Practice effects on strategy selection and strategy efficiency in simple mental arithmetic

Psychological Research

Volumn 72, Issue 5, 2008, Pages 528-541

  Imbo, Ineke ^a   Vandierendonck, André ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ADULT; ARTICLE; COGNITION; FEMALE; HUMAN; LEARNING; MALE; MATHEMATICS; REACTION TIME;

ADULT; COGNITION; FEMALE; HUMANS; MALE; MATHEMATICS; PRACTICE (PSYCHOLOGY); REACTION TIME;

EID: 46349105781     PISSN: 03400727     EISSN: 14302772     Source Type: Journal    
DOI: 10.1007/s00426-007-0128-0     Document Type: Article

References (69)

1. Anderson, J. R. (1993). Rules of the mind. Hillsdale, NJ: Erlbaum.
2. Ashcraft, M. H. (1982). The development of mental arithmetic: A chronometric approach. Developmental Review, 2, 213-236.
3. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75-106.
4. Baroody, A. J. (1983). The development of procedural knowledge: An alternative explanation for chronometric trends of mental arithmetic. Developmental Review, 3, 225-230.
5. Baroody, A. J. (1984). A re-examination of mental arithmetic models and data: A reply to Ashcraft. Developmental Review, 4, 148-156.
6. Baroody, A. J. (1985). Mastery of the basic number combinations: Internalization of relationships or facts? Journal of Research in Mathematics Education, 16, 83-98.
7. Brigman, S., & Cherry, K. E. (2002). Age and skilled performance: Contributions of working memory and processing speed. Brain and Cognition, 50, 242-256.
8. Butterworth B. (1999). The mathematical brain. London: Macmillan.
9. Campbell J. I. D. (1987). Network interference and mental multiplication. Journal of Experimental Psychology: Learning, Memory, & Cognition, 13, 109-123.
10. Campbell J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121-164.
11. 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.
12. Campbell J. I. D., & Austin, S. (2002). Effects of response time deadlines on adults' strategy choices for simple addition. Memory & Cognition, 30, 988-994.
13. Campbell J. I. D., & Graham, D. J. (1985). Mental multiplication skill: Structure, process and acquisition. Canadian Journal of Psychology, 39, 338-366.
14. Campbell J. I. D., Gunter R. (2002). Calculation, culture, and the repeated operand effect. Cognition, 86, 71-96.
15. Campbell J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299-315.
16. Campbell J. I. D., Fuchs-Lacelle, S., & Phenix, T. L. (2006). Identical elements model of arithmetic memory: Extension to addition and subtraction. Memory & Cognition, 34, 633-647.
17. Compton B. J., & Logan, G. D. (1991). The transition from algorithm to retrieval in memory-based theories of automaticity. Memory & Cognition, 19, 151-158.
18. Dehaene S. (1997). The number sense. New York: Oxford University Press.
19. Delaney, P. F., Reder, L. M., Staszewski, J. J., & Ritter, F. E. (1998). The strategy-specific nature of improvement: The power law applies by strategy within task. Psychological Science, 9, 1-7.
20. Delazer, M., Ischebeck, A., Domahs, F., Zamarian, L., Koppelstaetter, F., Siedentopf, C. M., Kaufmann, L., Benke, T., & Felber, S. (2005). Learning by strategies and learning by drill-Evidence from an fMRI study. Neuroimage, 25, 838-849.
21. Fendrich, D. W., Healy, A. F., & Bourne, L. E. (1993). Mental arithmetic: Training and retention of multiplication skill. In C. Izawa (Ed.), Applied Cognitive Psychology: Applications of Cognitive Theories and Concepts (pp. 111-133). Hillsdale, NJ: Erlbaum.
22. French J. W., Ekstrom R. B., & Price, I. A. (1963). Kit of reference tests for cognitive factors. Princeton, NJ: Educational Testing Service.
23. Fuson, K. C. (1982). An analysis of the counting-on procedure in addition. In T. H. Carpenter, J. M. Moser, & T. H. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 67-78). Hillsdale NJ: Lawrence Erlbaum.
24. Fuson, K. C. (1988). Children's counting and concepts of number. New York: Springer.
25. Geary, D. C. (1996). The problem-size effect in mental addition: Developmental and cross-national trends. Mathematical Cognition, 2, 63-93.
26. Geary, D. C., Salthouse, T. A., Chen, G. -P., & Fan, L. (1996). Are East Asian versus American differences in arithmetic ability a recent phenomenon? Developmental Psychology, 32, 254-262.
27. Geary, D. C., Hamson, C. O., Chen, G. -P., Fan, L., Hoard, M. K., & Salthouse, T. A. (1997). Computational and reasoning in arithmetic: Cross-generational change in China and the United States. Psychonomic Bulletin and Review, 4, 254-263.
28. Gelman R., & Gallistel, R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
29. Hoyer, W. J., Cerella, J., & Onyper, S. V. (2003). Item learning in cognitive skill training: Effects of item difficulty. Memory & Cognition, 31, 1260-1270.
30. Imbo, I., & Vandierendonck, A. (in press a). The role of phonological and executive working-memory resources in simple-arithmetic strategies. European Journal of Cognitive Psychology.
31. Imbo, I., & Vandierendonck, A. (in press b). Do multiplication and division strategies rely on executive and phonological working-memory resources? Memory & Cognition.
32. Imbo, I., Vandierendonck, A., & Rosseel, Y. (2007). The influence of problem features and individual differences on strategic performance in simple arithmetic. Memory & Cognition, 35, 454-463.
33. Kirk, E. P., & Ashcraft, M. H. (2001). Telling stories: The perils and promise of using verbal reports to study math strategies. Journal of Experimental Psychology: Learning, Memory, & Cognition, 27, 157-175.
34. Klapp, S. T., Boches, C. A., Trabert, M. L., Logan, G. D. (1991). Automatizing alphabet arithmetic: II. Are there practice effects after automaticity is achieved? Journal of Experimental Psychology: Learning, Memory, & Cognition, 17, 196-209.
35. Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs: A meta-analysis. Remedial and Special Education, 24, 97-114.
36. LeFevre, J. -A., & Liu, J. (1997). The role of experience in numerical skill: Multiplication performance in adults from Canada and China. Mathematical Cognition, 3, 31-62.
37. LeFevre, J.-A., 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.
38. LeFevre, J. -A., 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, & Cognition, 22, 216-230.
39. Lewis, A. B. (1989). Training students to represent arithmetic word problems. Journal of Educational Psychology, 81, 521-531.
40. Logan, G. D. (1988). Toward an instance theory of automatization. Psychological Review, 95, 492-527.
41. Logan, G. D., & Klapp, S. T. (1991). Automatizing alphabet arithmetic: I. Is extended practice necessary to produce automaticity? Journal of Experimental Psychology: Learning, Memory, & Cognition, 17, 179-195.
42. McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Brain and Cognition, 4, 171-196.
43. Mulhern, G., & Wylie, J. (2004). Changing levels of numeracy and other core mathematical skills among psychology undergraduates between 1992 and 2002. British Journal of Psychology, 95, 355-370.
44. Newell, A., & Rosenbloom, P. S. (1981). Mechanisms of skill acquisition and the law of practice. In J. R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 1-55). Hillsdale, NJ: Erlbaum.
45. Onyper, S. V., Hoyer, W. J., & Cerella, J. (2006). Determinants of retrieval solutions during cognitive skill training: Source confusions. Memory & Cognition, 34, 538-549.
46. Pauli, P., Lutzenberger, W., Rau, H., Birbaumer, N., Rickard, T. C., Yaroush, R. A., & Bourne, L. E. (1994). Brain potentials during mental arithmetic-Effects of extensive practice and problem difficulty. Cognitive Brain Research, 2, 21-29.
47. Pauli, P., Lutzenberger, W., Birbaumer, N., Rickard, T. C., & Bourne, L. E. (1996). Neurophysiological correlates of mental arithmetic. Psychophysiology, 33, 522-529.
48. Pauli, P., Bourne, L. E., & Birbaumer, N. (1998). Extensive practice in mental arithmetic and practice transfer over a ten-month retention interval. Mathematical Cognition, 4, 21-46.
49. Rickard, T. C. (1997). Bending the power law: A CMPL theory of strategy shifts and the automatization of cognitive skills. Journal of Experimental Psychology: General, 126, 288-311.
50. Rickard, T. C. (2004). Strategy execution in cognitive skill learning: An item-level test of candidate models. Journal of Experimental Psychology, 30, 65-82.
51. Rickard, T. C. (2005). A revised identical elements model of arithmetic fact representation. Journal of Experimental Psychology: Learning, Memory, & Cognition, 31, 250-257.
52. Rickard, T. C., & Bourne, L. E. (1996). Some tests of an identical elements model of basic arithmetic skills. Journal of Experimental Psychology: Learning, Memory, & Cognition, 22, 1281-1295.
53. Rickard, T. C., Healy, A. F., & Bourne, L. E. (1994). On the cognitive structure of basic arithmetic skills: Operation, order, and symbol transfer effects. Journal of Experimental Psychology: Learning, Memory, & Cognition, 20, 1139-1153.
54. Royer, J. M., Tronsky, L. N., Chan, Y., Jackson, S. J., & Marchant, H. III. (1999). Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance. Contemporary Educational Psychology, 24, 181-266.
55. Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary subtraction. Journal of Experimental Psychology: Learning, Memory, & Cognition, 29, 1339-1352.
56. Shrager, J., & Siegler, R. S. (1998). SCADS: A model of children's strategy choices and strategy discoveries. Psychological Science, 9, 405-410.
57. Siegler, R. S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258-275.
58. Siegler, R. S., & Araya, R. (2005). A computational model of conscious and unconscious strategy discovery. Advances in Child Development and Behavior, 33, 1-42.
59. Siegler, R. S., & Shipley, C. (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.
60. Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition, subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229-294). Hillsdale, NJ: Erlbaum.
61. Spelke, E., & Dehaene, S. (1999). Biological foundations of numerical thinking: response to T.J. Simon. Trends in Cognitive Science, 3, 365-366.
62. Steel, S., & Funnell, E. (2001). Learning multiplication facts: A study of children taught by discovery methods in England. Journal of Experimental Child Psychology, 79, 37-55.
63. Touron, D. R., Hoyer, W. J., & Cerella, J. (2004). Cognitive skill learning: Age-related differences in strategy shifts and speed of component operations. Psychology and Aging, 19, 565-580.
64. Van der Goten, K., & Vandierendonck, A. (1997). Software to calculate measures of sensitivity and response bias based on detection theory and threshold theory. Behavior Research Methods, Instruments, & Computers, 29, 461-463.
65. Verguts, T., & Fias, W. (2005). Interacting neighbors: A connectionist model of retrieval in single-digit multiplication. Memory & Cognition, 33, 1-16.
66. Whetstone, T. (1998). The representation of arithmetic facts in memory: Results from retraining a brain-damaged patient. Brain and Cognition, 36, 290-309.
67. Wynn, K. (1990). Children's understanding of counting. Cognition, 36, 155-193.
68. Zbrodoff, N. J. (1995). Why is 9 + 7 harder than 2 + 3? Strength and interference as explanations of the problem-size effect. Memory & Cognition, 23, 689-700.
69. Zbrodoff, N. J. (1999). Effects of counting in alphabet arithmetic: Opportunistic stopping and priming of intermediate steps. Journal of Experimental Psychology: Learning, Memory, & Cognition, 25, 299-317.