Does solution of mental arithmetic problems such as 2 + 6 and 3 × 8 rely on the process of "memory updating"?

Experimental Psychology

Volumn 53, Issue 3, 2006, Pages 198-208

  Deschuyteneer, Maud ^a   Vandierendonck, André ^a   Muyllaert, Isabel ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Executive processes; Memory updating; Simple mental arithmetic

Indexed keywords

ADOLESCENT; ADULT; ARTICLE; COGNITION; FEMALE; HUMAN; MALE; MATHEMATICS; MEMORY; PROBLEM SOLVING;

ADOLESCENT; ADULT; COGNITION; FEMALE; HUMANS; MALE; MATHEMATICS; MEMORY; PROBLEM SOLVING;

EID: 33747838121     PISSN: 16183169     EISSN: None     Source Type: Journal    
DOI: 10.1027/1618-3169.53.3.198     Document Type: Article

References (56)

1. Ashcraft, M. H. (1982). The development of mental arithmetic: A Chronometric approach. Developmental Review, 3, 213-236.
2. Ashcraft, M. H. (1987) Children's knowledge in simple arithmetic: A developmental model and simulation. In J. Bisanz, C. J. Brainerd, & R. Kail (Eds.), Formal methods in developmental psychology: Progress in cognitive development research (pp. 302-338). New York: Springer-Verlag.
3. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 76-106.
4. 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.
5. Baddeley, A. D. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology, 49A, 5-28.
6. Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. H. Bower (Ed.), The psychology of learning and motivation, (Vol. 8, pp. 47-89). New York: Academic Press.
7. Baroody, A. J. (1985). Mastery of the basic number combinations: Internalization of relationships or facts? Journal for Research in Mathematics Education, 16, 83-98.
8. Bunge, S. A., Hazeltine, E., Scanlon, M. D., Rosen, A. C., & Gabrieli, J. D. E. (2002). Dissociable contributions of prefrontal and parietal cortices to response selection. NeuroImage, 17, 1562-1571.
9. Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network interference theory and simulation. Mathematical Cognition, 1, 121-164.
10. Campbell, J. I. D. (1997). On the relation between skilled performance of simple division and multiplication. Journal of Experimental Psychology: Learning, Memory & Cognition, 23, 1140-1159.
11. Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299-315.
12. Cohen, J. (1988). Statistical power analysis for the behavioural sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
13. Collins, A. M., & Loftus, E. F. (1975). A spreading activation theory of semantic processing. Psychological Review, 82, 407-428.
14. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.
15. 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.
16. De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (2001). Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved? Memory & Cognition, 29, 267-273.
17. De Rammelaere, S., & Vandierendonck, A. (2001). Are executive processes used to solve simple mental arithmetic production tasks? Current Psychology Letters: Behaviour, Brain & Cognition, 2, 79-89.
18. Deschuyteneer, M., & Vandierendonck, A. (2005a). Are "input monitoring" and "response selection" involved in solving simple mental arithmetical sums? European Journal of Cognitive Psychology, 17, 347-370.
19. Deschuyteneer, M., & Vandierendonck, A. (2005b). The role of response selection and input monitoring in solving simple arithmetical products. Memory & Cognition, 33, 1472-1483.
20. DeStefano, D., & LeFevre, J.-A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16, 353-386.
21. Galfano, G., Mazza, V., Angrilli, A., & Umiltà, C. (2004). Electrophysiological correlates of stimulus-driven multiplication facts retrieval. Neuropsychologia, 42, 1370-1382.
22. Galfano, G., Rusconi, E., & Umiltà, C. (2003). Automatic activation of multiplication facts: Evidence from the nodes adjacent to the product. Quarterly Journal of Experimental Psychology, 56A, 31-61.
23. Geary, D. C., Widaman, K. F., & Little, T. D. (1986). Cognitive addition and multiplication: Evidence for a single memory network. Memory & Cognition, 14, 478-487.
24. Geary, D. C., & Wiley, J. G. (1991). Cognitive addition: Strategy choice and speed of processing differences in young and elderly adults. Psychology & Aging, 6, 474-483.
25. Groen, G. J., & Parkman, J. M. (1972). A Chronometric analysis of simple addition. Psychological Review, 79, 329-343.
26. Hecht, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults. Memory & Cognition, 27, 1097-1107.
27. Hecht, S. A. (2002). Counting on working memory in simple arithmetic when counting is used for problem solving. Memory & Cognition, 30, 447-455.
28. Hitch, G. J. (1978). The role of short-term working memory in mental arithmetic. Cognitive Psychology, 10, 302-323.
29. Imbo, I., Vandierendonck, A., & Rosseel, Y. (in press). The influence of problem features and individual differences on strategic performance in simple arithmetic. Memory & Cognition.
30. Jiang, Y., & Kanwisher, N. (2003a). Common neural substrates for response selection across modalities and mapping paradigms. Journal of Cognitive Neuroscience, 15, 1080-1094.
31. Jiang, Y., & Kanwisher, N. (2003b). Common neural mechanisms for response selection and perceptual processing. Journal of Cognitive Neuroscience, 15, 1095-1110.
32. Kirk, E. P., & Ashcraft, M. H. (2001). The perils and promise of using verbal reports to study math strategies. Journal of Experimental Psychology: Learning, Memory, & Cognition, 27, 157-175.
33. LeFevre, J.-A., Bisanz, J., Daley, 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.
34. LeFevre, J.-A., Bisanz, J., & Mrkonjic, L. (1988). Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts. Memory & Cognition, 16, 45-53.
35. LeFevre, J.-A., 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 & Cognition, 22, 216-230.
36. Lien, M. C., & Proctor, R. W. (2002). Stimulus-response compatibility and psychological refractory period effects: Implications for response selection. Psychonomic Bulletin & Review, 9, 212-238.
37. Logie, R. H., & Baddeley, A. D. (1987). Cognitive processes in counting. Journal of Experimental Psychology: Learning, Memory,& Cognition, 13, 310-326.
38. Miller, K. F., Perlmutter, M., & Keating, D. (1984). Cognitive arithmetic: Comparison of operations. Journal of Experimental Psychology: Learning, Memory, & Cognition, 10, 46-60.
39. 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.
40. Morris, N., & Jones, D. M. (1990). Memory updating in working memory : The role of the central executive. British Journal of Psychology, 81, 111-121.
41. Passolunghi, M. C., & Pazzaglia, F. (2004). Individual differences in memory updating in relation to arithmetic problem solving. Learning & Individual Differences, 14, 219-230.
42. Rusconi, E., Galfano, G., Speriani, V., & Umiltà, C. (2004). Capacity and contextual constraints on product activation: Evidence from task-irrelevant fact retrieval. Quarterly Journal of Experimental Psychology A, 57, 1485-1511.
43. Schubert, T. (1999). Processing differences between simple and choice reactions affect bottleneck localization in overlapping tasks. Journal of Experimental Psychology: Human Perception & Performance, 2, 408-425.
44. Schumacher, E. H., Elston, P. A., & D'Esposito, M. (2003). Neural evidence for representation-specific response selection. Journal of Cognitive Neuroscience, 15, 1111-1121.
45. Seitz, K., & Schumann-Hengsteler, R. (2000). Mental multiplication and working memory. European Journal of Cognitive Psychology, 12, 552-570.
46. Seitz, K., & Schumann-Hengsteler, R. (2002). Phonological loop and central executive processes in mental addition and multiplication. Psychologische Beiträge, 44, 275-302.
47. Siegler, R. S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258-275.
48. Siegler, R. S., & Lemaire, P. (1997). Older and younger adults' strategy choices in multiplication: Testing predictions of ASCM using the choice/no-choice method. Journal of Experimental Psychology: General, 126, 71-92.
49. Siegler, R. S., & Shipley, E. (1995). Variation, selection, and cognitive change. In G. Halford & T. Simon (Eds.), Developing cognitive competence: New approaches to process modeling (pp. 31-76). Hillsdale, NJ: Erlbaum.
50. Szmalec, A., & Vandierendonck, A. (2006). Estimating the executive demands of a one-back choice RT task by means of the selective interference paradigm. Manuscript submitted for publication.
51. Szmalec, A., Vandierendonck, A., & Kemps, E. (2005). Response selection involves executive control: Evidence from the selective interference paradigm. Memory & Cognition, 33, 531-541.
52. Thibodeau, M. H., LeFevre, J.-A., & Bisanz, J. (1996). The extension of the interference effect to multiplication. Canadian Journal of Experimental Psychology, 50, 393-396.
53. Vandierendonck, A. (2000a). Bias and processing capacity in the generation of random time intervals. Cognitive Science Quarterly, 2, 205-233.
54. Vandierendonck, A. (2000b). Is judgement of random time intervals biased and capacity-limited? Psychological Research, 63, 199-209.
55. Verguts, T., & Fias, W. (2005). Interacting neighbors: A connectionist model of retrieval in single-digit multiplication. Memory & Cognition, 33, 1-16.
56. Widaman, K. F., Geary, D. C., Cormier, P., & Little, T. D. (1989). A componential model for mental addition. Journal of Experimental Psychology: Learning, Memory, & Cognition, 15, 898-919.