The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children

Journal of Experimental Child Psychology

Volumn 116, Issue 2, 2013, Pages 139-156

  Träff, Ulf ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Arithmetic fact retrieval; Basic number abilities; Calculation; Domain general cognitive abilities; Reading; Word problem solving

Indexed keywords

ADOLESCENT; APTITUDE; APTITUDE TEST; ARITHMETIC FACT RETRIEVAL; ARTICLE; BASIC NUMBER ABILITIES; CALCULATION; CHILD; COGNITION; DOMAIN-GENERAL COGNITIVE ABILITIES; FEMALE; HUMAN; MALE; MATHEMATICS; NEUROPSYCHOLOGICAL TEST; PROBLEM SOLVING; PSYCHOLOGIC TEST; READING; WORD PROBLEM SOLVING;

ARITHMETIC FACT RETRIEVAL; BASIC NUMBER ABILITIES; CALCULATION; DOMAIN-GENERAL COGNITIVE ABILITIES; READING; WORD PROBLEM SOLVING;

ADOLESCENT; APTITUDE; APTITUDE TESTS; CHILD; COGNITION; FEMALE; HUMANS; MALE; MATHEMATICS; NEUROPSYCHOLOGICAL TESTS; PROBLEM SOLVING; PSYCHOLOGICAL TESTS;

EID: 84879127375     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jecp.2013.04.007     Document Type: Article

References (86)

1. Ackerman P.L. Determinants of Individual Differences During Skill Acquisition: Cognitive Abilities and Information Processing. Journal of Experimental Psychology General 1988, 117:288-318.
2. Ackerman P.L. Predicting individual differences in complex skill acquisition: Dynamics of ability determinants. Journal of Applied Psychology 1992, 77:598-614.
3. Ackerman P.L. New developments in understanding skilled performance. Current Directions in Psychological Science 2007, 16:235-239.
4. Andersson U. The contribution of working memory to children's mathematical word problem solving. Applied Cognitive Psychology 2007, 21:1201-1216.
5. Andersson U. Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions. British Journal of Educational Psychology 2008, 78:181-203.
6. Andersson U. The contribution of working memory capacity to foreign language comprehension in children. Memory 2010, 18:458-472.
7. Andersson U. Skill development in different components of arithmetic and basic cognitive functions: Findings from a three-year longitudinal study of children with different types of learning difficulties. Journal of Educational Psychology 2010, 102:115-134.
8. Andersson U., Lyxell B. Working memory deficit in children with mathematical difficulties: A general or specific deficit?. Journal of Experimental Child Psychology 2007, 96:197-228.
9. Ansari D. Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience 2008, 9:278-291.
10. Ashcraft M.H. Cognitive arithmetic: A review of data and theory. Cognition 1992, 44:75-106.
11. Ashcraft M.H. Cognitive psychology and simple arithmetic: A review and summary of new directions. Mathematical Cognition 1995, 1:3-34.
12. Aunola K., Leskinen E., Lerkkanen M.-K., Nurmi J.-E. Developmental dynamics of math performance from preschool to Grade 2. Journal of Educational Psychology 2004, 96:699-713.
13. Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities 2007, Paul H. Brookes, Baltimore, MD. D.B. Berch, M.M.M. Mazzocco (Eds.).
14. Berg D.H. Working memory and arithmetic calculation in children: The contributory roles of processing speed, short-term memory, and reading. Journal of Experimental Child Psychology 2008, 99:288-308.
15. Booth J.L., Siegler R.S. Developmental and individual differences in pure numerical estimation. Developmental Psychology 2006, 41:189-201.
16. Bull R., Espy K.A., Wiebe S.A. Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7years. Developmental Neuropsychology 2008, 33:205-228.
17. Butterworth B. The mathematical brain 1999, Macmillan, London.
18. Butterworth B. Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences 2010, 14:534-541.
19. Butterworth B., Zorzi M., Girelli L., Jonckheere A.R. Storage and retrieval of addition facts: The role of number comparison. Quarterly Journal of Experimental Psychology A 2001, 54:1005-1029.
20. Carey S. Bootstrapping and the origin of concepts. Daedalus 2004, 133:59-68.
21. Clark C.A.C., Pritchard V.E., Woodward L.J. Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology 2010, 46:1176-1191.
22. Clarke B., Shinn M.R. Preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psychology Review 2004, 33:234-248.
23. D'Amico A., Passolunghi M.C. Naming speed and effortful and automatic inhibition in children with arithmetic learning disabilities. Learning and Individual Differences 2009, 19:170-180.
24. de Hevia M.D., Vallar G., Girelli L. Visuo-spatial components of numerical representation. Imagery and spatial cognition: Methods, models, and cognitive assessment 2006, 165-181. John Benjamins, Amsterdam, The Netherlands. T. Vecchi, G. Bottini (Eds.).
25. Dehaene S. The number sense 2011, Oxford University Press, New York.
26. Dehaene S., Bossini S., Giraux P. The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 1993, 122:371-396.
27. Desoete A., Ceulemans A., De Weerdt F., Pieters S. Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology 2012, 82:64-81.
28. Duncan G.J., Dowsett C.J., Claessens A., Magnuson K., Huston A.C., Klebanov P., et al. School readiness and later achievement. Developmental Psychology 2007, 43:1428-1446.
29. 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.
30. Feigenson L., Dehaene S., Spelke E. Core systems of number. Trends in Cognitive Sciences 2004, 8:309-314.
31. Fuchs L.S., Compton D.L., Fuchs D., Paulsen K., Bryant J.D., Hamlett C.L. The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology 2005, 97:493-513.
32. Fuchs L.S., Fuchs D., Compton D.L., Powell S.R., Seethaler P.M., Capizzi A.M., et al. The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology 2006, 98:29-43.
33. Fuchs L.S., Geary D.C., Compton D.L., Fuchs D., Hamlett C.L., Bryant J.D. The contributions of numerosity and domain-general abilities to school readiness. Child Development 2010, 81:1520-1533.
34. Fuchs L.S., Geary D.C., Compton D.L., Fuchs D., Hamlett C.L., Seethaler P.M., et al. Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?. Developmental Psychology 2010, 46:1731-1746.
35. Fürst A.J., Hitch G.J. Separate roles for executive and phonological components of working memory in mental arithmetic. Memory & Cognition 2000, 28:774-782.
36. Geary D.C. Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin 1993, 114:345-362.
37. Geary D. Mathematics and learning disabilities. Journal of Learning Disabilities 2004, 37:4-15.
38. Geary D.C. Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology 2011, 47:1539-1552.
39. Geary D.C., Bailey D.H., Hoard M.K. Predicting mathematical achievement and mathematical learning disability with a simple screening tool: The Number Sets Test. Journal of Psychoeducational Assessment 2009, 27:265-279.
40. Geary D.C., Hoard M.K., Byrd-Craven J., Nugent L., Numtee C. Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development 2007, 78:1343-1359.
41. Geary D., Hoard M. Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. Handbook of mathematical cognition 2005, 253-267. Psychology Press, New York. J.I.D. Campbell (Ed.).
42. 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.
43. Halberda J., Mazzocco M., Feigenson L. Individual differences in non-verbal number acuity correlate with math achievement. Nature 2008, 455:665-668.
44. Hannula M.M., Lepola J., Lehtinen E. Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. Journal of Experimental Child Psychology 2010, 107:394-406.
45. 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.
46. Jordan N.C., Kaplan D., Ramineni C., Locuniak M.N. Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology 2009, 45:850-867.
47. Kintsch W., Greeno J.G. Understanding and solving word arithmetic problems. Psychological Review 1985, 92:109-129.
48. Krajewski K., Schneider W. 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. Journal of Experimental Child Psychology 2009, 103:516-531.
49. 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.
50. Lee K., Ng E.-L., Ng S.-F. The Contributions of Working Memory and Executive Functioning to Problem Representation and Solution Generation in Algebraic Word Problems. Journal of Educational Psychology 2009, 101:373-387.
51. Lee K., Ng S.F., Bull R., Pe M.L., Ho R.H.M. Are patterns important? An investigation of the relationships between proficiencies in patterns, computation, executive functioning, and algebraic word problems. Journal of Educational Psychology 2011, 103:269-281.
52. Lee K., Ng S.-F., Ng E.-L., Lim Z.-Y. Working memory and literacy as predictors of performance on algebraic word problems. Journal of Experimental Child Psychology 2004, 89:140-158.
53. LeFevre J.A., Fast L., Smith-Chant B., Skwarchuk S.L., Bisanz J., Kamawar D., et al. Pathways to mathematics: Longitudinal predictors of performance. Child Development 2010, 81:1753-1767.
54. Logie R., Baddeley A.D. Cognitive processes in counting. Journal of Experimental Psychology: Learning, Memory, & Cognition 1987, 13:310-326.
55. Logie R.H., Gilhooly K.J., Wynn V. Counting on working memory in arithmetic problem solving. Memory & Cognition 1994, 22:395-410.
56. Malmquist E. Reading and writing difficulties in children. Analysis and treatment 1977, Gleerups, Lund.
57. Maybery M., Do N. Relationships between facets of working memory and performance on a curriculum-based mathematics test in children. Educational and Child Psychology 2003, 20:77-92.
58. Mayer R.E., Hegarty M. The process of understanding mathematical problems. The nature of mathematical thinking 1996, 29-53. Lawrence Erlbaum, Mahwah NJ. R.J. Sternberg, T. Ben-Zeev (Eds.).
59. Mazzocco M.M.M., Feigenson L., Halberda J. Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS One 2011, 6:e23749. 10.1371/journal.pone.0023749.
60. McCloskey M., Caramazza A., Basili A. Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia. Brain and Cognition 1985, 4:171-196.
61. McLean J.F., Hitch G.J. Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology 1999, 74:240-260.
62. Mundy E., Gilmore C.K. Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology 2009, 103:490-502.
63. Passolunghi M.C., Cornoldi C., De Liberto S. Working memory and intrusions of irrelevant information in a group of specific poor problem solvers. Memory & Cognition 1999, 27:779-790.
64. Passolunghi M.C., Lanfranchi S. Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade. British Journal of Educational Psychology 2012, 82:42-63.
65. Passolunghi M.C., Mammarella I.C., Altoè G. Cognitive abilities as precursors of the early acquisition of mathematical skills during first through second grades. Developmental Neuropsychology 2008, 33:229-250.
66. Passolunghi M.C., Pazzaglia F. Individual differences in memory updating in relation to arithmetic problem solving. Learning and Individual Differences 2004, 14:219-230.
67. Passolunghi M.C., Pazzaglia F. A comparison of updating processes in children good or poor in arithmetic word problem-solving. Learning and Individual Differences 2005, 15:257-269.
68. Piazza M. Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences 2010, 14:542-551.
69. Raven J.C. Standard progressive matrices 1976, Oxford Psychologists Press, Oxford, UK.
70. Ruff R.M., Light R.H., Parker S.B., Levin H.S. The psychological construct of word fluency. Brain and Language 1997, 57:394-405.
71. Runeson S., Juslin P., Olsson H. Visual perception of dynamic properties: Cue heuristics versus direct-perceptual competence. Psychological Review 2000, 107:525-555.
72. Russell R.L., Ginsburg H.P. Cognitive analysis of children's mathematical difficulties. Cognition and Instruction 1984, 1:217-244.
73. Schneider M., Grabner R.H., Paetsch J. Mental number line, number line estimation, and mathematical achievement: Their interrelations in Grades 5 and 6. Journal of Educational Psychology 2009, 101:359-372.
74. Siegler R.S., Booth J.L. Development of numerical estimation in young children. Child Development 2004, 75:428-444.
75. Siegler R.S., Opfer J. The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science 2003, 14:237-243.
76. 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.
77. Swanson H.L. Short-term memory and working memory: Do both contribute to our understanding of academic achievement in children and adults with learning disabilities?. Journal of Learning Disabilities 1994, 27:34-50.
78. Swanson H.L. Working memory and phonological processing as predictors of children's mathematical problem solving at different ages. Memory & Cognition 2004, 32:648-661.
79. Swanson H.L. Cross-sectional and incremental changes in working memory and mathematical problem solving. Journal of Educational Psychology 2006, 98:265-281.
80. Swanson H.L. Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children. Journal of Educational Psychology 2011, 103:821-837.
81. Swanson H.L., Beebe-Frankenberger M. The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology 2004, 96:471-491.
82. Swanson H.L., Sachse-Lee C. Mathematical problem solving and working memory in children with learning disabilities: Both executive and phonological processes are important. Journal of Experimental Child Psychology 2001, 79:294-321.
83. Temple C.M., Sherwood S. Representation and retrieval of arithmetical facts: Developmental difficulties. Quarterly Journal of Experimental Psychology: Human Experimental Psychology A 2002, 55:733-752.
84. von Aster M.G., Shalev R.S. Number development and developmental dyscalculia. Developmental Medicine & Child Neurology 2007, 49:868-873.
85. Wechsler D. Wechsler individual achievement Test-II-abbreviated 2001, Psychological Corporation, Harcourt Brace, San Antonio, TX.
86. Wilson K.M., Swanson H.L. Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit?. Journal of Learning Disabilities 2001, 34:237-248.