abilities. Journal of Experimental Child Psychology, 150, 301–313.Google Scholar
  29. Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76(2), 104–122.Google Scholar
  30. Göbel, S. M., Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H. C. (2014). Language affects symbolic arithmetic in children: The case of number word inversion. Journal of Experimental Child Psychology, 119, 17–25.Google Scholar
  31. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–668.Google Scholar
  32. Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. New York: Routledge.Google Scholar
  33. Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10(4), 389–395.Google Scholar
  34. Holloway, I. D., & Ansari, D. (2008). Domain-specific and domain-general changes in children’s development of number comparison. Developmental Science, 11(5), 644–649.Google Scholar
  35. Hurst, M., Anderson, U., & Cordes, S. (2017). Mapping among number words, numerals, and nonsymbolic quantities in preschoolers. Journal of Cognition and Development, 18(1), 41–62.Google Scholar
  36. Hyde, D. C., & Spelke, E. S. (2011). Neural signatures of number processing in human infants: Evidence for two core systems underlying numerical cognition. Developmental Science, 14(2), 360–371.Google Scholar
  37. Imbo, I., Vanden Bulcke, C., De Brauwer, J., & Fias, W. (2014). Sixty-four or four-and-sixty? The influence of language and working memory on children’s number transcoding. Frontiers in Psychology, 5, 313.Google Scholar
  38. Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(9), 1701–1707.Google Scholar
  39. Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106(3), 1221–1247.Google Scholar
  40. Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85(2), 103–119.Google Scholar
  41. Jordan, N. C., & Levine, S. C. (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews, 15(1), 60–68.Google Scholar
  42. Karolis, V., & Butterworth, B. (2016). What counts in estimation? The nature of the preverbal system. Progress in Brain Research, 227, 29–51 Amsterdam: Elsevier.Google Scholar
  43. Kaufmann, L., Wood, G., Rubinsten, O., & Henik, A. (2011). Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation. Developmental Neuropsychology, 36(6), 763–787.Google Scholar
  44. Kucian, K., Loenneker, T., Dietrich, T., Dosch, M., Martin, E., & von Aster, M. (2006). Impaired neural networks for approximate calculation in dyscalculic children: A functional MRI study. Behavioral and Brain Functions, 2, 31.Google Scholar
  45. Landerl, K. (2013). Development of numerical processing in children with typical and dyscalculic arithmetic skills-a longitudinal study. Frontiers in Psychology, 4, 459.Google Scholar
  46. Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8-9-year-old students. Cognition, 93(2), 99–125.Google Scholar
  47. Landerl, K., & Kölle, C. (2009). Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology, 103(4), 546–565.Google Scholar
  48. Le Corre, M., & Carey, S. (2007). Conceptual sources of the verbal counting principles. Cognition, 105(2), 395–438.Google Scholar
  49. Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52(2), 130–169.Google Scholar
  50. Leslie, A. M., Gelman, R., & Gallistel, C. R. (2008). The generative basis of natural number concepts. Trends in Cognitive Sciences, 12(6), 213–218.Google Scholar
  51. Libertus, M. E., & Brannon, E. M. (2010). Stable individual differences in number discrimination in infancy. Developmental Science, 13(6), 900–906.Google Scholar
  52. Libertus, M. E., Odic, D., Feigenson, L., & Halberda, J. (2016). The precision of mapping between number words and the approximate number system predicts children’s formal math abilities. Journal of Experimental Child Psychology, 150, 207–226.Google Scholar
  53. Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271–290.Google Scholar
  54. Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS One, 6(9), e23749.Google Scholar
  55. Moeller, K., Neuburger, S., Kaufmann, L., Landerl, K., & Nuerk, H.-C. (2009). Basic number processing deficits in developmental dyscalculia: Evidence from eye-tracking. Cognitive Development, 24(4), 371–386.Google Scholar
  56. Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H.-C. (2011). Early place-value understanding as a precursor for later arithmetic performance–a longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837–1851.Google Scholar
  57. Moeller, K., Zuber, J., Olsen, N., Nuerk, H. C., & Willmes, K. (2015). Intransparent German number words complicate transcoding – a translingual comparison with Japanese. Frontiers in Psychology, 6, 740.Google Scholar
  58. Moore, A. M., Rudig, N. O., & Ashcraft, M. H. (2015). Affect, motivation, working memory, and mathematics. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford Handbook of Numerical Cognition (pp. 933–952). Oxford, UK: Oxford University Press.Google Scholar
  59. Moura, R., Wood, G., Pinheiro-Chagas, P., Lonnemann, J., Krinzinger, H., Willmes, K., et al. (2013). Transcoding abilities in typical and atypical mathematics achievers: The role of working memory and procedural and lexical competencies. Journal of Experimental Child Psychology, 116(3), 707–727.Google Scholar
  60. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519–1520.Google Scholar
  61. Mussolin, C., de Volder, A., Grandin, C., Schlögel, X., Nassogne, M.-C., & Noël, M.-P. (2009). Neural correlates of symbolic number comparison in developmental dyscalculia. Journal of Cognitive Neuroscience, 22(5), 860–874.Google Scholar
  62. Mussolin, C., Nys, J., Leybaert, J., & Content, A. (2016). How approximate and exact number skills are related to each other across development: A review. Developmental Review, 39, 1–15.Google Scholar
  63. Noël, M.-P., & Rousselle, L. (2011). Developmental changes in the profiles of dyscalculia: An explanation based on a double exact-and-approximate number representation model. Frontiers in Human Neuroscience, 5, 165.Google Scholar
  64. Nuerk, H.-C., Kaufmann, L., Zoppoth, S., & Willmes, K. (2004). On the development of the mental number line: More, less, or never holistic with increasing age? Developmental Psychology, 40(6), 1199–1211.Google Scholar
  65. Odic, D., Le Corre, M., & Halberda, J. (2015). Children’s mappings between number words and the approximate number system. Cognition, 138, 102–121.Google Scholar
  66. Pixner, S., Moeller, K., Hermanova, V., Nuerk, H. C., & Kaufmann, L. (2011). Whorf reloaded: Language effects on nonverbal number processing in first grade-a trilingual study. Journal of Experimental Child Psychology, 108(2), 371–382.Google Scholar
  67. Pixner, S., Moeller, K., Zuber, J., & Nuerk, H.-C. (2009). Decomposed but parallel processing of two-digit numbers in 1st graders. The Open Psychology Journal, 2, 40–48.Google Scholar
  68. Price, G. R., Holloway, I., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), R1042–R1043.Google Scholar
  69. Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012). Stability and change in markers of core numerical competencies. Journal of Experimental Psychology: General, 141(4), 649–666.Google Scholar
  70. Rotzer, S., Kucian, K., Martin, E., von Aster, M., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometry in children with developmental dyscalculia. NeuroImage, 39(1), 417–422.Google Scholar
  71. Rousselle, L., & Noël, M. P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361–395.Google Scholar
  72. Rubinsten, O., & Henik, A. (2006). Double dissociation of functions in developmental dyslexia and dyscalculia. Journal of Educational Psychology, 98(4), 854–867.Google Scholar
  73. Rubinsten, O., Henik, A., Berger, A., & Shahar-Shalev, S. (2002). The development of internal representations of magnitude and their association with Arabic numerals. Journal of Experimental Child Psychology, 81(1), 74–92.Google Scholar
  74. Rykhlevskaia, E., Uddin, L. Q., Kondos, L., & Menon, V. (2009). Neuroanatomical correlates of developmental dyscalculia: Combined evidence from morphometry and tractography. Frontiers in Human Neuroscience, 3, 51.Google Scholar
  75. Schleger, F., Landerl, K., Muenssinger, J., Draganova, R., Reinl, M., Kiefer-Schmidt, I., et al. (2014). Magnetoencephalographic signatures of numerosity discrimination in fetuses and neonates. Developmental Neuropsychology, 39(4), 316–329.Google Scholar
  76. Schleifer, P., & Landerl, K. (2011). Subitizing and counting in typical and atypical development. Developmental Science, 14(2), 280–291.Google Scholar
  77. Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., et al. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science , 20(3), e12372.Google Scholar
  78. Sekuler, R., & Mierkiewicz, D. (1977). Children’s judgments of numerical inequality. Child Development, 48(2), 630–633.Google Scholar
  79. Szűcs, D., & Myers, T. (2017). A critical analysis of design, facts, bias and inference in the approximate number system training literature: A systematic review. Trends in Neuroscience and Education, 6, 187–203.Google Scholar
  80. Vetter, P., Butterworth, B., & Bahrami, B. (2011). A candidate for the attentional bottleneck: Set-size specific modulation of right TPJ during attentive enumeration. Journal of Cognitive Neuroscience, 23(3), 728–736.Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Developmental Psychology, Department of PsychologyUniversity of GrazGrazAustria

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