Bilingualism and cognitive arithmetic

Cognitive Aspects of Bilingualism

Volumn , Issue , 2007, Pages 153-174

  Rusconi, Elena ^a   Galfano, Giovanni ^b   Job, Remo ^c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF PADOVA   (Italy)

^c UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 61949476146     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4020-5935-3_5     Document Type: Chapter

References (81)

1. Ashcraft, M. H., and 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.
2. Ashcraft, M. H. 1992. Cognitive arithmetic: a review of data and theory. Cognition, 44: 75-106.
3. Athanasopoulos, P. 2006. Effects of the grammatical representation of number on cognition in bilinguals. Bilingualism: Language and Cognition, 9: 89-96.
4. Balakrishnan, J. D., and Ashby, F. G. 1992. Subitizing: magical numbers or mere superstition. Psychological Research, 54: 80-90.
5. Barth, H., La Mont, K., Lipton, J., and Spelke, E. 2005. Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences, 102: 14116-14121.
6. Bernardo, A. B. I. 2001. Asymmetric activation of number codes in bilinguals: further evidence for the encoding complex model of number processing. Memory and Cognition, 29: 968-976.
7. Boysen, S. T., and Berntson, G. G. 1989. Quantity-based interference and symbolic representations in chimpanzees (Pan trogolodytes). Journal of Experimental Psychology: Animal Behavior Processes, 22: 76-86.
8. Boysen, S. T., and Capaldi, E. J. 1993. The development of numerical competence: animal and human models. Hillsdale, NJ: Erlbaum.
9. Brysbaert, M., Fias, W., and Nöel, 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.
10. Butterworth, B., Cipolotti, L., and Warrington, E. K. 1996. Short-term memory impairment and arithmetical ability. Quarterly Journal of Experimental Psychology, 49A: 251-262.
11. Butterworth, B. 1999. The mathematical brain. London: Macmillan.
12. Campbell, J. I. D., and Clark, J. M. 1988. An encoding-complex view of cognitive number processing: Comment on McCloskey, Sokol, and Goodman (1986). Journal of Experimental Psychology: General, 117: 204-214.
13. Campbell, J. I. D. 1994. Architectures for numerical cognition. Cognition, 53: 1-44.
14. Campbell, J. I. D. 1998. Linguistic influences in cognitive arithmetic: Comment on Noël, Fias and Brysbaert (1997). Cognition, 67: 353-364.
15. Campbell, J. I. D., Kanz, C. L., and Xue, Q. 1999. Number processing in Chinese-English bilinguals. Mathematical Cognition, 5: 1-39.
16. Campbell, J. I. D., and Xue, Q. 2001. Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130: 299-315.
17. Campbell, J. I. D., and Epp, L. J. 2004. An encoding-complex approach to numerical cognition in Chinese-English bilinguals. Canadian Journal of Experimental Psychology, 58: 229-244.
18. Campbell, J. I. D., and Epp, L. J. 2005. Architectures for arithmetic. In Campbell, J. I. D. (ed.), Handbook of mathematical cognition. New York: Psychology Press. 347-360.
19. Collins, A. M., and Loftus, E. F. 1975. A spreading activation theory of semantic processing. Psychological Review, 82: 407-428.
20. Cordes, S., Gelman, R., Gallistel, C. R., and Whalen, J. 2001. Variability signatures distinguish verbal from non-verbal counting for both large and small quantities. Psychonomic Bulletin and Review, 8: 698-707.
21. Damian, M. F. 2004. Asymmetries in the processing ofArabic digits and number words. Memory and Cognition, 32: 164-171.
22. Dehaene, S., Bossini, S., and Giraux, P. 1993. The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122: 371-396.
23. Dehaene, S., and Cohen, L. 1995. Towards an anatomical and functional model of number processing. Mathematical Cognition, 1: 83-120.
24. Dehaene, S. 1997. The number sense. New York: Oxford University Press.
25. Dehaene, S., Piazza, M., Pinel., P., and Cohen, L. 2003. Three parietal circuits for number processing. Cognitive Neuropsychology, 20: 487-506.
26. Dehaene, S., Molko, N., Cohen, L., and Wilson, A. J. 2004. Arithmetic and the brain. Current Opinion in Neurobiology, 14: 218-224.
27. Dehaene, S., Izard, V., Pica, P., and Spelke, E. 2006. Core knowledge of geometry in an Amazonian indigen group. Science, 311: 381-384.
28. Delazer, M., Domahs, F., Lochy, A., Karner, E., Benke, Th., and Poewe, W. 2004. Number processing and calculation in a case of Fahr's disease. Neuropsychologia, 42: 1050-1062.
29. Fias, W. 2001. Two routes for the processing of verbal numbers: evidence from the SNARC effect. Psychological Research, 65: 250-259.
30. Fias, W., Reynvoet, B., and Brysbaert, M. 2001. Are Arabic numerals processed as pictures in a Stroop interference task? Psychological Research, 65: 242-249.
31. Frenck-Mestre, C., and Vaid, J. 1993. Activation of number facts in bilinguals. Memory and Cognition, 21: 809-818.
32. Galfano, G., Rusconi, E., and Umiltà, C. 2003. Automatic activation of multiplication facts: evidence from the nodes adjacent to the product. Quarterly Journal of Experimental Psychology, 56A: 31-61.
33. Galfano, G., Mazza, V., Angrilli, A., and Umiltà, C. 2004. Electrophysiological correlates of stimulus-driven multiplication facts retrieval. Neuropsychologia, 42: 1370-1382.
34. Gallistel, C. R., and Gelman, R. 2000. Non-verbal numerical cognition: from real to integers. Trends in Cognitive Sciences, 2: 59-65.
35. Geary, D. C., Cormier, P., Goggin, J. P., Estrada, P., and Lunnhave, 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.
36. Gelman, R. 1991. Epigenetic foundations of knowledge structures: initial and transcendent constructions. In Carey, S., and Gelman, R. (eds.), The epigenesist of mind: essays on biology and cognition. Hillsdale NJ: Erlbaum. 293-322.
37. Gelman, R., and Gallistel, C. R. 1978. The child's understanding of number. Cambridge, MA: Harvard University Press.
38. Gelman, R., and Gallistel, C. R. 2004. Language and the origin of numerical concepts. Science, 306: 441-443.
39. Gelman, R., and Butterworth, B. 2005. Number and language: how are they related? Trends in Cognitive Sciences, 9: 6-10.
40. Gordon, P. 2004. Numerical cognition without words: evidence from Amazonia. Science, 306: 496-499.
41. Hauser, M., Carey, S., and Hauser, L. 2000. Spontaneous number representation in semi-free-ranging rhesus monkeys. Proceedings of the Royal Society of London B: Biological Sciences, 267: 829-833.
42. Ho, C. S. H., and Fuson, K. C. 1998. Children's knowledge of teen quantities as tens and ones: comparisons of Chinese, British, and American kindergartners. Journal of Educational Psychology, 90: 536-544.
43. Kilpatrick, J., Swafford, J., and Findell, B. 2001. Adding it up: helping children learn mathematics. Washington DC: National Academy Press.
44. LeFevre, J.-A., and Morris, J. 1999. More on the relation between division and multiplication in simple arithmetic: evidence for mediation of division solutions via multiplication. Memory and Cognition, 27: 803-812.
45. LeFevre, J.-A., Bisanz, J., and Mrkonjic, L. 1988. Cognitive arithmetic: evidence for obligatory activation of arithmetic facts. Memory and Cognition, 16: 45-53.
46. LeFevre, J.-A., Sadesky, G. S., and 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.
47. Ma, L. 1999. Knowing and teaching elementary school mathematics. Mahwah, NJ: Lawrence Erlbaum Associates.
48. Mägiste, E. 1980a. Arithmetical calculations in monolinguals and bilinguals. Psychological Research, 42: 363-373.
49. Mägiste, E. 1980b. Memory for numbers in monolinguals and bilinguals. Acta Psychologica, 46: 63-68.
50. Marsh, L. G., and Maki, R. H. 1976. Efficiency of arithmetical operations in bilinguals as a function of language. Memory and Cognition, 4: 459-464.
51. Matsuzawa, T. 1985. Use of numbers by a chimpanzee. Nature, 315: 57-59.
52. McClain, L., and Shih Huang, J. Y. 1982. Speed of simple arithmetic in bilinguals. Memory and Cognition, 10: 591-596.
53. McCloskey, M. 1992. Cognitive mechanisms in numerical processing: evidence from acquired dyscalculia. Cognition, 44: 107-157.
54. McNeil, J. E., and Warrington, E. K. 1994. A dissociation between addition and subtraction with written calculation. Neuropsychologia, 32: 717-728.
55. Niedeggen, M., and Rösler, F. 1999. N400 effects reflect activation spread during retrieval of arithmetic facts. Psychological Science, 10: 271-276.
56. Noël, M.-P., and Fias, W. 1998. Bilingualism and numeric cognition. Psychologica Belgica, 38: 231-250.
57. Noël, M.-P., Robert, A., and Brysbaert, M. 1998. Does language really matter when doing arithmetic? Reply to Campbell (1998). Cognition, 67: 365-373.
58. Olthof, A., Iden, C. M., and Roberts, W. A. 1997. Judgements of ordinality and summation of number symbols by squirrel monkeys (Saimiri sciureus). Journal of Experimental Psychology: Animal Behavior Processes, 23: 325-339.
59. Pavlenko, A. 2005. Bilingualism and thought. In Kroll, J. F. and De Groot, A. M. B. (eds.), Handbook of bilingualism: psycholinguistic approaches. New York: Oxford University Press. 433-454.
60. Pesta, B. J., Sanders, R. E., and Murphy, M. D. 2001. Misguided multiplication: creating false memories with numbers rather than words. Memory and Cognition, 29: 478-483.
61. Pica, P., Lemer, C., Izard, V., and Dehaene, S. 2004. Exact and approximate arithmetic in an Amazonian indigen group. Science, 306: 499-503.
62. Platt, J. R., and Johnson, D. M. 1971. Localization of position within a homogeneous behaviour chain: Effects of error contingencies. Learning and Motivation, 2: 386-414.
63. Premack, D., and Premack, A. 2005. Evolution versus invention. Science, 307: 673.
64. Rossor, M. N., Warrington, E. K., and Cipolotti, L. 1995. The isolation of calculation skills. Journal of Neurology, 242: 78-81.
65. Rusconi, E., Galfano, G., Speriani, V., and Umiltà, C. 2004. Capacity and contextual constraints on product activation: Evidence from task-irrelevant fact retrieval. Quarterly Journal of Experimental Psychology, 57A: 1485-1511.
66. Rusconi, E., Walsh, V., and Butterworth, B. 2005. Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing. Neuropsychologia, 43: 1609-1624.
67. Rusconi, E., Galfano, G., Rebonato, E., and Umiltà, C. 2006a. Bidirectional links in the network of multiplication facts. Psychological Research, 70: 32-42.
68. Rusconi, E., Priftis, K., Rusconi, M. L., and Umiltà, C. 2006b. Arithmetic priming from neglected numbers. Cognitive Neuropsychology, 23: 227-239.
69. Rusconi, E., Galfano, G., Umiltà, C., and Job, R. 2006c. Arithmetic priming from written number words. Poster presented at the Annual Meeting of the Cognitive Neuroscience Society, San Francisco, 2006.
70. Sholl, A. 1996. Animacy effects in picture naming and bilingual translation: Perceptual and semantic contributions to concept mediation. Unpublished doctoral dissertation, University of Massachussets, Amherst.
71. Shrager, J., and Siegler, R. S. 1998. SCADs: a model of children's strategy choices and discoveries. Psychological Science, 9: 405-410.
72. Spelke, E. S., and Tsivkin, S. 2001. Language and number: a bilingual training study. Cognition, 78: 45-88.
73. Stazyk, E. H., Ashcraft, M. H., and Hamann, M. S. 1982. A network approach to simple multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8: 320-335.
74. Trick, L. M., and Phylyshyn, Z. W. 1994. Why are small and large numbers enumerated differently? Alimited-capacity preattentive stage in vision. Psychological Review, 101: 80-102.
75. Vaid, J., and Menon, R. 2000. Correlates of bilinguals' preferred language for mental computations. Spanish Applied Linguistics, 4: 325-342.
76. Warrington, E. K. 1982. The fractionation of arithmetical skills: A single case study. Quarterly Journal of Experimental Psychology, 34A: 31-51.
77. Whalen, J., Gallistel, C. R., and Gelman, R. 1999. Nonverbal counting in humans: the psychophysics of number representation. Psychological Science, 10: 130-137.
78. Winkelman, J., and Schmidt, J. 1974. Associative confusions in mental arithmetic. Journal of Experimental Psychology, 102: 734-736.
79. Wynn, K. 1990. Children's understanding of counting. Cognition, 36: 155-193.
80. Zbrodoff, N. J., and Logan, G. D. 1986. On the autonomy of mental processes: A case study of arithmetic. Journal of Experimental Psychology: General, 115: 118-130.
81. Zhang, H., and Zhou, Y. 2003. The teaching of mathematics in Chinese elementary schools. International Journal of Psychology, 38: 286-298.