Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches

Learning and Individual Differences

Volumn 20, Issue 2, 2010, Pages 110-122

  Raghubar, Kimberly P ^a   Barnes, Marcia A ^b   Hecht, Steven A ^b  

^a UNIVERSITY OF HOUSTON   (United States)

^b UNIVERSITY OF TEXAS   (United States)

Author keywords

Development; Dual task studies; Individual differences; Mathematical processing; Working memory

Indexed keywords

EID: 75849135876     PISSN: 10416080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.lindif.2009.10.005     Document Type: Article

References (117)

1. Alibali M.W., and DiRusso A.A. The function of gesture in learning to count: More than keeping track. Cognitive Development 14 (1999) 37-56
2. Alloway T.P., Gathercole S.E., Kirkwood H., and Elliott J. The cognitive and behavioral characteristics of children with low working memory. Child Development 80 (2009) 606-621
3. Andersson U., and Lyxell B. Working memory deficit in children with mathematical difficulties: A general or specific deficit?. Journal of Experimental Child Psychology 96 (2007) 197-228
4. Ashcraft M.H., Donley R.D., Halas M.A., and Vakali M. Working memory, automaticity, and problem difficulty. In: Campbell J.I.D. (Ed). The nature and origins of mathematical skills (1992), Elsevier Science Publishers, Amsterdam 301-329
5. Baddeley A.D. Human memory: Theory and practice (1990), Allyn & Bacon, US
6. Baddeley A.D. Exploring the central executive. Quarterly Journal of Experimental Psychology: Human Experimental Psychology 49A (1996) 5-28
7. Baddeley A.D., and Hitch G.J. Working memory. In: Bower G.H. (Ed). The psychology of learning and motivation (1974), Academic Press, New York 47-90
8. Baddeley A.D., and Logie R.H. Working memory: The multiple-component model. In: Miyake A., and Shah P. (Eds). Models of working memory: Mechanisms of active maintenance and executive control (1999), Cambridge University Press, Cambridge 28-61
9. Baker S.C., Frith C.D., Frackowiak R.S.J., and Dolan R.J. Active representation of shape and spatial location in man. Cerebral Cortex 6 (1996) 612-619
10. Barnes M.A., and Fuchs L.S. Learning disabilities. In: Wolraich M.L., Drotar D., Dworkin P.H., et al. (Eds). Developmental-behavioral pediatrics: Evidence and practice (2008), Mosby, Philadelphia 445-466
11. Barnett W.S., Kwanghee J., Yarosz D.J., Thomas J., Hornbeck A., Stechuk R., et al. Educational effects of the Tools of the Mind curriculum: A randomized trial. Early Childhood Research Quarterly 23 (2008) 299-313
12. Berch D.B. Working memory and mathematical cognitive development: limitations of limited-capacity resource models. Developmental Neuropsychology 33 (2008) 427-446
13. 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 99 (2008) 288-308
14. Bisanz J., and LeFevre J. Strategic and nonstrategic processing in the development of mathematical cognition. In: Bjorklund D.F. (Ed). Children's strategies: Contemporary views of cognitive development (1990), Erlbaum, Hillsdale, NJ
15. Bisanz J., Sherman J.L., Rasmussen C., and Ho E. Development of arithmetic skills and knowledge in preschool children. In: Campbell J.I.D. (Ed). Handbook of mathematical cognition (2005), Psychology Press, New York 143-162
16. Bjorklund D.F. Children's thinking: Cognitive development and individual differences. 4th ed. (2005), Thomson/Wadsworth, Belmont, California
17. Blair C., Gamson D., Thorne S., and Baker D. Rising mean IQ: Cognitive demand of mathematics education for young children, population exposure to formal schooling, and the neurobiology of the prefrontal cortex. Intelligence 33 (2005) 93-106
18. Blair C., and Razza R.P. Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development 78 (2007) 647-663
19. Bull R., Espy K.A., and Wiebe S.A. Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at 7 years. Developmental Neuropsychology 33 (2008) 205-228
20. Bull R., Johnston R.S., and Roy J.A. Exploring the roles of the visual-spatial sketch pad and central executive in children's arithmetical skills: Views from cognition and developmental neuropsychology. Developmental Neuropsychology 15 (1999) 421-442
21. Butterworth B. The mathematical brain (1999), Macmillan, London
22. Butterworth B., and Reigosa V. Information processing deficits in dyscalculia. In: Berch D.B., and Mazzocco M.M.M. (Eds). Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (2007), Paul H. Brookes Publishing Co, Baltimore, Maryland 107-120
23. Campbell J.I.D., and Clarke J.M. Cognitive number processing: An encoding-complex perspective. In: Campbell J.I.D. (Ed). The nature and origins of numerical skills (1992), Elsevier Science Publishers, Amsterdam 457-492
24. Case R., and Okamoto Y. The role of central conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development 61 (1996) v-265
25. Connor C.M., Morrison F.J., and Katch L.E. Beyond the reading wars: Exploring the effect of child instruction interactions on growth in early reading. Scientific Studies of Reading 8 (2004) 305-336
26. Cornoldi C., Rigoni F., Venneri A., and Vecchi T. Passive and active processes in visuo-spatial memory: Double dissociation in developmental learning disabilities. Brain and Cognition 43 (2000) 117-120
27. D'Amico A., and Guarnera M. Exploring working memory in children with low arithmetical achievement. Learning and Individual Differences 15 (2005) 189-202
28. Dehaene S. Varieties of numerical abilities. Cognition 44 (1992) 1-42
29. De Rammelaere S., Stuyven E., and Vandierendonck A. The contribution of working memory resources in the verification of simple mental arithmetic sums. Psychological Research 62 (1999) 72-77
30. De Rammelaere S., Stuyven E., and Vandierendonck A. Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved?. Memory and Cognition 29 (2001) 267-273
31. DeStefano D., and LeFevre J. The role of working memory in mental arithmetic. European Journal of Cognitive Psychology 16 (2004) 353-386
32. Doehring D.G. The tangled web of behavioral research on developmental dyslexia. In: Benton A.L., and Pearl D. (Eds). Dyslexia: An appraisal of current knowledge (1978), Oxford University Press, New York 123-138
33. Duverne S., Lemaire P., and Vandierendonck A. Do working-memory executive components mediate the effects of age on strategy selection or on strategy execution? Insights from arithmetic problem solving. Psychological Research 72 (2008) 27-38
34. Engle R.W. Working memory capacity as executive attention. Current Directions in Psychological Science 11 (2002) 19-23
35. Engle R.W., Tuholski S.W., Laughlin J.E., and Conway A.R.A. The effect of memory load on negative priming: An individual differences investigation. Memory and Cognition 27 (1999) 1042-1050
36. English L.H., Barnes M.A., Taylor H.B., and Landry S.H. Mathematical development in spina bifida. Developmental Disabilities Research Reviews 15 (2009) 28-34
37. Fletcher J.M. Predicting math outcomes: Reading predictors and comorbidity. Journal of Learning Disabilities 38 (2005) 308-312
38. Fletcher J.M., Lyon G.R., Fuchs L.S., and Barnes M.A. Learning disabilities: From identification to intervention (2007), The Guilford Press, New York
39. Fuchs L.S., Compton D.L., Fuchs D., Paulsen K., Bryant J.D., and Hamlett C.L. The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology 97 (2005) 493-513
40. 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 98 (2006) 29-43
41. Fuchs L.S., Fuchs D., Stuebing K., Fletcher J.M., Hamlett C.L., and Lambert W. Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?. Journal of Educational Psychology 100 (2008) 30-47
42. Furst A.J., and Hitch G.J. Separate roles for executive and phonological components of working memory in mental arithmetic. Memory and Cognition 28 (2000) 774-782
43. Garon N., Bryson S.E., and Smith I.M. Executive function in preschoolers: A review using an integrative framework. Psychological Bulletin 134 (2008) 31-60
44. Geary D.C. Sexual selection and sex differences in mathematical abilities. Behavioral and Brain Sciences 19 (1996) 229-284
45. Geary D.C., Hamson C.O., and Hoard M.K. Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology 77 (2000) 236-263
46. Geary D.C., and Hoard M.K. Learning disabilities in arithmetic and mathematics. In: Campbell J.I.D. (Ed). The handbook of mathematical cognition (2005), Psychology Press, New York 253-267
47. Geary D.C., Hoard M.K., Byrd-Craven J., and DeSoto M.C. 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 (2004) 121-151
48. Geary D.C., Hoard M.K., Byrd-Craven J., Nugent L., and Numtee C. Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development 78 (2007) 1343-1359
49. Geary D.C., Hoard M.K., and Hamson C.O. Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology 74 (1999) 213-239
50. Geary D.C., Hoard M.K., Nugent L., and Byrd-Craven J. Strategy use, long-term memory, and working memory capacity. In: Berch D.B., and Mazzocco M.M.M. (Eds). Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (2007), Paul H. Brookes Publishing Co, Baltimore, Maryland 83-105
51. Geary D.C., Hoard M.K., Nugent L., and Byrd-Craven J. Development of number line representations in children with mathematical learning disability. Developmental Neuropsychology 33 (2008) 277-299
52. Gerton B.K., Brown T.T., Meyer-Lindenberg A., Kohn P., Holt J.L., Olsen R.K., et al. Shared and distinct neurophysiological components of the digits forward and backward tasks as revealed by functional neuroimaging. Neuropsychologia 42 (2004) 1781-1787
53. Ginsburg H.P., Klein A., and Starkey P. The development of children's mathematical thinking: Connecting research with practice. In: Damon W., Sigel I.E., and Renninger A.K. (Eds). Handbook of child psychology. 5th ed. Child psychology in practice Vol. 4 (1998), John Wiley & Sons Inc., NJ 401-476
54. Halberda J., Mazzocco M.M.M., and Feigenson. Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455 (2008) 665-669
55. Hale S., Bronik M.D., and Fry A.F. Verbal and spatial working memory in school-age children: Developmental differences in susceptibility to interference. Developmental Psychology 33 (1997) 364-371
56. Hecht S.A. Counting on working memory in simple arithmetic when counting is used for problem solving. Memory and Cognition 30 (2002) 447-455
57. Hecht S.A., Torgesen J.K., Wagner R.K., and Rashotte C.A. The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology 79 (2001) 192-227
58. Hitch G.J., and McAuley E. Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology 82 (1991) 375-386
59. Holmes J., and Adams J.W. Working memory and children's mathematical skills: Implications for mathematical development and mathematical curricula. Educational Psychology 26 (2006) 339-366
60. Holmes J., Adams J.W., and Hamilton C.J. The relationship between visuospatial sketchpad capacity and children's mathematical skills. European Journal of Cognitive Psychology 20 (2008) 272-289
61. Hulme C., Thomson N., Muir C., and Lawrence A. Speech rate and the development of short-term memory span. Journal of Experimental Child Psychology 38 (1984) 241-253
62. Huttenlocher J., Jordan N.C., and Levine S.C. A mental model for early arithmetic. Journal of Experimental Psychology: General 123 (1994) 284-296
63. Imbo I., and Vandierendonck A. The role of phonological and executive working memory resources in simple arithmetic strategies. European Journal of Cognitive Psychology 19 (2007) 910-933
64. Imbo I., and Vandierendonck A. The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology 96 (2007) 284-309
65. Imbo I., Vandierendonck A., and De Rammelaere S. The role of working memory in the carry operation of mental arithmetic: Number and value of the carry. Quarterly Journal of Experimental Psychology 60 (2007) 708-731
66. Imbo I., Vandierendonck A., and Vergauwe E. The role of working memory in carrying and borrowing. Psychological Research 71 (2008) 467-483
67. Kalaman D.A., and LeFevre J. Working memory demands of exact and approximate addition. European Journal of Cognitive Psychology 19 (2007) 187-212
68. Kintsch W., and Greeno J.G. Understanding and solving word arithmetic problems. Psychological Review 92 (1985) 109-129
69. Klein J.S., and Bisanz J. Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology 54 (2000) 105-115
70. Knops A., Thirion B., Hubbard E.M., Michel V., and Dehaene S. Recruitment of an area involved in eye movements during mental arithmetic. Science 324 (2009) 1583-1585
71. Kroesbergen E.H., Van Luit J.E.H., Van Lieshout E.C.D.M., Van Loosbroek E., and Van de Rijt B.A.M. Individual differences in early numeracy: The role of executive functions and subitizing. Journal of Psychoeducational Assessment 27 (2009) 226-236
72. Kyttala M., and Lehto J.E. Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education 23 (2008) 77-94
73. Landerl K., Bevan A., and Butterworth B. Developmental dyscalculia and basic numerical capacities: A study of 8-9 year-old students. Cognition 93 (2004) 99-125
74. Lee K., and Kang S. Arithmetic operation and working memory: Differential suppression in dual tasks. Cognition 83 (2002) B63-B68
75. LeFevre J., DeStefano D., Coleman B., and Shanahan T. Mathematical cognition and working memory. In: Campbell J.I.D. (Ed). The handbook of mathematical cognition (2005), Psychology Press, New York 361-378
76. LeFevre J., Lei Q., Smith-Chant B., and Mullins D. Multiplication by eye and by ear for Chinese-speaking and English-speaking adults. Canadian Journal of Experimental Psychology 55 (2001) 277-284
77. LeFevre J., and Liu J. Numerical cognition: Single-digit multiplication skills of adults from China and Canada. Mathematical Cognition 3 (1997) 31-62
78. Lemaire P., Abdi H., and Fayol M. The role of working memory resources in simple cognitive arithmetic. European Journal of Cognitive Psychology 8 (1996) 73-103
79. Li S.-C., and Lewandowsky S. Forward and backward recall: Different retrieval processes. Journal of Experimental Psychology. Learning, Memory, and Cognition 21 (1995) 837-847
80. Liu M., and Tannock R. Working memory and inattentive behavior in a community sample of children. Behavioral and Brain Functions 3 (2007)
81. Logie R.H., Gilhooly K.J., and Wynn V. Counting on working memory in arithmetic problem solving. Memory and Cognition 22 (1994) 395-410
82. Mabbot D.J., and Bisanz J. Computational skills, working memory, and conceptual knowledge in older children with mathematics learning disabilities. Journal of Learning Disabilities 41 (2008) 15-28
83. Mazzocco M.M.M. Defining and differentiating mathematical learning disabilities and difficulties. In: Berch D.B., and Mazzocco M.M.M. (Eds). Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (2007), Paul H. Brookes Publishing Co, Baltimore, Maryland 7-27
84. Mazzocco M.M., and Kover S.T. A longitudinal assessment of executive function skills and their association with math performance. Child Neuropsychology 13 (2007) 18-45
85. McCloskey M. Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition 44 (1992) 107-157
86. McKenzie B., Bull R., and Gray C. The effects of phonological and visual-spatial interference on children's arithmetical performance. Educational and Child Psychology 20 (2003) 93-108
87. McLean J.F., and Hitch G.J. Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology 74 (1999) 240-260
88. Miyake A., and Shah P. Models of working memory: Mechanisms of active maintenance and executive control (1999), Cambridge University Press, Cambridge, UK
89. Noel M.-P., Desert M., Aubrun A., and Seron X. Involvement of short-term memory in complex mental calculation. Memory and Cognition 29 (2001) 34-42
90. Olesen P.J., Westerberg H., and Klingberg T. Increased prefrontal and parietal activity after training of working memory. Nature Neuroscience 7 (2003) 75-79
91. Passolunghi M.C., and Cornoldi C. Working memory failures in children with arithmetical difficulties. Child Neuropsychology 14 (2008) 387-400
92. Passolunghi M.C., and Siegel L.S. Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology 80 (2001) 44-57
93. Passolunghi M.C., and Siegel L.S. Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology 88 (2004) 348-367
94. Raghubar K.P. The role of working memory and finger representation in single-digit calculation [Abstract]. Journal of the International Neuropsychological Society (2009) 15 Suppl. 1. 175
95. Raghubar K.P., Cirino P., Barnes M.A., Ewing-Cobbs L., Fletcher J., and Fuchs L. Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties. Journal of Learning Disabilities 42 (2009) 356-371
96. Rasmussen C., and Bisanz J. Representation and working memory in early arithmetic. Journal of Experimental Child Psychology 91 (2005) 137-157
97. Reukhala M. Mathematical skills in ninth-graders: Relationship with visuo-spatial abilities and working memory. Educational Psychology 21 (2001) 387-399
98. Rosen V.M., and Engle R.W. The role of working memory capacity in retrieval. Journal of Experimental Psychology. General 126 (1997) 211-227
99. Rosselli M., Matute E., Pinto N., and Ardila A. Memory abilities in children with subtypes of dyscalculia. Developmental Neuropsychology 30 (2006) 801-818
100. Rourke B.P. Arithmetic disabilities, specific and otherwise: A neuropsychological perspective. Journal of Learning Disabilities 26 (1993) 214-226
101. Seitz K., and Schumann-Hengsteler R. Mental multiplication and working memory. European Journal of Cognitive Psychology 12 (2000) 552-570
102. Seitz K., and Schumann-Hengsteler R. Phonological loop and central executive processes in mental addition and multiplication. Psychologische Beitrage 44 (2002) 275-302
103. Seyler D.J., Kirk E.P., and Ashcraft M.H. Elementary subtraction. Journal of Experimental Psychology. Learning, Memory, and Cognition 29 (2003) 1339-1352
104. Siegel L.S., and Ryan E.B. The development of working memory in normally achieving and subtypes of learning disabled children. Child Development 60 (1989) 973-980
105. Siegler R.S., and Booth J.L. Development of numerical estimation: A review. In: Campbell J.I.D. (Ed). The handbook of mathematical cognition (2005), Psychology Press, New York 197-212
106. Simon T.J., and Rivera S.M. Neuroanatomical approaches to the study of mathematical ability and disability. In: Berch D.B., and Mazzocco M.M.M. (Eds). Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (2007), Paul H. Brookes Publishing Co, Baltimore, Maryland 283-305
107. Swanson H.L. Working memory and phonological processing as predictors of children's mathematical problem solving at different ages. Memory and Cognition 32 (2004) 648-661
108. Swanson H.L., and 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 96 (2004) 471-491
109. Swanson H.L., and Jerman O. Math disabilities: A selective meta-analysis of the literature. Review of Educational Research 76 (2006) 249-274
110. Temple C.M., and Sherwood S. Representation and retrieval of arithmetical facts: Developmental difficulties. Quarterly Journal of Experimental Psychology Section A, Human Experimental Psychology 55A (2002) 733-752
111. Thorell L.B., Lindqvist S., Bergman S., Bohlin G., and Klingberg T. Training and transfer effects of executive functions in preschool children. Developmental Science 11 (2008) 969-976
112. Tronsky L.N. Strategy use, the development of automaticity, and working memory involvement in complex multiplication. Memory & Cognition 33 (2005) 927-940
113. van der Sluis S., van der Leij A., and de Jong P.F. Working memory in Dutch children with reading- and arithmetic-related LD. Journal of Learning Disabilities 38 (2005) 207-221
114. Wilson K.M., and Swanson H.L. Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit?. Journal of Learning Disabilities 34 (2001) 237-248
115. Wu S.S., Meyer M.L., Maeda U., Salimpoor V., Tomiyama S., Geary D.C., et al. Standardized assessment of strategy use and working memory in early mental arithmetic performance. Developmental Neuropsychology 33 (2008) 365-393
116. Zentall S.S. Math performance of students with ADHD: Cognitive and behavioral contributors and interventions. In: Berch D.B., and Mazzocco M.M.M. (Eds). Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (2007), Paul H. Brookes Publishing Co, Baltimore, Maryland 219-243
117. Zorzi M., Priftis K., and Umilta C. Neglect disrupts the mental number line. Nature 417 (2002) 138