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

Volumn 2, Issue 2, 2013, Pages 48-55

  De Smedt, Bert ^a   Noël, Marie Pascale ^b   Gilmore, Camilla ^c   Ansari, Daniel ^d  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^d UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Approximate number system; Comparison; Dyscalculia; Magnitude representation; Mathematical learning disabilities

Indexed keywords

ACADEMIC ACHIEVEMENT; ARITHMETIC; BRAIN FUNCTION; COGNITION; DEVELOPMENTAL DISORDER; DYSCALCULIA; EDUCATION PROGRAM; FUNCTIONAL MAGNETIC RESONANCE IMAGING; HUMAN; INTRAPARIETAL SULCUS; LEARNING; MATHEMATICAL COMPUTING; MENTAL CAPACITY; MENTAL DEVELOPMENT; MENTAL TASK; METHODOLOGY; NEUROIMAGING; NUMERICAL MAGNITUDE PROCESSING; PRIORITY JOURNAL; PROBLEM SOLVING; REVIEW; SYMBOLISM;

EID: 84882252002     PISSN: 22119493     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tine.2013.06.001     Document Type: Review

References (83)

1. Anderson U., Ostergren R. Number magnitude processing and basic cognitive functions in children with mathematical learning disabilities. Learning and Individual Differences 2012, 22:701-714.
2. Ansari D. Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience 2008, 9:278-291.
3. Ansari D., Dhital B. Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: an event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience 2006, 18:1820-1828.
4. Ansari D., Garcia N., Lucas E., Hamon K., Dhital B. Neural correlates of symbolic number processing in children and adults. Neuroreport 2005, 16:1769-1773.
5. Bonny J.W., Lourenco S.F. The approximate number system and its relation to early math achievement: evidence from the preschool years. Journal of Experimental Child Psychology 2013, 114:375-388.
6. Bugden S., Ansari D. Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition 2011, 118:32-44.
7. Bugden S., Price G.R., McLean D.A., Ansari D. The role of the left intraparietal sulcus in the relationship between symbolic number processing and children's arithmetic competence. Developmental Cognitive Neuroscience 2012, 2:448-457.
8. Butterworth B. The mathematical brain 1999, Macmillan, London.
9. Butterworth B. Developmental dyscalculia. Handbook of mathematical cognition 2005, 455-467. Psychology Press, New York. J.I.D. Campbell (Ed.).
10. Butterworth B., Varma S., Laurillard D. Dyscalculia: from brain to education. Science 2011, 332:1049-1053.
11. Cantlon J.F., Libertus M.E., Pinel P., Dehaene S., Brannon E.M., Pelphrey K.A. The neural development of an abstract concept of number. Journal of Cognitive Neuroscience 2009, 21:2217-2229.
12. Cantlon J.F., Li R. Neural activity during natural viewing of Sesame Street statistically predicts test scores in early childhood. PLOS Biology 2013, 11:e1001462.
13. Cantlon J.F. Math, monkeys and the developing brain. Proceedings of the National Academy of Sciences USA 2012, 109:10725-10732.
14. Carey S. Bootstrapping and the origin of concepts. Daedalus 2004, 133:59-68.
15. Carey S. The origin of concepts 2009, Oxford University Press, Oxford.
16. Castronovo J., Göbel S.M. Impact of high mathematics education on the number sense. PLoS One 2012, 7(4):e33832.
17. Cohen-Kadosh R., Lammertyn J., Izard V. Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology 2008, 84:132-147.
18. De Smedt B., Gilmore C.K. Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology 2011, 108:278-292.
19. De Smedt B., Ansari D., Grabner R.H., Hannula M.M., Schneider M., Verschaffel L. Cognitive neuroscience meets mathematics education. Educational Research Review 2010, 5:97-105.
20. De Smedt B., Verschaffel L., Ghesquière P. The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology 2009, 103:469-479.
21. Dehaene S., Piazza M., Pinel P., Cohen L. Three parietal circuits for number processing. Cognitive Neuropsychology 2003, 20:487-506.
22. Dehaene S., Izard V., Spelke E., et al. Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science 2008, 320:1217-1220.
23. Durand M., Hulme C., Larkin R., Snowling M. The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds. Journal of Experimental Child Psychology 2005, 91:113-136.
24. Dyson N.I., Jordan N.C., Glutting J. A number sense intervention for low-income kindergartners at risk for mathematical difficulties. Journal of Learning Disabilities 2013, 46:166-181.
25. Emerson R.W., Cantlon J.F. Early math achievement and functional connectivity in the fronto-parietal network. Developmental Cognitive Neuroscience 2012, 15:S139-S151.
26. Ferreira F.O., Wood G., Pinheiro-Chagas P., Lonnemann J., Krinzinger H., Willmes K., et al. Explaining school mathematics performance from symbolic and nonsymbolic magnitude processing: similarities and differences between typical and low-achieving children. Psychology and Neuroscience 2012, 5:37-46.
27. Fuhs M.W., McNeil N.M. ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control. Developmental Science 2013, 16:136-148.
28. Gebuis T., Reynvoet B. The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General 2012, 141:642-648.
29. Griffin S. Building number sense with Number Worlds: a mathematics program for young children. Early Childhood Research Quarterly 2004, 19:173-180.
30. Halberda J., Feigenson L. Developmental change in the acuity of the number sense: the approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology 2008, 44:1457-1465.
31. Halberda J., Ly R., Wilmer J.B., Naiman D.Q., Germine L. Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences 2012, 109:11116-11120.
32. Halberda J., Mazzocco M.M.M., Feigenson L. Individual differences in non-verbal number acuity correlate with maths achievement. Nature 2008, 455(7213):665-668.
33. Holloway I.D., Ansari D. Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement. Journal of Experimental Child Psychology 2009, 103:17-29.
34. Inglis M., Attridge N., Batchelor S., Gilmore C. Non-verbal number acuity correlates with symbolic mathematics achievement: but only in children. Psychonomic Bulletin and Review 2011, 18:1222-1229.
35. Iuculano T., Tang J., Hall C.W.B., Butterworth B. Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science 2008, 11:669-680.
36. Kaufmann L., Wood G., Rubinsten O., Henik A. Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation. Developmental Neuropsychology 2011, 36:763-787.
37. Kolkman M.E., Kroesbergen E.H., Leseman P.P.M. Early numerical development and the role of non-symbolic and symbolic skills. Learning and Instruction 2013, 25:95-103.
38. Kucian K., Loenneker T., Martin E., von Aster M. Non-symbolic distance effect in children with and without developmental dyscalculia: a parametric fMRI study. Developmental Neuropsychology 2011, 36:741-762.
39. Landerl K., Kölle C. Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology 2009, 103:546-565.
40. Landerl K., Bevan A., Butterworth B. Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition 2004, 93:99-125.
41. Landerl K., Fussenegger B., Moll K., Willburger E. Dyslexia and dyscalculia: two learning disorders with different cognitive profiles. Journal of Experimental Child Psychology 2009, 103:309-324.
42. Libertus M.E., Feigenson L., Halberda J. Preschool acuity of the approximate number system correlates with school math ability. Developmental Science 2011, 14:1292-1300.
43. Libertus M.E., Feigenson M., Halberda J. Is the approximate number precision a stable predictor of math ability?. Learning and Individual Differences 2013, 25:126-133.
44. Libertus M.E., Odic D., Halberda J. Intuitive sense of number correlates with math scores on college-entrance examination. Acta Psychologica 2012, 141:373-379.
45. Lonnemann J., Linkersdörfer J., Hasselhorn M., Lindberg S. Symbolic and non-symbolic distance effects in children and their connection with arithmetic skills. Journal of Neurolinguistics 2011, 24:583-591.
46. Lourenco S.F., Bonny J.W., Fernandez E.P., Rao S. Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence. Proceedings of the National Academy of Sciences 2012, 109:18737-18742.
47. Lyons I.M., Beilock S.L. Numerical ordering ability mediates the relation between number sense and arithmetic competence. Cognition 2011, 121:256-261.
48. Lyons I.M., Ansari D., Beilock S.L. Symbolic estrangement: evidence against a strong association between numerical symbols and the quantities they represent. Journal of Experimental Psychology: General 2012, 141:635-641.
49. Mazzocco M.M.M., Feigenson L., Halberda J. Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development 2011, 82:1224-1237.
50. Mazzocco M.M.M., Feigenson L., Halberda J. Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS One 2011, 6:9.
51. McCandliss B.D. Educational neuroscience: the early years. Proceedings of the National Academy of Sciences of the United States of America 2010, 107:8049-8050.
52. Mejias S., Mussolin C., Rousselle L., Grégoire J., Noël M.-P. Numerical and non-numerical estimation in children with and without mathematical learning disabilities. Child Neuropsychology 2012, 18:550-575.
53. Mundy E., Gilmore C.K. Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology 2009, 103:490-502.
54. Mussolin C., De Volder A., Grandin C., Schloegel X., Nassongne M.C., Noel M.-P. Neural correlates of symbolic number comparisons in developmental dyscalculia. Journal of Cognitive Neuroscience 2010, 22:860-874.
55. Mussolin C., Mejias S., Noël M.-P. Symbolic and non-symbolic number comparison in children with and without dyscalculia. Cognition 2010, 115:10-25.
56. Noël M.-P., Rousselle L. Developmental changes in the profiles of dyscalculia: an explanation based on a double exact-and-approximate number representation model. Frontiers in Human Neuroscience 2011, 5:165. 10.3389/fnhum.2011.00165.
57. Noël M.-P., Grégoire J., Meert G., Seron X. The innate schema of natural numbers does not explain historical, cultural, and developmental differences. Behavioral and Brain Sciences 2008, 31(6):664-665.
58. Obersteiner A., Reiss K., Ufer S. How training on exact or approximate mental representations of number can enhance first-grade students' basic number processing and arithmetic skills. Learning and Instruction 2013, 23:125-135.
59. Piazza M., Facoetti A., Trussardi A.N., Berteletti I., Conte S., Lucangeli D., et al. Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition 2010, 116:33-41.
60. Piazza M., Pica P., Izard V., Spelke E., dehaene S. Education enhances the acuity of the non-verbal approximate number system. Psychological Science 2013, http://dx.doi.org/10.1177/0956797612464057, (in press).
61. Price G.R., Holloway I., Rasanen P., Vesterinen M., Ansari D. Impaired parietal magnitude processing in developmental dyscalculia. Current Biology 2007, 17:R1042-R1043.
62. Price G.R., Palmer D., Battista C., Ansari D. Nonsymbolic numerical magnitude comparison: reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica 2012, 140:50-57.
63. Ramani G.B., Siegler R.S. Reducing the gap in numerical knowledge between low- and middle-income preschoolers. Journal of Applied Developmental Psychology 2011, 32:146-159.
64. Ramani G.B., Siegler R.S. Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. Child Development 2008, 79:375-394.
65. Rasanen P., Salminen J., Wilson A.J., Aunio P., Dehaene S. Computer-assisted intervention for children with low numeracy skills. Cognitive Development 2009, 24:450-472.
66. Rousselle L., Noël M.-P. Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic versus non-symbolic number magnitude processing. Cognition 2007, 102:361-395.
67. Sasanguie D., Göbel S.M., Moll K., Smets K., Reynvoet B. Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?. Journal of Experimental Child Psychology 2013, 114:418-431.
68. Sasanguie D., Van den Bussche E., Reynvoet B. Predictors for mathematics achievement? Evidence from a longitudinal study. Mind, Brain, and Education 2012, 6:119-128.
69. Sasanguie D., De Smedt B., Defever E., Reynvoet B. Association between basic numerical abilities and mathematics achievement. British Journal of Developmental Psychology 2012, 30:344-357.
70. Sekuler R., Mierkiewicz D. Children's judgments of numerical inequality. Child Development 1977, 48:630-633.
71. Siegler R.S., Ramani G.B. Playing linear number board games - but not circular ones - improves low-income preschoolers' numerical understanding. Journal of Educational Psychology 2009, 101:545-560.
72. Siegler R.S. Improving the numerical understanding of children from low-income families. Child Development Perspectives 2009, 3:118-124.
73. Soltesz F., Szücs D., Szücs L. Relationships among magnitude representation, counting, and memory in 4- to 7-year-old children: a developmental study. Behavioral and Brain Functions 2010, 6:13. 10.1186/1744-9081-6-13.
74. Toll S., van Luit J.E.H. Accelerating the early numeracy development of kindergartners with limited working memory skills through remedial education. Research in Developmental Disabilities 2013, 34:745-755.
75. Vanbinst K., Ghesquière P., De Smedt B. Numerical magnitude representations and individual differences in Children's arithmetic strategy use. Mind, Brain, and Education 2012, 6:129-136.
76. Vilette B., Mawart C., Rusinek S. L'outil estimator, la ligne numérique mentale et les habiletés arithmétiques. Pratiques Psychologiques 2010, 16:203-214.
77. Whyte J.C., Bull R. Number games, magnitude representation, and basic number skills in preschoolers. Developmental Psychology 2008, 44:588-596.
78. Wiese H. Numbers, language and the human mind 2003, Cambridge University Press, Cambridge.
79. Wiese H. The co-evolution of number concepts and counting words. Lingua 2007, 117:758-772.
80. Wilson A.J., Dehaene S., Dubois O., Fayol M. Effects of an adaptive game intervention on accessing number sense in low-socioeconomic-status kindergarten children. Mind, Brain, and Education 2009, 3:224-234.
81. Wilson A.J., Dehaene S. Number sense and developmental dyscalculia. Human behavior, learning, and the developing brain: atypical development 2007, 212-237. Guilford Press, New York. 2nd ed. D. Coch, G. Dawson, K. Fischer (Eds.).
82. Wilson A.J., Revkin S.K., Cohen D., Cohen L., Dehaene S. An open trial assessment of The Number Race, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions 2006, 2:20.
83. Zebian S., Ansari D. Differences between literates and illiterates on symbolic but not nonsymbolic numerical magnitude processing. Psychonomic Bulletin and Review 2012, 19:93-100.