Numerical and nonnumerical estimation in children with and without mathematical learning disabilities

Child Neuropsychology

Volumn 18, Issue 6, 2012, Pages 550-575

  Mejias, Sandrine ^a   Mussolin, Christophe ^b   Rousselle, Laurence ^a   Grégoire, Jacques ^a   Nol, Marie Pascale ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Dyscalculia; Learning disabilities; Mathematical development; Mathematical learning disabilities; Number magnitude; Number magnitude representation; Numerical estimation

Indexed keywords

ANALYSIS OF VARIANCE; ARTICLE; CASE CONTROL STUDY; CHILD; COLOR VISION; FEMALE; HUMAN; LEARNING DISORDER; MALE; MATHEMATICAL PHENOMENA; STATISTICAL MODEL;

ANALYSIS OF VARIANCE; CASE-CONTROL STUDIES; CHILD; COLOR PERCEPTION; FEMALE; HUMANS; LEARNING DISORDERS; LINEAR MODELS; MALE; MATHEMATICAL CONCEPTS;

EID: 84867443583     PISSN: 09297049     EISSN: 17444136     Source Type: Journal    
DOI: 10.1080/09297049.2011.625355     Document Type: Article

References (64)

1. Berteletti, I., Lucangeli, D., Piazza, M., Dehaene, S., & Zorzi, M. (2010). Numerical estimation in preschoolers. Developmental Psychology, 46(2), 545-551.
2. Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42(1), 189-201. (Pubitemid 43172338)
3. Butterworth, B. (1999). The mathematical brain. London, United Kingdom: Macmillan.
4. Butterworth, B. (2005). Developmental dyscalculia. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 455-467). New York, NY: Psychology Press.
5. Castronovo, J., & Seron, X. (2007). Numerical estimation in blind subjects: Evidence of the impact of blindness and its following experience. Journal of Experimental Psychology-Human Perception and Performance, 33, 1089-1106.
6. Chillier, L. (2002). La ligne numérique et les codages du nombre chez l'enfant [The number line and the number coding in children]. In J. Bideaud & H. Lehalle (Eds.), Le développement des activités numériques chez l'enfant [The development of numerical activities for children] (pp. 129-150). Paris, France: Hermes, Lavoisier.
7. Cordes, S., Gelman, R., Gallistel, C. R., & Whalen, J. (2001). Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin & Review, 8(4), 698-707. (Pubitemid 33604221)
8. Crollen, V., Castronovo, J., & Seron, X. (2011). Under-and over-estimation: A bi-directional mapping process between symbolic and non-symbolic representations of number? Experimental Psychology, 58(1), 39-49.
9. Cuneo, D. O. (1982). Children's judgments of numerical quantity: A new view of early quantification. Cognitive Psychology, 14, 13-44.
10. De Smedt, B., & Gilmore, C. K. (2011). Defective number module or impaired access?: Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278-292.
11. Dehaene, S. (2003). The neural basis of the Weber-Fechner law: A logarithmic mental number. Trends in Cognitive Sciences, 7(4), 145-147. (Pubitemid 36411817)
12. Feigenson, L., Carey, S., & Spelke, E. S. (2002). Infants' discrimination of number vs. continuous extent. Cognitive Psychology, 44(1), 33-66. (Pubitemid 39659798)
13. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44(1-2), 43-74.
14. Geary, D. C. (1993). Mathematical disabilities-Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345-362.
15. Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15. (Pubitemid 38157438)
16. Geary, D. C. (2005). Les troubles d'apprentissage en arithmétique : Rôle la mémoire de travail et des connaissances conceptuelles [Learning disabilities in arithmetic: The role of working memory and conceptual knowledge]. In M. P. Noël (Ed.), La dyscalculie: Trouble du développement numérique de l'enfant [Dyscalculia: A disorder of the numerical development of the child]. Marseille, France: Solal.
17. Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88(2), 121-151. (Pubitemid 38613211)
18. Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78(4), 1343-1359.
19. Geary, D. C., Hoard,M. K., & Hamson, C. O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for amathematical disability. Journal of Experimental Child Psychology, 74(3), 213-239.
20. Geary, D. C., Hoard, M. K., Nugent, L., & Byrd-Craven, J. (2008). Development of number line representations in children with mathematical learning disability. Developmental Neuropsychology, 33(3), 277-299. (Pubitemid 351883457)
21. Halberda, J., & Feigenson, L. (2008). 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, 44(5), 1457-1465.
22. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665-662.
23. Hanich, L. B., Jordan, N. C., Kaplan, D., & Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93(3), 615-626.
24. Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children's mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17-29.
25. Huntley-Fenner, G. (2001). Children's understanding of number is similar to adults' and rats': Numerical estimation by 5-7-year-olds. Cognition, 78(3), B27-B40.
26. Iuculano, T., Tang, J., Hall, C.W. B., & Butterworth, B. (2008). Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science, 11, 669-680.
27. Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106(3), 1221-1247. (Pubitemid 351181211)
28. Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74(3), 834-850. (Pubitemid 37244643)
29. Khomsi, A. (1998). Epreuve d'évaluation de la compétence en lecture. Lecture de mots et compréhension-révisée (L.M.C-R) [Test for assessing reading proficiency. Word reading and understanding-Revised]. Paris, France: Editions du Centre de Psychologie Appliquée.
30. Koontz, K. L., & Berch, D. B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2(1), 1-23.
31. 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. (Pubitemid 39451866)
32. Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense: Large-number discrimination in human infants. Psychological Science, 14(5), 396-401. (Pubitemid 37282801)
33. Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271-290. (Pubitemid 40259896)
34. Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002). Multiple cues for quantification in infancy: Is number one of them? Psychological Bulletin, 128(2), 278-294.
35. Mundy, E., & Gilmore, C. K. (2009). Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology, 103(4), 490-502.
36. Mussolin, C., Mejias, S., & Noël, M.-P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115(1), 10-25.
37. Noël, M.-P., & Rousselle, L. (in press). How understanding mathematical learning disability may guide mathematics teaching. British Journal of Educational Psychology. Conference Monographs Series.
38. Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., et al. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33-41.
39. Platt, J. R., & Johnson, D. M. (1971). Localization of position within a homogeneous behavior chain: Effects of error contingencies. Learning and Motivation, 2(4), 386-414.
40. Price, G. R., Holloway, I., Rasanen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), R1042-R1043. (Pubitemid 350236850)
41. Robinson, C. S., Menchetti, B. M., & Torgesen, J. K. (2002). Toward a two-factor theory of one type of mathematics disabilities. Learning Disabilities Research & Practice, 17(2), 81-89.
42. Rourke, B. P., & Conway, J. A. (1997). Disabilities of arithmetic and mathematical reasoning: Perspectives from neurology and neuropsychology. Journal of Learning Disabilities, 30(1), 34-46.
43. 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. (Pubitemid 46107408)
44. Rousselle, L., & Noël, M. P. (2008a). The development of automatic numerosity processing in preschoolers: Evidence for numerosity-perceptual interference. Developmental Psychology, 44(2), 544-560.
45. Rousselle, L., & Noël, M. P. (2008b). Mental arithmetic in children with mathematics learning disabilities: The adaptive use of approximate calculation in an addition verification task. Journal of Learning Disabilities, 41, 498-513.
46. Rousselle, L., Palmers, E., & Noël, M. P. (2004). Magnitude comparison in preschoolers: What counts? Influence of perceptual variables. Journal of Experimental Child Psychology, 87(1), 57-84. (Pubitemid 38033292)
47. Rubinsten, O., & Henik, A. (2009). Developmental dyscalculia: Heterogeneity might not mean different mechanisms. Trends in Cognitive Sciences, 13(2), 92-99.
48. Russell, R. L., & Ginsburg, H. P. (1984). Cognitive analysis of children's mathematics difficulties. Cognition and Instruction, 1(2), 217-244.
49. Sattler, J. M. (1982). Assessment of children's intelligence and special abilities. Boston, MA: Allyn and Bacon.
50. Schneider, W., Eschmann, A., & Zuccolotto, A. (2002) (E-Prime, Version 1.2). Pittsburgh, PA: Psychology Software Tools.
51. Shalev, R. S. (2007). Prevalence of developmental dyscalculia. In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 49-60). Baltimore, MD: Paul H. Brookes.
52. Shalev, R. S., Manor, O., & Gross-Tsur, V. (2005). Developmental dyscalculia: A prospective sixyear follow-up. Developmental Medicine & Child Neurology, 47, 121-125. (Pubitemid 40246493)
53. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444. (Pubitemid 39080065)
54. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237-243. (Pubitemid 37282433)
55. Simonart, G. (1998). Echelle d'apprentissage scolaires primaires [Scale of primary school learning]. Braine-le-Château, Belgique: Application des Techniques Modernes (ATM).
56. Temple, C. M. (1992). Developmental dyscalculia. In S. J. S. a. I. Rapin (Ed.), Handbook of neuropsychology (Vol. 7, pp. 211-222). New York, NY: Elsevier.
57. von Aster, M. G., & Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine and Child Neurology, 49(11), 868-873. (Pubitemid 350020450)
58. Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483-488. (Pubitemid 37324731)
59. Wechsler, D. (2005). Manuel du WISC-IV [Manual:Wechsler Intelligence Scale for Children]. Paris, France: Editions du Centre de Psychologie Appliquée (ECPA).
60. Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Non verbal counting in humans: The psychophysics of number representation. Psychological Science, 10(2), 130-137.
61. Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson, & K. Fischer (Eds.), Human behavior, learning, and the developing brain: Atypical development (2nd ed., pp. 212-237). New York, NY: Guilford Press.
62. Wilson, J. T. L., Scott, J. H., & Power, K. G. (1987). Developmental differences in the span of visual memory for pattern. British Journal of Developmental Psychology, 5, 249-255.
63. Wood, J. N., & Spelke, E. S. (2005). Infants' enumeration of actions: Numerical discrimination and its signature limits. Developmental Science, 8(2), 173-181. (Pubitemid 40344685)
64. Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1-B11.