Developmental Change and Individual Differences in Children's Multiplication

Child Development

Volumn 74, Issue 4, 2003, Pages 1091-1107

  Mabbott, Donald J ^a,b   Bisanz, Jeffrey ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

^b HOSPITAL FOR SICK CHILDREN   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141988376     PISSN: 00093920     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-8624.00594     Document Type: Article

References (60)

1. Alberta Education. (1990). Program of studies: Elementary schools. Edmonton, Canada: Ministry of Education.
2. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75-106.
3. Ashcraft, M. H., & Christy, K. S. (1995). The frequency of arithmetic facts in elementary texts: Addition and multiplication in grades 1-6. Journal for Research in Mathematics Education, 26, 396-421.
4. Ashcraft, M. H., Fierman, B. A., & Bartolotta, R. (1984). The production and verification tasks in mental addition: An empirical comparison. Developmental Review, 4, 157-170.
5. 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 189-253). Amsterdam: Elsevier.
6. Baddeley, A. D. (1986). Working memory. New York: Oxford University Press.
7. Baddeley, A. D. (2001). Is working memory still working? American Psychologist, 56, 851-864.
8. Baroody, A. J. (1995). The role of the number-after rule in the invention of computational shortcuts. Cognition and Instruction, 13, 189-219.
9. Baroody, A. J. (1999). The roles of estimation and the commutativity principle in the development of third graders' mental multiplication. Journal of Experimental Child Psychology, 74, 157-193.
10. Baroody, A. J. (2003) The development of adaptive expertise and flexibility: The integration of conceptual knowledge and procedural knowledge. In A. J. Baroody & A. Dowker. (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1-33). Mahwah, NJ: Erlbaum.
11. Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 75-112). Hillsdale, NJ: Erlbaum.
12. Baroody, A. J., & Tiilikainen, S. H. (2003). Two perspectives on addition development. In A. J. Baroody & A. Dowker. (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 75-125). Mahwah, NJ: Erlbaum.
13. Bisanz, J., & LeFevre, J. (1990). Strategic and nonstrategic processing in the development of mathematical cognition. In D. F. Bjorklund (Ed.), Children's strategies: Contemporary views of cognitive development (pp. 213-244). Hillsdale, NJ: Erlbaum.
14. 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.
15. Bull, R., & Johnston, R. S. (1997). Children's arithmetic difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology, 65, 1-24.
16. Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777-786.
17. Campbell, J. I. D. (1987). Network interference and mental multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 109-123.
18. 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 mathematical skills (pp. 457-492). Amsterdam: Elsevier.
19. Campbell, J. I. D., & Graham, D. J. (1985). Mental multiplication skill: Structure, process, and acquisition. Canadian Journal of Psychology, 39, 338-366.
20. Cooney, J. B., Swanson, H. L., & Ladd, S. F. (1988). Acquisition of mental multiplication skill: Evidence for the transition between counting and retrieval strategies. Cognition & Instruction, 5, 323-345.
21. Dennis, M., Hetherington, C. R., & Spiegier, B. J. (1998). Memory and attention after childhood brain tumors, Medical and Pediatric Oncology Supplement, 1, 25-33.
22. Dixon, J. A., & Moore, C. F. (1996). The developmental role of intuitive principles in choosing mathematical strategies. Developmental Psychology, 32, 241-253.
23. 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.
24. Geary, D. C. (1994). Children's mathematical development. Washington, DC: American Psychological Association.
25. 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.
26. Ginsburg, H. P., Klein, A., & Starkey, P. (1998). The development of children's mathematical thinking: Connecting research with practice. In W. Damon (Series Ed.), I. E. Siegel, & K. A. Renninger (Vol. Eds.), Handbook of child psychology: Vol. 4, Child psychology in practice (5th ed., pp. 401-476). New York: Wiley.
27. Goldman, S. R., Pellegrino, J. W., & Mertz, D. L. (1988). Extended practice of basic addition facts: Strategy changes in learning-disabled children. Cognition and Instruction, 5, 223-265.
28. Graham, D. J., & Campbell, J. I. D. (1992). Network interference and number-fact retrieval: Evidence from children's alphaplication. Canadian Journal of Psychology, 46, 65-91.
29. Hiebert, J., & LeFevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.
30. Jastak, J. F., & Jastak, S. (1993). Manual for the Wide Range Achievement Test: Third Revision. Wilmington, DE: Jastak Associates.
31. Keil, F. C. (1989). Concepts, kinds, and cognitive development. Cambridge, MA: MIT Press.
32. 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.
33. Koshmider, J. W., & Ashcraft, M. H. (1991). The development of children's mental multiplication skills. Journal of Experimental Child Psychology, 51, 53-89.
34. LeFevre, J. (1993). Individual differences in working memory. Unpublished manuscript.
35. 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.
36. 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.
37. LeFevre, J., Smith-Chant, B. L., Hiscock, K., Daley, K. E., & Morris, J. (2003). 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: Constructing adaptive expertise (pp. 203-228). Mahwah, NJ: Erlbaum.
38. 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.
39. 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.
40. Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory and Cognition, 22, 395-410.
41. Mabbott, D. J. (1998). Developmental change and individual differences in children's multiplication. Unpublished doctoral thesis, University of Alberta, Edmonton, Canada.
42. 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.
43. Nunes, T., & Bryant, P. (1995). Do problem situations influence children's understanding of the commutativity of multiplication? Mathematical Cognition, 1, 245-260.
44. Robinson, K. (2001). The validity of verbal reports in children's subtraction. Journal of Educational Psychology, 93, 211-222.
45. Rourke, B. P., & Strang, J. D. (1983). Subtypes of reading and arithmetic disabilities: A neuropsychological analysis. In M. Rutter (Ed.), Developmental Neuropsychiatry (pp. 473-188). London: Guildford.
46. Seo, K. -H., & Ginsburg, H. P. (2003). "You've got to carefully read the rod equation: Classroom context and children's interpretations of the equals sign. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: The development of adaptive expertise (pp. 161-187). Mahwah, NJ: Erlbaum.
47. Shrager, J., & Siegler, R. S. (1998). SCADS: A model of children's strategy choices and strategy discoveries. Psychological Science, 9, 405-410.
48. 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.
49. Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General, 116, 250-264.
50. Siegler, R. S. (1988a). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258-275.
51. Siegler, R. S. (1988b). Individual differences in strategy choices: Good children not - so - good children, and perfectionists. Child Development, 59, 833-851.
52. Siegler, R. S. (1989). Hazards of mental chronometry: An example from children's subtraction. Journal of Educational Psychology, 81, 497-506.
53. Siegler, R. S., & McGilly, K. (1989). Strategy choices in children's time telling. In I. Levin, & D. Zakay (Eds.), Time and human cognition: A life-span perspective (pp. 181-218). New York: North-Holland.
54. 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.
55. Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Saffron (Ed.), Origins of cognitive skills (pp. 229-293). Hillsdale, NJ: Erlbaum.
56. Strang, J. D., & Rourke, B. P. (1985). Adaptive behavior of children who exhibit specific arithmetic disabilities and associated neuropsychological abilities and deficits. In B. P. Rourke (Ed.), Neuropsychology of learning disabilities: Essentials of subtype analysis (pp. 167-183). London: Guilford.
57. Turner, M. L., & Engle, R. W. (1989). Is working memory capacity task dependent? Journal of Memory and Language, 28, 127-154.
58. Wechsler, D. (1989). Wechsler Intelligence Scale for Children-Third Revision. San Antonio, TX: Psychological Corporation.
59. Widaman, K. F., Geary, D. C., Cormier, P., & Little, T. D. (1989). A componential model for mental addition. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 898-919.
60. Widaman, K. F., & Little, T. D. (1992). The development of skill in mental arithmetic: An individual differences perspective. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp 189-253). Amsterdam: Elsevier.