Mathematical cognition and working memory

The Handbook of Mathematical Cognition

Volumn , Issue , 2005, Pages 361-377

  LeFevre, Jo Anne ^a   DeStefano, Diana ^a   Coleman, Benjamin ^a   Shanahan, Tina ^a  

^a CARLETON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85078642176     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (131)

1. Ackerman, P. L., Beier, M. E., & Boyle, M. D. (2002). Individual differences in working memory within a nomological network of cognitive and perceptual speed abilities. Journal of Experimental Psychology: General, 131, 567-589.
2. Adams, J. W., & Hitch, G. J. (1997). Working memory and children's mental addition. Journal of Experimental Child Psychology, 67, 21-38.
3. Aiken, L. R., Jr. (1972). Language factors in learning mathematics. Review of Educational Research, 42, 359-385.
4. Anderson, J. R., & Lebiere, C. (1998). The atomic components of thought. Mahwah, NJ: Erlbaum.
5. Ashcraft, M. H. (1985). Is it farfetched that some of us remember our arithmetic facts? Journal for Research in Mathematics Education, 16, 99-105.
6. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75-106.
7. Achcraft, M. H. (1995). Cognitive psychology and simple arithmetic: A review and summary of new directions. Mathematical Cognition, 1, 3-34.
8. Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11, 181-185.
9. Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition and Emotion, 8, 97-125.
10. Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130, 224-237.
11. Ashcraft, M. H., Kirk, E. P., & Hopko, D. (1998). On the cognitive consequences of mathematics anxiety. In C. Donlan (Ed.), The development of mathematical skills (pp. 175-196). Hove, UK: Psychology Press.
12. Ayres, P. L. (1993). Why goal-free problems can facilitate learning. Contemporary Educational Psychology, 18, 376-381.
13. Ayres, P. L. (2001). Systematic mathematical errors and cognitive load. Contemporary Educational Psychology, 26, 227-248.
14. Ayres, P., & Sweller, J. (1990). Locus of difficulty in multistage mathematics problems. American Journal of Psychology, 103, 167-193.
15. Baddeley, A. D. (1986). Working memory. New York, NY: Clarendon Press/Oxford University Press.
16. Baddeley, A. D. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology: Human Experimental Psychology, 49A, 5-28.
17. Baddeley, A. D. (2002). Is working memory still working? European Psychologist, 7, 85-97.
18. Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G.H. Bower (Ed.), The psychology of learning and motivation (pp. 47-90). New York: Academic Press.
19. Baddeley, A. D., Lewis, V., & Vallar, G. (1984). Exploring the articulatory loop. Quarterly Journal of Experimental Psychology: Human Experimental Psychology, 36A, 233-252.
20. Baddeley, A. D., & Logie, R. H. (1999). Working memory: The multiple-component model. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 28-61). Cambridge: Cambridge University Press.
21. Baddeley, A., & Wilson, B. (2002). Prose recall and amnesia: Implications for the structure of working memory. Neuropsychologia, 40, 1737-1743.
22. 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: Mechanisms of active maintenance and executive control (pp. 298-339). Cambridge: Cambridge University Press.
23. Bull, R., & Johnston, R. S. (1997). Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology, 65, 1-24.
24. 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.
25. 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.
26. Campbell, J. I. D. (1994). Architectures for numerical cognition. Cognition, 53, 1-44.
27. Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121-164.
28. Campbell, J. I. D. (1998). Notational and linguistic influence in cognitive arithmetic: Comment on Noël, Fias, and Brysbaert (1997). Cognition, 67, 353-364.
29. Campbell, J. I. D., & Charness, N. (1990). Age-related declines in working memory skills: Evidence from a complex calculation task. Developmental Psychology, 26, 879-888.
30. Campbell, J. I. D., & Gunter, R. (2002). Calculation, culture, and the repeated operand effect. Cognition, 86, 71-96.
31. Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299-315.
32. Case, R. (1985). Intellectual development: Birth to adulthood. Orlando, FL: Academic Press.
33. 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.
34. Cocchini, G., Logie, R. H., Della Sala, S., MacPherson, S. E., & Baddeley, A. D. (2002). Concurrent performance of two memory tasks: Evidence for domain-specific working memory systems. Memory and Cognition, 30, 1086-1095.
35. Conway, A. R. A., & Engle, R. W. (1994). Working memory and retrieval: A resource-dependent inhibition model. Journal of Experimental Psychology: General, 123, 354-373.
36. Cowan, N. (1999). An embedded-processes model of working memory. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 62-101). Cambridge: Cambridge University Press.
37. Daneman, M., & Carpenter, P. A. (1980). Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19, 450-466.
38. Daneman, M., & Carpenter, P. A. (1983). Individual differences in integrating information between and within sentences. Journal of Experimental Psychology: Learning, Memory, and Cognition, 9, 561-583.
39. Daneman, M., & Merikle, P. M. (1996). Working memory and language comprehension: A meta-analysis. Psychonomic Bulletin and Review, 3, 422-433.
40. Dark, V. J., & Benbow, C. P. (1990). Enhanced problem translation and short-term memory: Components of mathematical talent. Journal of Educational Psychology, 82, 420-29.
41. Dark, V. J., & Benbow, C. P. (1991). Differential enhancement of working memory with mathematical versus verbal precocity. Journal of Educational Psychology, 83, 48-60.
42. De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (1999). The contribution of working memory resources in the verification of simple mental arithmetic sums. Psychological Research/Psychologische Forschung, 62, 72-77.
43. 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.
44. De Rammelaere, S., & Vandierendonck, A. (2001). Are executive processes used to solve simple arithmetic production tasks. Current Psychology Letters: Behavior, Brain and Cognition, 79-90.
45. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.
46. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970-974.
47. DeStefano, D., & LeFevre, J., (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16, 353-386.
48. 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.
49. Engle, R. W., Carullo, J. J., & Collins, K. W. (1991). Individual differences in working memory for comprehension and following directions. Journal of Educational Research, 84, 253-262.
50. Engle, R. W., Tuholski, S. W., Laughlin, J. E., & Conway, A. R. A. (1999). The effect of memory load on negative priming: An individual differences investigation. Memory and Cognition, 27, 1042-1050.
51. Ericsson, K. A., & Delaney, P. F. (1999). Long-term working memory as an alternative to capacity models of working memory in everyday skilled performance. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 257-297). New York: Cambridge University Press.
52. Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102, 211-245.
53. Fürst, A. J., & Hitch, G. J. (2000). Separate roles for executive and phonological components of working memory in mental arithmetic. Memory and Cognition, 28, 774-782.
54. Gathercole, S. E., & Pickering, S. J. (2000). Assessment of working memory in six- and seven-year-old children. Journal of Educational Psychology, 92, 377-390.
55. Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345-362.
56. Geary, D. C. (1994). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
57. Geary, D. C., Brown, S. C., & Samaranayake, V. A. (1991). Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Developmental Psychology, 27, 787-797.
58. Geary, D. C., Hoard, M. K., & Hamson, C. O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74, 213-239.
59. Griffin, S., & Case, R. (1997). Rethinking the primary school math curriculum: An approach based on cognitive science. Issues in Education, 3, 1-65.
60. Hambrick, D. Z., & Engle, R. W. (2002). Effects of domain knowledge, working memory capacity, and age on cognitive performance: An investigation of the knowledge-is-power hypothesis. Cognitive Psychology, 44, 339-387.
61. 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, 615-626.
62. 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.
63. Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition of multi-digit addends. Cahiers de Psychologie Cognitive/Current Psychology of Cognition, 13, 207-245.
64. Hecht, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults. Memory and Cognition, 27, 1097-1107.
65. Hecht, S. A. (2002). Counting on working memory in simple arithmetic when counting is used for problem solving. Memory and Cognition, 30, 447-455.
66. Hiebert, J., Carpenter, T. P., & Moser, J. M. (1982). Cognitive development and children's solutions to verbal arithmetic problems. Journal for Research in Mathematics Education, 13, 83-98.
67. Hitch, G. J. (1978). The role of short-term working memory in mental arithmetic. Cognitive Psychology, 10, 302-323.
68. Hitch, G. J., Halliday, M. S., & Littler, J. E. (1989). Item identification time and rehearsal rate as predictors of memory span in children. Quarterly Journal of Experimental Psychology: Human Experimental Psychology, 41, 321-337.
69. Hitch, G. J., & McAuley, E. (1991). Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 82, 375-386.
70. 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.
71. Hopko, D. R., Ashcraft, M. H., Gute, J., Ruggiero, K. J., & Lewis, C. (1998). Mathematics anxiety and working memory: Support for the existence of a deficient inhibition mechanism. Journal of Anxiety Disorders, 12, 343-355.
72. Jordan, N. C. (1995). Clinical assessment of early mathematics disabilities: Adding up the research findings. Learning Disabilities Research and Practice, 10, 59-69.
73. Jordan, N. C., & Hanich, L. B. (2000). Mathematical thinking in second-grade children with different forms of LD. Journal of Learning Disabilities, 33, 567-578.
74. Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003a). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85, 103-119.
75. Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003b). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74, 834-850.
76. Jordan, N. C., & Montani, T. O. (1997). Cognitive arithmetic and problem solving: A comparison and children with specific and general mathematics difficulties. Journal of Learning Disabilities, 30, 624-634.
77. Just, M. A., & Carpenter, P. A. (1992). A capacity theory of comprehension: Individual differences in working memory. Psychological Review, 99, 122-149.
78. Kail, R. (1991). Processing time declines exponentially during childhood and adolescence. Developmental Psychology, 27, 259-266.
79. Kail, R., & Hall, L. K. (1999). Sources of developmental change in children's word-problem performance. Journal of Educational Psychology, 91, 660-668.
80. Kail, R., & Hall, L. K. (2001). Distinguishing short-term memory from working memory. Memory and Cognition, 29, 1-9.
81. Kail, R., & Park, Y. (1994). Processing time, articulation rate, and memory span. Journal of Experimental Child Psychology, 57, 281-291.
82. 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.
83. Keeler, M. L., & Swanson, H. L. (2001). Does strategy knowledge influence working memory in children with mathematical disabilities? Journal of Learning Disabilities, 34, 418-434.
84. Kieras, D. E., Meyer, D. E., Mueller, S., & Seymour, T. (1999). Insights into working memory form 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: Mechanisms of active maintenance and executive control (pp. 183-223). Cambridge: Cambridge University Press.
85. Kintsch, W., Healy, A. F., Hegarty, M., Pennington, B. F., & Salthouse, T. A. (1999). Models of working memory: Eight questions and some general issues. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 412-441). Cambridge: Cambridge University Press.
86. 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, 105-116.
87. Koontz, K. L., & Berch, D. B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2, 1-23.
88. 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.
89. Lee, K. M., & Kang, S. Y. (2002). Arithmetic operation and working memory: Differential suppression in dual tasks. Cognition, 83, B63-B68.
90. LeFevre, J. (2003). Individual differences in working memory and arithmetic. Unpublished manuscript.
91. LeFevre, J., Bisanz, J., Daley, K. E., Buffone, L., Greenham, S. L., & Sadesky, G. S. (1996). Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology: General, 125, 284-306.
92. LeFevre, J., Bisanz, J., & Mrkonjic, L. (1988). Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts. Memory and Cognition, 16, 45-53.
93. LeFevre, J., Sadesky, G. S., & Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem-size effect in adults. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 216-230.
94. 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.
95. Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124, 83-97.
96. Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory and Cognition, 22, 395-410.
97. Majumder, S. (2003). Factors in mathematical word problem solving. Unpublished doctoral thesis, York University, Toronto, Canada.
98. McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44, 107-157.
99. McCloskey, M., & Macaruso, P. (1995). Representing and using numerical information. American Psychologist, 50, 351-363.
100. McCloskey, M., Sokol, S. M., & Goodman, R. A. (1986). Cognitive processes in verbal-number production: Inferences from the performance of brain-damaged subjects. Journal of Experimental Psychology: General, 115, 307-330.
101. 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.
102. Miyake, A. (2001). Individual differences in working memory: Introduction to the special section. Journal of Experimental Psychology: General, 130, 163-168.
103. Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex "frontal lobe" tasks: A latent variable analysis. Cognitive Psychology, 41, 49-100.
104. Miyake, A., Friedman, N. P., Rettinger, D. A., Shah, P., & Hegarty, M. (2001). How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. Journal of Experimental Psychology: General, 130, 621-640.
105. Miyake, A., & Shah, P. (1999). Toward unified theories of working memory: Emerging general consensus, unresolved theoretical issues, and future research directions. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 442-481). Cambridge: Cambridge University Press.
106. Miller, K., Perlmutter, M., & Keating, D. (1984). Cognitive arithmetic: Comparison of operations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 46-60.
107. Muth, K. D. (1984). Solving arithmetic word problems: Role of reading and computational skills. Journal of Educational Psychology, 76, 205-210.
108. Noël, M. P., Fias, W., & Brysbaert, M. (1997). About the influence of the presentation format on arithmetical-fact retrieval processes. Cognition, 63, 335-374.
109. Oberauer, K., Süb, H.-M., Schulze, R., Wilhelm, O., & Wittmann, W. W. (2000). Working memory capacity-facets of a cognitive ability construct. Personality and Individual Differences, 29, 1017-1045.
110. Ostad, S. A. (1997). Developmental differences in addition strategies: A comparison of mathematically disabled and mathematically normal children. British Journal of Educational Psychology, 67, 345-357.
111. Ostad, S. A. (1998). Developmental differences in solving simple arithmetic word problems and simple number-fact problems: A comparison of mathematically normal and mathematically disabled children. Mathematical Cognition, 4, 1-19.
112. Passolunghi, M. C., & Siegel, L. S. (2001). Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology, 80, 44-57.
113. 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, 1160-1167.
114. Reuhkala, M. (2001). Mathematical skills in ninth-graders: Relationship with visuo-spatial abilities and working memory. Educational Psychology, 21, 387-399.
115. Rourke, B. P. (1993). Arithmetic disabilities, specific and otherwise: A neuropsychological perspective. Journal of Learning Disabilities, 26, 214-226.
116. Salthouse, T. A., & Babcock, R. L. (1991). Decomposing adult age differences in working memory. Developmental Psychology, 27, 763-776.
117. Seitz, K., & Schumann-Hengsteler, R. (2000). Mental multiplication and working memory. European Journal of Cognitive Psychology, 12, 552-570.
118. Seitz, K., & Schumann-Hengsteler, R. (2002). Phonological loop and central executive processes in mental addition and multiplication. Psychologische Beitrage, 44, 275-302.
119. Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary subtraction. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 1339-1352.
120. Shrager, J., & Siegler, R. S. (1998). SCADS: A model of children's strategy choices and strategy discoveries. Psychological Science, 9, 405-410.
121. Siegler, R. S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258-275.
122. Siegel, L. S., & Linder, B. A. (1984). Short-term memory processes in children with reading and arithmetic learning disabilities. Developmental Psychology, 20, 200-207.
123. Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60, 973-980.
124. Siegler, R. S., & Shrager, J. (1984). Strategy choice in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229-293). Hillsdale, NJ: Erlbaum.
125. Swanson, H. L. (1993). Working memory in learning disability subgroups. Journal of Experimental Child Psychology, 56, 87-114.
126. Swanson, H. L. (2001). Research on interventions for adolescents with learning disabilities: A meta-analysis of outcomes related to higher-order processing. Elementary School Journal, 101, 331-348.
127. Swanson, H. L., & Sachse-Lee, C. (2001). A subgroup analysis of working memory in children with reading disabilities: Domain-general or domain-specific deficiency? Journal of Learning Disabilities, 34, 249-263.
128. Trbovich, P. L., & LeFevre, J. (2003). Phonological and visual working memory in mental addition. Memory and Cognition, 31, 738-745.
129. Turner, M. L., & Engle, R. W. (1989). Is working memory capacity task dependent? Journal of Memory and Language, 28, 127-154.
130. Webster, R. E. (1979). Visual and aural short-term memory capacity deficits in mathematics disabled students. Journal of Educational Research, 72, 277-283.
131. Wilson, K. M., & Swanson, H. L. (2001). Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit? Journal of Learning Disabilities, 34, 237-248.