Quantitative deficits of preschool children at risk for mathematical learning disability

Frontiers in Psychology

Volumn 4, Issue MAY, 2013, Pages

  Chu, Felicia W ^a   vanMarle, Kristy ^a   Geary, David C ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Approximate number system; Dyscalculia; executive control; Learning disability; Mathematics achievement; Quantitative knowledge; Title I preschool

Indexed keywords

EID: 84878936756     PISSN: None     EISSN: 16641078     Source Type: Journal    
DOI: 10.3389/fpsyg.2013.00195     Document Type: Article

References (71)

1. Barbaresi, W. J., Katusic, S. K., Colligan, R. C., Weaver, A. L., and Jacobsen, S. J. (2005). Math learning disorder: incidence in a population-based birth cohort, 1976-1982, Rochester, Minn. Ambul. Pediatr. 5, 281-289.
2. Beck, D. M., Schaefer, C., Pang, K., and Carlson, S. M. (2011). Executive function in preschool children: test-retest reliability. J. Cogn. Dev. 12, 169-193.
3. Berch, D. B., and Mazzocco, M. M. M. (eds). (2007). Why is Math So Hard for Some Children? The Nature and Origins of Mathematical Learning Difficulties and Disabilities. Baltimore, MD: Paul H. Brookes Publishing Co.
4. Blair, C., and Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Dev. 78, 647-663.
5. Blatchford, R., Burke, J., Farquhar, C., Plewis, I., and Tizard, B. (1987). Associations between pre-school reading related skills and later reading achievement. Br. Educ. Res. J. 13, 15-23.
6. Briars, D., and Siegler, R. S. (1984). A featural analysis of preschoolers' counting knowledge. Dev. Psychol. 20, 607-618.
7. Bugden, S., and Ansari, D. (2011). Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition 118, 32-44.
8. Bull, R., Espy, K. A., and Wiebe, S. A. (2008). Short-term memory, working memory, and executive functions in preschoolers: longitudinal predictors of mathematical achievement at age 7 years. Dev. Neuropsychol. 33, 205-228.
9. Butterworth, B. (2005). "Developmental dyscalculia," in Handbook of Mathematical Cognition, ed. J. I. D. Campbell (Hove: Psychology Press), 455-467.
10. Bynner, J. (1997). Basic skills in adolescents' occupational preparation. Career Dev. Q. 45, 305-321.
11. Clark, C. A. C., Pritchard, V. E., and Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Dev. Psychol. 46, 1176-1191.
12. De Smedt, B., and Gilmore, C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. J. Exp. Child Psychol. 108, 278-292.
13. Deary, I. J., Strand, S., Smith, P., and Fernandes, C. (2007). Intelligence and educational achievement. Intelligence 35, 13-21.
14. Denvir, B., and Brown, M. (1986). Understanding of number concepts in low attaining 7-9 year olds: part I. Development of descriptive framework and diagnostic instrument. Educ. Stud. Math. 17, 15-36.
15. Dowker, A. (2005a). Individual Differences in Arithmetic: Implications for Psychology, Neuroscience and Education. Hove: Psychology Press.
16. Dowker, A. (2005b). Individual differences in numerical abilities in preschoolers. Dev. Sci. 11, 650-654.
17. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Dev. Psychol. 43, 1428-1446.
18. Feigenson, L., Carey, S., and Hauser, M. (2002). The representations underlying infants' choice of more: object-files versus analog magnitudes. Psychol. Sci. 13, 150-156.
19. Feigenson, L., Dehaene, S., and Spelke, E. (2004). Core systems of number. Trends Cogn. Sci. (Regul. Ed.) 8, 307-314.
20. Gallistel, C. R. (2007). Commentary on Le Corre & Carey. Cognition 105, 439-445.
21. Gallistel, C. R., and Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition 44, 43-74.
22. Gallistel, C. R., and Gelman, R. (2000). Non-verbal numerical cognition: from reals to integers. Trends Cogn. Sci. (Regul. Ed.) 4, 59-65.
23. Gallistel, C. R., and Gelman, R. (2005). "Mathematical cognition," in The Cambridge Handbook of Thinking and Reasoning, Vol. 23, eds K. Holyoak and R. Morrison (Cambridge: Cambridge University Press), 559-588.
24. Geary, D. C. (1990). A componential analysis of an early learning deficit in mathematics. J. Exp. Child Psychol. 49, 363-383.
25. Geary, D. C. (2011). Cognitive predictors of individual differences in achievement growth in mathematics: a five year longitudinal study. Dev. Psychol. 47, 1539-1552.
26. Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Curr. Dir. Psychol. Sci. 22, 23-27.
27. Geary, D. C., Bow-Thomas, C. C., and Yao, Y. (1992). Counting knowledge and skill in cognitive addition: a comparison of normal and mathematically disabled children. J. Exp. Child Psychol. 54, 372-391.
28. Geary, D. C., Brown, S. C., and Samaranayake, V. A. (1991). Cognitive addition: a short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Dev. Psychol. 27, 787-797.
29. Geary, D. C., Hoard, M. K., and Bailey, D. H. (2012a). Fact retrieval deficits in low achieving children and children with mathematical learning disability. J. Learn. Disabil. 45, 291-307.
30. Geary, D. C., Hoard, M. K., Nugent, L., and Bailey, D. H. (2012b). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: a five year prospective study. J. Educ. Psychol. 104, 206-223.
31. Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., and Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Dev. 78, 1343-1359.
32. Geary, D. C., Hoard, M. K., Nugent, L., and Bailey, H. D. (2013). Adolescents' functional numeracy is predicted by their school entry number system knowledge. PLoS ONE 8:e54651. doi:10.1371/journal.pone.0054651
33. Gelman, R., and Gallistel, C. R. (1978). The Child's Understanding of Number. Cambridge, MA: Harvard University Press.
34. Gilmore, C. K., McCarthy, S. E., and Spelke, E. S. (2010). Non-symbolic arithmetic skills and mathematics achievement in the first year of formal schooling. Cognition 115, 394-406.
35. Ginsburg, H. P., and Baroody, A. J. (2003). Test of Early Mathematical Ability, 3rd Edn. Austin, TX: Pro-Ed.
36. Gorsuch, R. L. (1983). Factor Analysis, 2nd Edn. Hillsdale: Lawrence Erlbaum Associates.
37. Halberda, J., and 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. Dev. Psychol. 44, 1457-1465.
38. Halberda, J., Mazzocco, M., and Feigenson, L. (2008). Individual differences in nonverbal number acuity correlate with maths achievement. Nature 455, 665-669.
39. Hannula, M. M., Lepola, J., and Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. J. Exp. Child Psychol. 107, 394-406.
40. Invernizzi, M., Sullivan, A., Meier, J., and Swank, L. (2004). PreK Teacher's Manual: Phonological Awareness and Literacy Screening. Charlottesville, VA: University of Virginia.
41. Iuculano, T., Tang, J., Hall, C. W. B., and Butterworth, B. (2008). Core information processing deficits in developmental dyscalculia and low numeracy. Dev. Sci. 11, 669-680.
42. Jordan, J.-A., Mulhern, G., and Wylie, J. (2009a). Individual differences in trajectories of arithmetical development in typically achieving 5- to 7-year olds. J. Exp. Child Psychol. 103, 455-468.
43. Jordan, N. C., Kaplan, D., Ramineni, C., and Locuniak, M. N. (2009b). Early math matters: kindergarten number competence and later mathematics outcomes. Dev. Psychol. 45, 850-867.
44. Koontz, K. L., and Berch, D. B. (1996). Identifying simple numerical stimuli: processing inefficiencies exhibited by arithmetic learning disabled children. Math. Cogn. 2, 1-23.
45. Krajewski, K., and Schneider, W. (2009). Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: findings from a 3-year longitudinal study. J. Exp. Child Psychol. 103, 516-531.
46. Landerl, K., Bevan, A., and Butterworth, B. (2003). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition 93, 99-125.
47. Le Corre, M., and Carey, S. (2007). One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. Cognition 105, 395-438.
48. LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., et al. (2010). Pathways to mathematics: longitudinal predictors of performance. Child Dev. 81, 1753-1767.
49. Levine, S. C., Huttenlocher, J., and Jordan, N. (1992). Development of calculation abilities in young children. J. Exp. Child Psychol. 53, 72-93.
50. Lewis, C., Hitch, G. J., and Walker, P. (1994). The prevalence of specific arithmetic difficulties and specific reading difficulties in 9-year-old to 10-year-old boys and girls. J. Child Psychol. Psychiatry 35, 283-292.
51. Libertus, M. E., Halberda, J., and Feigenson, L. (2011). Preschool acuity of the approximate number system correlates with math abilities. Dev. Sci. 14, 1292-1300.
52. Locuniak, M. N., and Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. J. Learn. Disabil. 41, 451-459.
53. Lyons, I. M., and Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition 121, 256-261.
54. Mazzocco, M. M. M., Feigenson, L., and Halberda, J. (2011a). Impaired acuity of the approximate number system underlies mathematical learning disability (Dyscalculia). Child Dev. 82, 1224-1237.
55. Mazzocco, M., Feigenson, L., and Halberda, J. (2011b). Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS ONE 6:e23749. doi:10.1371/journal.pone.0023749
56. Morgan, P. L., Farkas, G., and Wu, Q. (2009). Five-year growth trajectories of kindergarten children with learning difficulties in mathematics. J. Learn. Disabil. 42, 306-321.
57. Murphy, M. M., Mazzocco, M. M. M., Hanich, L. B., and Early, M. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. J. Learn. Disabil. 40, 458-478.
58. Piazza, M., Facoetti, A., Trussardi, A. M., Berteletti, I., Conte, S., Lucangeli, D., et al. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition 116, 33-41.
59. Rivera-Batiz, F. (1992). Quantitative literacy and the likelihood of employment among young adults in the United States. J. Hum. Resour. 27, 313-328.
60. Rousselle, L., and Noël, M.-P. (2007). Basic numerical skills in children with mathematical learning disabilities: a comparison of symbolic vs. non-symbolic number magnitude processing. Cognition 102, 361-395.
61. Sarnecka, B. W., and Carey, S. (2008). How counting represents number: what children must learn and when they learn it. Cognition 108, 662-674.
62. SAS Institute. (2004). Statistical Analysis System 7.5. Cary, NC: SAS Institute.
63. Shalev, R. S., Manor, O., and Gross-Tsur, V. (2005). Developmental dyscalculia: a prospective six-year follow-up. Dev. Med. Child Neurol. 47, 121-125.
64. Starkey, P. (1992). The early development of numerical reasoning. Cognition 43, 93-126.
65. Strauss, M. S., and Curtis, L. E. (1984). "Development of numerical concepts in infancy," in Origins of Cognitive Skills: The Eighteenth Annual Carnegie Symposium on Cognition, ed. C. Sophian (Hillsdale, NJ: Erlbaum), 131-155.
66. vanMarle, K. (2013). Infants use different mechanisms to make small and large number ordinal judgments. J. Exp. Child Psychol. 114, 102-110.
67. vanMarle, K., Aw, J., McCrink, K., and Santos, L. R. (2006). How capuchin monkeys (Cebus apella) quantify objects and substances. J. Comp. Psychol. 120, 416-426.
68. vanMarle, K., and Wynn, K. (2001). "Preschoolers' detection of magical events," in Poster Presented at the 2001 Meeting of the Society for Research in Child Development, Minneapolis, MN.
69. vanMarle, K., and Wynn, K. (2011). Tracking and quantifying objects and non-cohesive substances. Dev. Sci. 14, 302-316.
70. Wechsler, D. (2002). Wechsler Preschool and Primary Scale of Intelligence-III. San Antonio, TX: The Psychological Corporation, Harcourt Brace & Co.
71. Wynn, K. (1990). Children's understanding of counting. Cognition 36, 155-193.