The role of working memory in mental arithmetic

European Journal of Cognitive Psychology

Volumn 16, Issue 3, 2004, Pages 353-386

  DeStefano, Diana ^a   LeFevre, Jo Anne ^a  

^a CARLETON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARITHMETIC; DEPTH PERCEPTION; HUMAN; INSTRUMENTAL CONDITIONING; MEDICAL LITERATURE; PHONETICS; PRIORITY JOURNAL; REVIEW; TASK PERFORMANCE; WORKING MEMORY;

EID: 2342488769     PISSN: 09541446     EISSN: None     Source Type: Journal    
DOI: 10.1080/09541440244000328     Document Type: Review

References (115)

1. Adams, J. W., & Hitch, G. J. (1997). Working memory in children's mental arithmetic. Journal of Experimental Child Psychology, 67, 21-38.
2. Adams, J. W., & Hitch, G. J. (1998). Children's mental arithmetic and working memory. In C. Donlan (Ed.), The development of mathematical skills (pp. 153-174). Hove, UK: Psychology Press.
3. Anderson, J. R., Reder, L. M., & Lebiere, C. (1996). Working memory: Activation limitations on retrieval. Cognitive Psychology, 30, 221-256.
4. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75-106.
5. Ashcraft, M. H. (1995). Cognitive psychology and simple arithmetic: A review and summary of new directions. Mathematical Cognition, 1, 3-34.
6. Ashcraft, M. H., & Battaglia, J. (1978). Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition. Journal of Experimental Psychology: Human Learning and Memory, 4, 527-538.
7. Ashcraft, M. H., Donley, R. D., Halas, M. A., & Vakali, M. (1992). Working memory, automaticity, and problem difficulty. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 301-329). Amsterdam: Elsevier Science Publishers.
8. Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130, 224-237.
9. Ashcraft, M. H., Kirk, E. P., & Hopko, D. (1998). On the cognitive consequences of math anxiety. In C. Donlan (Ed.), The development of mathematical skills (pp. 175-196). Hove, UK: Psychology Press.
10. Baddeley, A. D. (1986). Working memory. Oxford, UK: Oxford University Press.
11. Baddeley, A. D. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology: Human Experimental Psychology, 49A, 5-28.
12. Baddeley, A. D. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4, 417-423.
13. Baddeley, A. D., Emslie, H., Kolodny, J., & Duncan, J. (1998). Random generation and the executive control of working memory. Quarterly Journal of Experimental Psychology: Human Experimental Psychology, 51A, 819-852.
14. Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. Bower (Ed.), The psychology of learning and motivation (Vol. 8, pp. 47-90). New York: Academic Press.
15. Baddeley, A. D., Lewis, V. J., & Vallar, G. (1984). Exploring the articulatory loop. Quarterly Journal of Experimental Psychology, 36, 233-252.
16. Baddeley, A. D., & Logie, R. H. (1999). Working memory: The multiple-component model. In A. Miyake & P. Shah (Eds.), Models of working memory (pp. 28-61). Cambridge, UK: Cambridge University Press.
17. Barnard, P. J. (1999). Interacting cognitive subsystems: Modeling working memory phenomena within a multiprocessor architecture. In A. Miyake & P. Shah (Eds.), Models of working memory (pp. 298-339). Cambridge, UK: Cambridge University Press.
18. Bisanz, J., & LeFevre, J. (1992). Understanding elementary mathematics. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 113-136). Amsterdam: Elsevier Science Publishers.
19. Blankenberger, S. (2001). The arithmetic tie effect is mainly encoding-based. Cognition, 82, B15-B24.
20. Bull, R., Johnston, R. S., & Roy, J. A. (1999). 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, 421-442.
21. Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children's mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273-293.
22. Butterworth, B., Cipolotti, L., & Warrington, E. K. (1996). Short-term memory impairment and arithmetical ability. Quarterly Journal of Experimental Psychology, 49A, 251-262.
23. Campbell, J. I. D. (1987). Production, verification, and priming of multiplication facts. Memory and Cognition, 15, 349-364.
24. Campbell, J. I. D. (1994). Architectures for numerical cognition. Cognition, 53, 1-44.
25. Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121-164.
26. Campbell, J. I. D. (1997). On the relation between skilled performance of simple division and multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 1140-1159.
27. Campbell, J. I. D. (1998). Notational and linguistic influence in cognitive arithmetic: Comment on Noël, Fias, and Brysbaert (1997). Cognition, 67, 353-364.
28. Campbell, J. I. D. (1999). Division by multiplication. Memory and Cognition, 18, 245-275.
29. Campbell, J. I. D., & Clark, J. M. (1988). An encoding-complex view of cognitive number processing: Comment on McCloskey, Sokol, & Goodman (1986). Journal of Experimental Psychology: General, 117, 204-214.
30. Campbell, J. I. D., & Clark, J. M. (1992). Cognitive number processing: An encoding-complex perspective. In J. I. D. Campbell (Ed.), The nature and origins of numerical skills (pp. 457-492). Amsterdam: Elsevier Science Publishers.
31. Campbell, J. I. D., & Fugelsang, J. (2001). Strategy choice for arithmetic verification: Effects of numerical surface form. Cognition, 80, B21-B30.
32. Campbell, J. I. D., Kanz, C. L., & Xue, Q. (1999). Number processing in Chinese-English bilinguals. Mathematical Cognition, 5, 1-39.
33. Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299-315.
34. Case, R., Kurland, D. M., & Goldberg, J. (1982). Operational efficiency and the growth of short-term memory span. Journal of Experimental Child Psychology, 33, 386-404.
35. Cowan, N. (1999). An embedded-processes model of working memory. In A. Miyake & P. Shah (Eds.), Models of working memory (pp. 62-101). Cambridge, UK: Cambridge University Press.
36. Daneman, M., & Carpenter, P. A. (1980). Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19, 450-466.
37. Daneman, M., & Merikle, P. M. (1996). Working memory and language comprehension: A meta-analysis. Psychonomic Bulletin and Review, 3, 422-433.
38. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.
39. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
40. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.
41. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970-974.
42. Della Sala, S., Gray, C., Baddeley, A., Allamano, N., & Wilson, L. (1999). Pattern span: A tool for unwelding visuo-spatial memory. Neuropsychologia, 37, 1189-1199.
43. De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (1999). The contribution of working memory resources in the verification of simple mental arithmetic sums. Psychological Research, 62, 72-77.
44. De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (2001). Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved? Memory and Cognition, 29, 267-273.
45. Dowker, A. (1998). Individual differences in normal arithmetical development. In C. Donlan (Ed.), The development of mathematical skills (pp. 275-302). Hove, UK: Psychology Press.
46. Engle, R. W., Cantor, J., & Carullo, J. J. (1992). Individual differences in working memory and comprehension: A test of four hypotheses. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18, 972-992.
47. Engle, R. W., Kane, M. J., & Tuholski, S. W. (1999). Individual differences in working memory capacity and what they tell use about controlled attention, general fluid intelligence and functions of the prefrontal cortex. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 102-134). New York: Cambridge University Press.
48. Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102, 211-245.
49. Fürst, A. J., & Hitch, G. J. (2000). Different roles for executive and phonological components of working memory in mental arithmetic. Memory and Cognition, 28, 774-782.
50. Geary, D. C., & Widaman, K. F. (1992). Numerical cognition: On the convergence of componential and psychometric models. Intelligence, 16(1), 47-80.
51. Geary, D. C., & Wiley, J. G. (1991). Cognitive addition: Strategy choice and speed of processing differences in young and elderly adults. Psychology and Aging, 6, 474-483.
52. Gilhooly, K. J., Logie, R. H., Wetherick, N., & Wynn, V. (1993). Working memory and strategies in syllogistic reasoning tasks. Memory and Cognition, 21, 115-124.
53. Hayes, J. R. (1973). On the function of visual imagery in elementary mathematics. In W. Chase (Ed.), Visual information processing (pp. 177-214). New York: Academic Press.
54. Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition of multi-digit addends. Current Psychology of Cognition, 13, 207-245.
55. Hecht, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults. Memory and Cognition, 27, 1097-1107.
56. Hecht, S. A. (2002). Counting on working memory in simple arithmetic when counting is used for problem solving. Memory and Cognition, 30(3), 447-455.
57. Hitch, G. J. (1978a). Mental arithmetic: Short-term storage and information processing in a cognitive skill. In A. M. Lesgold, J. W. Pellegrino, S. D. Fokkema, & R. Glaser (Eds.), Cognitive psychology and instruction (pp. 331-338). New York: Plenum.
58. Hitch, G. J. (1978b). The role of short-term working memory in mental arithmetic. Cognitive Psychology, 10, 302-323.
59. Hitch, G. J., Towse, J. N., & Hutton, U. (2001). What limits children's working memory span? Theoretical accounts and applications for scholastic development. Journal of Experimental Psychology: General, 130, 184-198.
60. Jurden, F. H. (1995). Individual differences in working memory and complex cognition. Journal of Educational Psychology, 87, 93-102.
61. Just, M. A., & Carpenter, P. A. (1992). A capacity theory of comprehension: Individual differences in working memory. Psychological Review, 99, 122-149.
62. Kane, M. J., Bleckley, M. K., Conway, A. R. A., & Engle, R. W. (2001). A controlled-attention view of working-memory capacity. Journal of Experimental Psychology: General, 130, 169-183.
63. Kaye, D. B., deWinstanley, P., Chen, Q., & Bonnefil, V. (1989). Development of efficient arithmetic computation. Journal of Educational Psychology, 81, 467-480.
64. Kieras, D. E., Meyer, D. E., Mueller, S., & Seymour, T. (1999). Insights into working memory from the perspective of the EPIC architecture for modeling skilled perceptual-motor and cognitive human performance. In A. Miyake & P. Shah (Eds.), Models of working memory (pp. 183-223). Cambridge, UK: Cambridge University Press.
65. Klein, J. S., & Bisanz, J. (2000). Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology, 54, 105-115.
66. Kulak, A. (1993). Spatial processing and arithmetic performance. Unpublished PhD thesis, Carleton University, Ottawa, Canada.
67. Leather, C. V., & Henry, L. A. (1994). Working memory span and phonological awareness tasks as predictors of early reading ability. Journal of Experimental Child Psychology, 58, 88-111.
68. Lee, K., & Kang, S. (2002). Arithmetic operation and working memory: Differential suppression in dual tasks. Cognition, 83, B63-B68.
69. LeFevre, J. (1998). Interactions among encoding, calculation, and production processes in the multiplication performance of Chinese-speaking adults. Mathematical Cognition, 4, 47-65.
70. LeFevre, J., Bisanz, J., Hubbard, K. E., Buffone, L., Greenham, S. L., & Sadesky, G. S. (1996a). Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology: General, 125, 284-306.
71. LeFevre, J., Bisanz, J., & Mrkonjic, L. (1988). Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts. Memory and Cognition, 16, 45-53.
72. LeFevre, J., & Kulak, A. G. (1994). Individual differences in the obligatory activation of addition facts. Memory and Cognition, 22, 188-200.
73. LeFevre, J., Kulak, A. G., & Bisanz, J. (1991). Individual differences and developmental change in the associative relations among numbers. Journal of Experimental Child Psychology, 52, 256-274.
74. LeFevre, J., Lei, Q., Smith-Chant, B., & Mullins, D. (2001). Multiplication by eye and by ear for Chinese-speaking and English-speaking adults. Canadian Journal of Experimental Psychology, 55, 277-284.
75. LeFevre, J., & Liu, J. (1997). Numerical cognition: Single-digit multiplication skills of adults from China and Canada. Mathematical Cognition, 3, 31-62.
76. LeFevre, J., & Morris, J. (1999). More on the relation between division and multiplication in simple arithmetic: Evidence for mediation of division solutions via multiplication. Memory and Cognition, 27, 803-812.
77. LeFevre, J., Sadesky, G. S., & Bisanz, J. (1996b). Selection of procedures in mental addition: Reassessing the problem-size effect in adults. Journal of Experimental Psychology: Learning Memory, and Cognition, 22, 216-230.
78. LeFevre, J., Smith-Chant, B. L., Hiscock, K., Daley, K. E., & Morris, J. (in press). Young adults' strategic choices in simple arithmetic: Implications for the development of mathematical representations. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Recent research and theory. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
79. Lemaire, P., Abdi, H., & Fayol, M. (1996). The role of working memory resources in simple cognitive arithmetic. European Journal of Cognitive Psychology, 8, 73-103.
80. Lemaire, P., Barrett, S., Fayol, M., & Abdi, H. (1994). Automatic activation of addition and multiplication facts in elementary school children. Journal of Experimental Child Psychology, 57, 224-258.
81. Little, T. D., & Widaman, K. F. (1995). A production task evaluation of individual differences in mental addition skill development: Internal and external validation of chronometric models. Journal of Experimental Child Psychology, 60, 361-392.
82. Logie, R. H. (1995). Visuo-spatial working memory. Hove, UK: Lawrence Erlbaum Associates Ltd.
83. Logie, R. H., & Baddeley, A. D. (1987). Cognitive processes in counting. Journal of Experimental Psychology: Learning, Memory and Cognition, 13, 310-326.
84. Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in mental arithmetic. Memory and Cognition, 22, 395-410.
85. Logie, R. H., & Marchetti, C. (1991). Visuo-spatial working memory: Visual, spatial, or central executive? In R. H. Logie & M. Denis (Eds.), Mental images in human cognition (pp. 105-115). Amsterdam: North Holland Press.
86. Lovett, M. C., Reder, L. M., & Lebiere, C. (1999). Modeling working memory in a unified architecture: An ACT-R perspective. In A. Miyake & P. Shah (Eds.), Models of working memory (pp. 135-181). Cambridge, UK: Cambridge University Press.
87. McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44, 107-157.
88. McCloskey, M., Caramazza, A., & Basili, A. (1985). Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia. Brain and Cognition, 4, 171-196.
89. McCloskey, M., & Macaruso, P. (1995). Representing and using numerical information. American Psychologist, 50, 351-363.
90. McLean, J. F., & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology, 74, 240-260.
91. Miller, K. F., Perlmutter, M., & Keating, D. (1984). Cognitive arithmetic: Comparison of operations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 46-60.
92. Miyake, A. (2001). Individual differences in working memory: Introduction to the special section. Journal of Experimental Psychology: General, 130, 163-168.
93. Miyake, A., & Shah, P. (1999). Models of working memory: Mechanisms of active maintenance and executive control. Cambridge, UK: Cambridge University Press.
94. Noël, M., Désert, M., Aubrun, A., & Seron, X. (2001). Involvement of short-term memory in complex mental calculation. Memory and Cognition, 29, 34-42.
95. Noël, M., Fias, W., & Brysbaert, M. (1997). About the influence of the presentation format on arithmetical-fact retrieval processes. Cognition, 63, 335-374.
96. Noël, M., & Seron, X. (1997). On the existence of intermediate representations in numerical processing. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 697-720.
97. Penner-Wilger, M., Leth-Steensen, C., & LeFevre, J. (2002). Decomposing the problem-size effect: A comparison of response time distributions across cultures. Memory and Cognition, 30(7), 1160-1167.
98. Perfetti, C. A. (1985). Reading ability. New York: Oxford University Press.
99. Quinn, J. G., & McConnell, J. (1999). Manipulation of interference in the passive visual store. European Journal of Cognitive Psychology, 11, 313-389.
100. Robinson, K. M. (2001). The validity of verbal reports in children's subtraction. Journal of Educational Psychology, 93, 211-222.
101. Salthouse, T. A., Mitchell, R. D., Skovronek, E., & Babcock, R. L. (1989). Effects of adult age and working memory on reasoning and spatial abilities. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 507-516.
102. Seitz, K., & Schumann-Hengsteler, R. (2000). Mental multiplication and working memory. European Journal of Cognitive Psychology, 12, 552-570.
103. Seitz, K., & Schumann-Hengsteler, R. (2002). Phonological loop and central executive processes in mental addition and multiplication. Psychologische Beiträge, 44, 275-302.
104. Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2002). Elementary subtraction. Manuscript under review.
105. Shah, P., & Miyake, A. (1996). The separability of working memory resources for spatial thinking and language processing: An individual differences approach. Journal of Experimental Psychology: General, 125, 4-27.
106. Siegel, L. S. (1994). Working memory and reading: A life-span perspective. International Journal of Behavioral Development, 17, 109-124.
107. Smith-Chant, B. L., & LeFevre, J. (in press). Doing as they are told and telling it like it is: Self-reports in mental arithmetic. Memory and Cognition.
108. Stazyk, E. H., Ashcraft, M. H., & Hamann, M. S. (1982). A network approach to simple multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8, 320-335.
109. Thibodeau, M. H., LeFevre, J., & Bisanz, J. (1996). The extension of the interference effect to multiplication. Canadian Journal of Experimental Psychology, 50, 393-396.
110. Trbovich, P. L., & LeFevre, J. (2002). Phonological and visual-spatial working memory in mental addition. Manuscript under review.
111. Turner, M. L., & Engle, R. W. (1989). Is working memory capacity task dependent? Journal of Memory and Language, 28, 127-154.
112. Vandierendonck, A. (2000). Analyzing human random time generation behavior: A methodology and a computer program. Behavior Research Methods, Instruments, and Computers, 32, 555-565.
113. Widaman, K. F., Geary, D. C., Cormier, O., & Little, T. D. (1989). A componential model of mental addition. Journal of Experimental Psychology: Learning, Memory and Cognition, 15, 898-919.
114. Zago, L., Pesenti, M., Mellet, E., Crivello, F., Mazoyer, B., & Tzourio-Mazoyer, N. (2001). Neural correlates of simple and complex mental calculation. NeuroImage, 13, 314-327.
115. Zbrodoff, N. J., & Logan, G. D. (1990). On the relation between production and verification tasks in the psychology of simple arithmetic. Journal of Experimental Psychology: Learning, Memory, and Cognition, 16, 83-97.