An encoding-complex approach to numerical cognition in Chinese-English bilinguals

Canadian Journal of Experimental Psychology

Volumn 58, Issue 4, 2004, Pages 229-244

  Campbell, Jamie I D ^a   Epp, Lynette J ^a  

^a UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11144263648     PISSN: 11961961     EISSN: None     Source Type: Journal    
DOI: 10.1037/h0087447     Document Type: Article

References (64)

1. Bernardo, A. B. I. (2001). Asymmetric activation of number codes in bilinguals: Further evidence for the encoding-complex model of number processing. Memory & Cognition, 29, 968-976.
2. Blankenberger, S., & Vorberg, D. (1997). The single-format assumption in arithmetic fact retrieval. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 721-738.
3. Brysbaert, M., Fias, W., & Noel, M. P. (1998). The Whorfian hypothesis and numerical cognition: Is 'twenty-four' processed in the same way as 'four-and-twenty'? Cognition, 66, 51-77.
4. Butterworth, B. (1999). What counts: How every brain is hardwired for math. New York: The Free Press.
5. Campbell, J. I. D. (1992). In defense of the encoding-complex approach: Reply to McCloskey, Macaruso, & Whetstone. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 539-556). Amsterdam: Elsevier.
6. Campbell, J. I. D. (1994). Architectures for numerical cognition. Cognition, 53, 1-44.
7. Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121-164.
8. Campbell, J. I. D. (1997). Reading-based interference in cognitive arithmetic. Canadian Journal of Experimental Psychology, 51, 74-81.
9. Campbell, J. I. D. (1998). Notational and linguistic influences in cognitive arithmetic: Comment on Noël, Fias, & Brysbaert (1997). Cognition, 67, 353-564.
10. Campbell, J. I. D., & Clark, J. M. (1988). An encoding-complex view of cognitive number processing: Comment on McCloskey, Sokol, & Goodman (1986). Journal of Experimental Psychology; General, 117, 204-214.
11. Campbell, J. I. D., & Clark, J. M. (1992). Numerical cognition: An encoding-complex perspective. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 457-491). Amsterdam: Elsevier Science.
12. Campbell, J. I. D., & Epp, L. J. (in press). Architectures for arithmetic. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition. New York: Psychology Press.
13. Campbell, J. I. D., & Fugelsang, J. (2001). Strategy choice for arithmetic verification: Effects of numerical surface form. Cognition, 80, B21-B30.
14. Campbell, J. I. D., Kanz, C. L., & Xue, Q. (1999). Number processing in Chinese-English bilinguals. Mathematical Cognition, 5, 1-39.
15. Campbell, J. I. D., Parker, H. R., & Doetzel, N. L. (2004). Interactive effects of numerical surface form and operand parity in cognitive arithmetic. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30, 51-64.
16. Campbell, J. I. D., & Thompson, V. A. (2002). More power to you: Simple power calculations for treatment effects with one degree of freedom. Behavior Research Methods, Instrumentation, and Computers, 34, 332-337.
17. Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299-315.
18. Cipolotti, L. (1995). Multiple routes for reading words, why not numbers? Evidence from a case of Arabic numeral dyslexia. Cognitive Neuropsychology, 12, 313-342.
19. Cipolotti, L., & Butterworth, B. (1995). Toward a multiroute model of number processing: Impaired number processing with preserved calculation skills. Journal of Experimental Psychology: General, 124, 375-390.
20. Cipolotti, L., Warrington, E. K., & Butterworth, B. (1995). Selective impairment in manipulating Arabic numerals. Cortex, 31, 73-86.
21. Clark, J. M., & Campbell, J. I. D. (1991). Integrated versus modular theories of number skills and acalculia. Brain and Cognition, 17, 204-239.
22. Cohen, L., Dehaene, S., Chochon, F., Lehericy, S., & Naccache, L. (2000). Language and calculation within the parietal lobe: A combined cognitive, anatomical, and fMRI study. Neuropsychologia, 38, 1426-1440.
23. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.
24. Dehaene, S. (1996). The organization of brain activations in number comparison: Event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience, 8, 47-68.
25. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
26. Dehaene, S. (2003). The neural basis of the Weber-Fechner law: A logarithmic mental number line. Trends in Cognitive Sciences, 7, 145-147.
27. Dehaene, S., & Akhavein, R. (1995). Attention, automaticity, and levels of representation in number processing. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21, 314-326.
28. Dehaene, S., & Cohen, L. (1991). Two mental calculation systems: A case study of severe acalculia with preserved approximation. Neuropsychologia, 29, 1045-1074.
29. Dehaene, S., & Cohen, L. (1995). Toward an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.
30. Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: Double dissociation between Gerstmann's acalculia and subcortical acalculia. Cortex, 33, 219-250.
31. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506.
32. Dehaene, S., Spelke, E., Pinal, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970-974.
33. French-Mestre, C. A., & Vaid, J. (1993). Activation of number fact in bilinguals. Memory & Cognition, 21, 809-818.
34. Geary, D. C. (1995). Reflections of evolution and culture in children's cognition: Implications for mathematical development and instruction. American Psychologist, 50, 24-37.
35. Geary, D. C. (1996). The problem-size effect in mental addition: Developmental and cross-national trends. Mathematical Cognition, 2, 63-93.
36. Geary, D. C., Bow-Thomas, C. C., Fan, L., & Siegler, R. S. (1996). Development of arithmetical competencies in Chinese and American children: Influence of age, language, and schooling. Child Development, 67, 2022-2044.
37. Geary, D. C., Cormier, P., Goggin, J. P., Estrada, P., & Lunn, M. C. E. (1993). Mental arithmetic: A componential analysis of speed-of-processing across monolingual, weak bilingual, and strong bilingual adults. International Journal of Psychology, 28, 185-201.
38. Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
39. Ischebeck, A. (2003). Differences between digit naming and number word reading in a flanker task. Memory & Cognition, 31, 529-537.
40. Kashiwagi, A., Kashiwagi, T., & Hasegawa, T. (1987). Improvement of deficits in mnemonic rhyme for multiplication in Japanese aphasics. Neuropsycho-logia, 25, 443-447.
41. Koechlin, E., Naccache, L., Block, E., & Dehaene, S. (1999). Primed numbers: Exploring the modularity of numerical representations with masked and unmasked semantic priming. Journal of Experimental Psychology: Human Perception and Performance, 25, 1882-1905.
42. Lakoff, G., & Núǹez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
43. LeFevre, J., & Liu, J. (1997). The role of experience in numerical skill: Multiplication performance in adults from China and Canada. Mathematical Cognition, 3, 31-62.
44. Mägiste, E. (1980). Arithmetical calculations in monolingual and bilinguals. Psychological Research, 42, 363-373.
45. Marsh, L. G., & Maki, R. H. (1976). Efficiency of arithmetic operations in bilinguals as a function of language. Memory & Cognition, 4, 459-464.
46. McClain, L., & Shih Huang, J. Y. (1982). Speed of simple arithmetic in bilinguals. Memory & Cognition, 10, 591-596.
47. Masson, M. E. J., & Loftus, G. R. (2003). Using confidence intervals for graphically based data interpretation. Canadian Journal of Experimental Psychology, 57, 203-220.
48. McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44, 107-157.
49. McCloskey, M., & Macaruso, P. (1994). Architecture of cognitive numerical processing mechanisms: Contrasting perspectives on theory development and evaluation. Cahiers de Psychologie Cognitive/ Current Psychology of Cognition, 13, 275-295.
50. McCloskey, M., & Macaruso, P. (1995). Representing and using numerical information. American Psychologist, 50, 351-363.
51. McNeil, J., & Warrington, E. K. (1994). A dissociation between addition and subtraction with written calculation, Neuropsychologia, 32, 717-728.
52. Meuter, R. F. I., & Allport, A. (1999). Bilingual language switching in naming: Asymmetrical costs of language selection. Journal of Memory and Language, 40, 25-40.
53. Noël, M.-P., & Fias, W. (1999). Bilingualism and numeric cognition. Psycbologica-Belgica, 38, 231-250.
54. Noël, M.-P., Fias, W., & Brysbaert, M. (1997). About the influence of the presentation format on arithmetical-fact retrieval processes. Cognition, 63, 335-374.
55. Noël, M.-P., Robert, A., & Brysbaert, M. (1998). Does language really matter when doing arithmetic? Reply to Campbell (1998). Cognition, 67, 365-373.
56. Reynvoet, B., Brysbaert, M., & Fias, W. (2002). Semantic priming in number naming. The Quarterly Journal of Experimental Psychology, 55A, 1127-1139.
57. Sciama, S., Semenza, C., & Butterworth, B. (1999). Repetition priming in simple addition depends on surface form and typicality. Memory & Cognition, 27, 116-127.
58. Spelke, E. S., & Tsivkin, S. (2001). Language and number: A bilingual training study. Cognition, 78, 45-88.
59. Szucs, D., & Csépe, V. (2004). Access to numerical information is dependent on the modality of stimulus presentation in mental addition: A combined ERP and behavioral study. Cognitive Brain Research, 19, 10-27.
60. Vaid, J., & Corina, D. (1989). Visual field asymmetries in numerical size comparisons of digits, words, and signs. Brain and Language. 36, 117-126.
61. Verguts, T., & Fias, W. (in press). Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience.
62. Whalen, J., McCloskey, M., Lindemann, M., & Bouton, G. (2002). Representing arithmetic table facts in memory: Evidence from acquired impairments. Cognitive Neuropsychology, 19, 505-522.
63. Zbrodoff, N. J., & Logan, G. D. (in press). What everyone finds: The problem size effect. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition. New York: Psychology Press.
64. Zorzi, M., Stoianov, I., & Umiltà, C (in press). Computational modeling of numerical cognition. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition. New York: Psychology Press.