The approximate number system and its relation to early math achievement: Evidence from the preschool years

Journal of Experimental Child Psychology

Volumn 114, Issue 3, 2013, Pages 375-388

  Bonny, Justin W ^a   Lourenco, Stella F ^a  

^a EMORY UNIVERSITY   (United States)

Author keywords

Analog magnitude; Approximate number system (ANS); Development; Mathematical cognition; Preschoolers; Ratio effect

Indexed keywords

ACHIEVEMENT; AGE DISTRIBUTION; ARTICLE; CHILD DEVELOPMENT; EDUCATION; EDUCATIONAL STATUS; FEMALE; HUMAN; MALE; MATHEMATICS; METHODOLOGY; PERCEPTIVE DISCRIMINATION; PHYSIOLOGY; PRESCHOOL CHILD; TASK PERFORMANCE;

ACHIEVEMENT; AGE DISTRIBUTION; CHILD DEVELOPMENT; CHILD, PRESCHOOL; DISCRIMINATION (PSYCHOLOGY); EDUCATIONAL MEASUREMENT; EDUCATIONAL STATUS; FEMALE; HUMANS; MALE; MATHEMATICS; TASK PERFORMANCE AND ANALYSIS;

EID: 84873296190     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jecp.2012.09.015     Document Type: Article

References (79)

1. Abedini M.J., Shaghaghian M.R. Exploring scaling laws in surface topography. Chaos, Solitons, and Fractals 2009, 42:2373-2383.
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 parietal sulcus during nonsymbolic magnitude processing: An event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience 2006, 18:1820-1828.
4. Ashcraft M.H. Cognitive arithmetic: A review of data and theory. Cognition 1992, 44:75-106.
5. Ashcraft M.H. Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science 2002, 11:181-185.
6. Brannon E.M., Abbott S., Lutz D.J. Number bias for the discrimination of large visual sets in infancy. Cognition 2004, 93:B59-B68.
7. Buckley P.B., Gillman C.B. Comparisons of digits and dot patterns. Journal of Experimental Psychology 1974, 103:1131-1136.
8. Butterworth B. The mathematical brain 1999, Macmillan, London.
9. Butterworth B. Mathematical expertise. Cambridge handbook of expertise and expert performance 2006, 553-568. Cambridge University Press, Cambridge, UK. K.A. Ericsson, N. Charness, P.J. Feltovich, R.R. Hoffmann (Eds.).
10. Butterworth B. Foundational numerical capacities and the origins of dyscalculia. Space, time, and number in the brain: Searching for the foundations of mathematical thought 2011, 249-265. Elsevier, London. S. Dehaene, E. Brannon (Eds.).
11. Butterworth B., Varma S., Laurillard D. Dyscalculia: From brain to education. Science 2011, 332:1049-1053.
12. Cantlon J.F., Brannon E.M., Carter E.J., Pelphrey K.A. Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology 2006, 4:e125.
13. Cappelletti M., Barth H., Fregni F., Spelke E.S., Pascual-Leone A. RTMS over the intraparietal sulcus disrupts numerosity processing. Experimental Brain Research 2007, 179:631-642.
14. Cleary T.J., Chen P.P. Self-regulation, motivation, and math achievement in middle school: Variations across grade level and math context. Journal of School Psychology 2009, 47:291-314.
15. Cohen J., Cohen P., West S.G., Aiken L.S. Applied multiple regression/correlation analysis for the behavioral sciences 2002, Lawrence Erlbaum, Mahwah, NJ.
16. Davis N., Cannistraci C.J., Rogers B.P., Gatenby J.C., Fuchs L.S., Anderson A.W., et al. The neural correlates of calculation ability in children: An fMRI study. Magnetic Resonance Imaging 2009, 27:1187-1197.
17. Dehaene S. Varieties of numerical abilities. Cognition 1992, 44:1-42.
18. Dehaene S. Origins of mathematical intuitions: The case of arithmetic. Annals of the New York Academy of Sciences 2009, 1156:232-259.
19. Dehaene S., Cohen L. Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 1997, 33:219-250.
20. Dehaene S., Spelke S., Pinel P., Stanescu R., Tsivkin S. Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science 1999, 284:970-974.
21. De Smedt B., Gilmore C.K. Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Psychology 2011, 108:278-292.
22. 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.
23. Droit-Volet S., Clément A., Fayol M. Time, number, and length: Similarities and differences in discrimination in adults and children. Quarterly Journal of Experimental Psychology 2008, 61:1827-1846.
24. Dunn L.M., Dunn D.M. Peabody picture vocabulary test 2007, Pearson, Minneapolis, MN. 4th ed.
25. Feigenson L., Dehaene S., Spelke E. Core systems of number. Trends in Cognitive Sciences 2004, 8:307-314.
26. Gallistel C.R., Gelman R. Preverbal and verbal counting and computation. Cognition 1992, 44:43-74.
27. Gelman R., Gallistel C.R. The child's understanding of number 1978, Harvard University Press, Cambridge, MA.
28. Gilmore C.K., McCarthy S.E., Spelke E.S. Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition 2010, 115:394-406.
29. Ginsberg H.P., Baroody A.J. Test of early mathematics ability 2003, Pro-Ed, Austin, TX. 3rd ed.
30. Gunderson E.A., Levine S.C. Some types of parent number talk count more than others: Relations between parents' input and children's cardinal-number knowledge. Developmental Science 2011, 14:1021-1032.
31. 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.
32. Halberda J., Mazzocco M.M., Feigenson L. Individual differences in non-verbal number acuity correlate with math achievement. Nature 2008, 455:665-669.
33. Holloway I.D., Ansari D. Domain-specific and domain-general changes in children's development of number comparison. Developmental Science 2008, 11:644-649.
34. 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.
35. Holloway I.D., Ansari D. Developmental specialization in the right intraparietal sulcus for the abstract representation of numerical magnitude. Journal of Cognitive Neuroscience 2010, 22:2627-2637.
36. 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.
37. Iuculano T., Tang J., Hall C.W., Butterworth B. Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science 2008, 11:669-680.
38. Izard V., Dehaene-Lambertz G., Dehaene S. Distinct cerebral pathways for object identity and number in human infants. PLoS Biology 2008, 6:e11.
39. Izard V., Sann C., Spelke E.S., Streri A. Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America 2009, 106:10382-10385.
40. Jordan N.C., Huttenlocher J., Levine S.C. Differential calculation abilities in young children from middle- and low-income families. Developmental Psychology 1992, 28:644-653.
41. Jordan N.C., Kaplan D., Locuniak M.N., Ramineni C. Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice 2007, 22:36-46.
42. Jordan N.C., Kaplan D., Oláh L.N., Locuniak M.N. Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development 2006, 77:153-177.
43. Knell R.J. On the analysis of non-linear allometries. Ecological Entomology 2009, 34:1-11.
44. Landerl K., Kölle C. Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology 2009, 103:546-565.
45. Le Corre M., Carey S. One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition 2007, 105:395-438.
46. Lemer C., Dehaene S., Spelke E., Cohen L. Approximate quantities and exact number words: Dissociable systems. Neuropsychologia 2003, 41:1942-1958.
47. Levine S.C., Suriyakham L.W., Rowe M.L., Huttenlocher J., Gunderson E.A. What counts in the development of young children's number knowledge?. Developmental Psychology 2010, 46:1309-1319.
48. Libertus M.E., Brannon E.M. Stable individual differences in number discrimination in infancy. Developmental Psychology 2010, 13:900-906.
49. 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.
50. Lipton J.S., Spelke E.S. Origins of number sense: Large-number discrimination in human infants. Psychological Science 2003, 14:396-401.
51. 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 United States of America 2012, 109:18737-18742.
52. Lyons I.M., Beilock S.L. Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition 2011, 121:256-261.
53. Mazzocco M.M., Feigenson L., Halberda J. Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development 2011, 82:1224-1237.
54. Mazzocco M.M., Feigenson L., Halberda J. Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS One 2011, 6:e23749.
55. Meintjes E.M., Jacobson S.W., Molteno C.D., Gatenby J.C., Warton C., Cannistraci C.J., et al. An fMRI study of magnitude comparison and exact addition in children. Magnetic Resonance Imaging 2010, 28:351-362.
56. Moyer R.S., Landauer T.K. Time required for judgments of numerical inequality. Nature 1967, 215:1519-1520.
57. Nieder A. Counting on neurons: The neurobiology of numerical competence. Nature Reviews Neuroscience 2005, 6:177-190.
58. Nieder A., Dehaene S. Representation of number in the brain. Annual Review of Neuroscience 2009, 32:185-208.
59. Noël M., 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, 5:1-4.
60. Oosterbaan, R. J. (2011). SegReg: Segmented linear regression with breakpoint and confidence intervals. Available from http://www.waterlog.info/segreg.htm.
61. Paulsen D.J., Woldorff M.G., Brannon E.M. Individual differences in nonverbal number discrimination correlate with event-related potentials and measures of probabilistic reasoning. Neuropsychologia 2010, 48:3687-3695.
62. Pesenti M., Zago L., Crivello F., Mellet E., Samson D., Duroux B., et al. Mental calculation in a prodigy is sustained by right prefrontal and medial temporal areas. Nature Neuroscience 2001, 4:103-107.
63. 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.
64. Piazza M., Izard V., Pinel P., Le Bihan D., Dehaene S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 2004, 44:547-555.
65. Pica P., Lemer C., Izard V., Dehaene S. Exact and approximate arithmetic in an Amazonian indigene group. Science 2004, 306:499-503.
66. Revkin S.K., Piazza M., Izard V., Cohen L., Dehaene S. Does subitizing reflect numerical estimation?. Psychological Science 2008, 19:607-614.
67. Rips L.J., Asmuth J., Bloomfield A. Do children learn the integers by induction?. Cognition 2008, 106:940-951.
68. 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.
69. Shalev R.S. Prevalence of developmental dyscalculia. Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities 2007, 49-60. Paul H. Brookes, Baltimore, MD. D. Berch, M. Mazzocco (Eds.).
70. Siegler R.S. The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General 1987, 116:250-264.
71. Siegler R.S., Booth J.L. Development of numerical estimation in young children. Child Development 2004, 75:428-444.
72. Smith P.L. Splines as a useful and convenient statistical tool. The American Statistician 1979, 33:57-62.
73. Soltész F., Szücs D., Szücs L. Relationships between magnitude representation, counting, and memory in 4- to 7-year-old children: A developmental study. Behavioral and Brain Functions 2010, 6. 10.1186/1744-9081-6-13.
74. Temple E., Posner M.I. Brain mechanisms of quantity are similar in 5-year-old children and adults. Proceedings of the National Academy of Sciences of the United States of America 1998, 95:7836-7841.
75. Torbeyns J., Verschaffel L., Ghesquiere P. Simple addition strategies in a first-grade class with multiple strategy instruction, cognition, and instruction. Cognition & Instruction 2005, 23:1-21.
76. vanMarle K., Wynn K. Infants' auditory enumeration: Evidence for analog magnitudes in the small number range. Cognition 2009, 111:302-316.
77. Wagner J.B., Johnson S.C. An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition 2011, 119:10-22.
78. Wynn K. Children's acquisition of the number words and the counting system. Cognitive Psychology 1992, 24:220-251.
79. Xu F., Spelke E.S. Large number discrimination in 6-month-old infants. Cognition 2000, 74:B1-B11.