Selecting between Competitors in Multiplication Tasks: An Explanation of the Errors Produced by Adolescents with Learning Difficulties

International Journal of Behavioral Development

Volumn 21, Issue 2, 1997, Pages 253-275

  Barrouillet, Pierre ^a,b   Fayol, Michel ^a   Lathulière, Eric ^a  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000497162     PISSN: 01650254     EISSN: None     Source Type: Journal    
DOI: 10.1080/016502597384857     Document Type: Article

References (64)

1. Anderson, J.R. (1976). Language, memory, and thought. Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
2. Anderson J.R. (1994). Learning and memory: An integrated approach. New York: Wiley.
3. Anderson, M.C., & Spellman, B.A. (1995). On the status of inhibitory mechanisms in cognition: Memory retrieval as a case model. Psychological Review, 102, 68-100.
4. Ashcraft, M.H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75-106.
5. 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.
6. Baddeley, A. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology, 49A, 5-28.
7. Benson, D.F., & Weir, W.F. (1972). Acaculia: Acquired anarithmetia. Cortex, 8, 465-472.
8. Bideaud, J., Meljac, C. & Fisher, J.P. (1993). Pathways to number. Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
9. Bjorklund, D.F., & Harnishfeger, K.K. (1990). The resources construct in cognitive development: Diverse sources of evidence and a theory of inefficient inhibition. Developmental Review, 10, 48-71.
10. Campbell, J.I.D. (1987a). Network interference and mental multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 349-364.
11. Campbell, J.I.D. (1987b). Production, verification, and priming of multiplication facts. Memory and Cognition, 15, 349-364.
12. Campbell, J.I.D. (1994). Numerical cognition: Evidence for hyperspecific, interactive operations. CPC/Current Psychology of Cognition, 13, 297-320.
13. Campbell, J.I.D., & Graham, D.J. (1985). Mental multiplication skill: Structure, process, and acquisition. Canadian Journal of Psychology, 39, 338-366.
14. Cantor, J., & Engle, R.W. (1993). Working-memory capacity as long-term memory activation: An individual-differences approach. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19, 1101-1114.
15. Case, R. (1985). Intellectual development: Birth to adulthood. New York: Academic Press.
16. Case, R. (1992). The mind's staircase: Exploring the conceptual underpinnings of children's thought and knowledge. Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
17. Conway, A.R.A., & Engle, R.W. (1994). Working memory and retrieval: A resource-dependent inhibition model. Journal of Experimental Psychology: General, 4, 354-373.
18. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396.
19. Dempster, F.N. (1991). Inhibitory processes: A neglected dimension of intelligence. Intelligence, 15, 157-173.
20. Engle, R.W., Conway, A.R.A., Tuholski, S.W., & Shisler, R. (1995). A resource account of inhibition. Psychological Science.
21. Fayol, M. (1990). L'enfant et le nombre. Neuchâtel: Delachaux & Niestlé.
22. Fleischner, J.E., Garnett, K., & Shepherd, M.J. (1982). Proficiency in arithmetic basic fact computation of learning disabled and non disabled children. Focus on Learning Problems in Mathematics, 4, 47-56.
23. Geary, D.C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363-383.
24. Geary, D.C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Review, 114, 345-362.
25. Geary, D.C., Bow-Thomas, C.C., & Yao, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54, 372-391.
26. Geary, D.C., & Brown, S.C. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27, 398-406.
27. 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, 398-406.
28. Geary, D.C., Widaman, K.F., Little, T.D., & Cormier, P. (1987). Cognitive addition: Comparison of learning disabled and academically normal elementary school children. Cognitive Development, 2, 249-269.
29. Gernsbacher, M.A. (1990). Language comprehension as structure building. Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
30. Goldman, S.R., Pellegrino, J.W., & Mertz, D.L. (1988). Extended practice of basic addition facts: Strategy changes in learning disabled students. Cognition and Instruction, 5, 223-265.
31. Graham, D.J. (1987). An associative retrieval model of arithmetic memory: How children learn to multiply. In J.A. Sloboda & D. Rogers (Eds.), Cognitive processes in mathematics. Oxford: Clarendon.
32. Groen, G.J., & Parkman, J.M., (1972). A chronometric analysis of simple addition. Psychological Review, 79, 329-343.
33. Halford, G.S. (1993). Children's understanding. Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
34. Hamann, M.S., & Ashcraft, M.H. (1985). Simple and complex mental addition across development. Journal of Experimental Child Psychology, 40, 49-70.
35. Hines, T.M. (1990). An odd effect: Lengthened reaction times for judgments about odd digits. Memory and Cognition, 18, 40-46.
36. Howell, R., Sidorenko, E., & Jurica, J. (1987). The effects of computer use on the acquisiton of multiplication facts by a student with learning disabilities. Journal of Learning Disabilities, 20, 336-341.
37. Koontz, K.L., & Berch, D.B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2, 1-23.
38. Koshmider, J.W., III, & Ashcraft, M.H. (1991). The development of children's multiplication skills. Journal of Experimental Child Psychology, 51, 53-89.
39. Krueger, L.E. (1986). Why 2 × 2 = 5 looks so wrong: On the odd-even rule in product verification. Memory & Cognition, 14, 141-149.
40. Krueger, L.E., & Hallford, E.W. (1984). Why 2 × 2 = 5 looks so wrong: On the odd even rule in sum verification. Memory & Cognition, 12, 171-180.
41. Lefevre, J., Bisanz, J., & Mrkonjic, L. (1988). Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts. Memory & Cognition, 16, 45-53.
42. 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.
43. 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.
44. Lemaire, P., & Fayol, M. (1995). When plausibility judgments supersede fact retrieval: The example of the odd-even rule effect on product verification. Memory and Cognition, 23, 34-48.
45. Lemaire, P., Fayol, M., & Abdi, H. (1991). Associative confusion effect in cognitive arithmetic: Evidence for partially autonomous processes. CPC: European Bulletin of Cognitive Psychology, 5, 587-604.
46. Miller, K.F., & Gelman, R. (1983). The child's representation of numbers: A multidimensional scaling analysis. Child Development, 54, 1470-1479.
47. Miller, K.F., & Paredes, D.R. (1990). Starting to add worse: Effects of learning to multiply on children's addition. Cognition, 37, 213-242.
48. Miller, K. Perlmutter, M., & Keating, D. (1984). Cognitive arithmetic: Comparison of operations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 46-60.
49. Pascual-Leone, J. (1970). A mathematical model for the transition rule in Piaget's developmental stages. Acta Psychologica, 32, 301-345.
50. Pascual-Leone, J. (1987). Organismic processes for neo-piagetian theories: a dialectical causal account of cognitive development. International Journal of Psychology, 22, 531-570.
51. Shepard, R.N., Kilpatric, D.W.J., & Cunningham, J.P. (1975). The internal representation of numbers. Cognitive Psychology, 7, 82-138.
52. Siegler, R.S. (1988). Strategy choice procedures and the development of multiplication skills. Journal of Experimental Psychology: General, 117, 258-275.
53. Siegler, R.S., & Jenkins, E.A. (1989). How children discover new strategies. Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
54. Siegler, R.S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills. Hillsdale, NJ: Lawrence Erlbaum Associates Inc.
55. Sokol, S.M., McCloskey, M., Cohen, N.J., & Aliminosa, D. (1991). Cognitive representations and processes in arithmetic: Inference from the performance of brain-damaged subjects. Journal of Experimental Psychology: General, 118, 105-110.
56. Sudevan, P., & Taylor, D.A. (1987). The cuing and priming of cognitive operations. Journal of Experimental Psychology: Human Perception and Performance, 13, 89-103.
57. Svenson, O. (1985). Memory retrieval of answers of simple additions as reflected in response latencies. Acta Psychologica, 59, 285-304.
58. Svenson, O., & Broquist, S. (1975). Strategies for solving simple addition problems: A comparison of normal and subnormal children. Scandinavian Journal of Psychology, 16, 143-151.
59. Temple, C.M. (1991). Procedural dyscalculia and number fact dyscalculia: Double dissociation in developmental dyscalculia. Cognitive Neuropsychology, 8, 155-176.
60. Temple, C. (1994). The cognitive neuropsychology of the developmental dyscalculia. CPC/Current Psychology of Cognition, 13, 351-370.
61. Wheeler, L.R. (1941). A comparative study of the difficulty of learning the multiplication combinations. Journal of Genetic Psychology, 59, 189-206.
62. Zbrodoff, N.J. (1995). Why is 9 + 7 harder than 2 + 3? Strength and interference as explanation of the problem-size effect. Memory and Cognition, 23, 689-700.
63. Zbrodoff, N.J., & Logan, G.D. (1986). On the autonomy of mental processes: A case study of arithmetic. Journal of Experimental Psychology: General, 115, 118-130.
64. 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.