Interacting neighbors: A connectionist model of retrieval in single-digit multiplication

Memory and Cognition

Volumn 33, Issue 1, 2005, Pages 1-16

  Verguts, Tom ^a,b   Fias, Wim ^a  

^a GHENT UNIVERSITY   (Belgium)

^b NONE   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ARITHMETIC; HUMAN; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PROBLEM SOLVING; REVIEW; SIMULATION; ADULT; ARTICLE; ARTIFICIAL NEURAL NETWORK; COGNITION; MATHEMATICS; NEUROPSYCHOLOGICAL TEST; REACTION TIME;

ADULT; COGNITION; HUMANS; MATHEMATICS; NEURAL NETWORKS (COMPUTER); NEUROPSYCHOLOGICAL TESTS; PROBLEM SOLVING; REACTION TIME;

EID: 20644449461     PISSN: 0090502X     EISSN: None     Source Type: Journal    
DOI: 10.3758/BF03195293     Document Type: Review

References (54)

1. ASHCRAFT, M. H. (1987). Children's knowledge of simple arithmetic: A developmental model and simulation. In C. J. Brainerd, R. Kail, & J. Bisanz (Eds.), Formal methods in developmental research (pp. 302-338). New York: Springer-Verlag.
2. ASHCRAFT, M. H., & BATTAGLIA, J. (1978). Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition. Journal of Experimental Psychology: Human Learning & Memory, 4, 527-538.
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, 5, 396-421.
4. BAROODY, A. J. (1999). The roles of estimation and the commutativity principle in third graders' mental multiplication. Journal of Experimental Child Psychology, 74, 157-193.
5. BUTTERWORTH, B., MARCHESINI, N., & GIRELLI, L. (2003). Multiplication facts: Passive storage or dynamic reorganization? In A. J. Baroody & A. Dowker (Eds.), The development of arithmetical concepts and skills (pp. 189-202). Mahwah, NJ: Erlbaum.
6. BUTTERWORTH, B., ZORZI, M., GIRELLI, L., & JONKHEERE, A. R. (2001). Storage and retrieval of addition facts: The role of number comparison. Quarterly Journal of Experimental Psychology, 54A, 1005-1029.
7. CAMPBELL, J. I. D. (1987). Network interference and mental arithmetic. Journal of Experimental Psychology: Learning, Memory, & Cognition, 13, 109-123.
8. CAMPBELL, J. I. D. (1994). Architectures for numerical cognition. Cognition, 53, 1-44.
9. CAMPBELL, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121-164.
10. 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.
11. CAMPBELL, J. I. D. (1999). Division by multiplication. Memory & Cognition, 27, 791-802.
12. CAMPBELL, J. I. D., & GRAHAM, D. J. (1985). Mental multiplication skill: Structure, process, and acquisition. Canadian Journal of Psychology, 39, 338-366.
13. CAMPBELL, J. I. D., & GUNTER, R. (2002). Calculation, culture, and the repeated operand effect. Cognition, 86, 71-96.
14. CAMPBELL, J. I. D., & OLIPHANT, M. (1992). Representation and retrieval of arithmetic facts: A network-interference model and simulation. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 331-364). Amsterdam: Elsevier.
15. CAMPBELL, J. I. D., & XUE, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299-315.
16. CIPOLOTTI, L., & BUTTERWORTH, B. (1995). Toward a multiroute model of number processing: Impaired number transcoding with preserved calculation skills. Journal of Experimental Psychology: General, 124, 375-390.
17. CIPOLOTTI, L., & DE LACY COSTELLO, A. (1995). Selective impairment for simple division. Cortex, 31, 433-449.
18. COLTHEART, M., RASTLE, K., PERRY, C., LANGDON, R., & ZIEGLER, J. (2001). DRC: A dual route cascaded model of visual word recognition and reading aloud. Psychological Review, 108, 204-256.
19. 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.
20. DEHAENE, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.
21. DEHAENE, S., & COHEN, L. (1997). Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219-250.
22. DEHAENE, S., PIAZZA, M., PINEL, P., & COHEN, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506.
23. GALFANO, G., RUSCONI, E., & UMILTÀ, C. (2003). Automatic activation of multiplication facts: Evidence from the nodes adjacent to the product. Quarterly Journal of Experimental Psychology, 56A, 31-61.
24. GEARY, D. C., WIDAMAN, K. F., & LITTLE, T. D. (1986). Cognitive addition and multiplication: Evidence for a single memory network. Memory & Cognition, 14, 478-487.
25. GROEN, G. J., & PARKMAN, J. M. (1972). A chronometric analysis of simple addition. Psychological Review, 79, 329-343.
26. GROSSBERG, S. (1980). How does the brain build a cognitive code? Psychological Review, 87, 1-51.
27. HECHT, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults. Memory & Cognition, 27, 1097-1107.
28. 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.
29. KOSHMIDER, J. W., & ASHCRAFT, M. H. (1991). The development of children's mental multiplication skills. Journal of Experimental Child Psychology, 51, 53-89.
30. 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.
31. 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.
32. 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, & Cognition, 22, 216-230.
33. 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.
34. MAURO, D. G., LEFEVRE, J., & MORRIS, J. (2003). Effects of problem format on division and multiplication performance: Division facts are mediated by multiplication-based representations. Journal of Experimental Psychology: Learning, Memory', & Cognition, 29, 163-170.
35. MCCLOSKEY, M., ALIMINOSA, D., & SOKOL, S. M. (1991). Facts, rules, and procedures in normal calculation: Evidence from multiple single-patient studies of impaired arithmetic fact retrieval. Brain & Cognition, 17, 154-203.
36. MCCLOSKEY, M., HARLEY, W., & SOKOL, S. M. (1991). Models of arithmetic fact retrieval: An evaluation in light of findings from normal and brain-damaged subjects. Journal of Experimental Psychology: Learning, Memory, & Cognition, 17, 377-397.
37. MCCLOSKEY, M., & LINDEMANN, A. M. (1992). Mathnet: Preliminary results from a distributed model of arithmetic fact retrieval. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 365-409). Amsterdam: Elsevier.
38. NIEDEGGEN, M., & RÖSLER, F. (1999). N400 effects reflect activation spread during retrieval of arithmetic facts. Psychological Science, 10, 271-276.
39. NOËL, M.-P., FIAS, W., & BRYSBAERT, M. (1997). About the influence of the presentation format on arithmetical-fact retrieval processes. Cognition, 63, 335-374.
40. NÜRK, H.-C., WEGER, U., & WILLMES, K. (2001). Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition, 82, B25-B33.
41. PAULI, P., BOURNE, L. E., JR., & BIRBAUMER, N. (1998). Extensive practice in mental arithmetic and practice transfer over a ten-month retention interval. Mathematical Cognition, 4, 21-46.
42. PLAUT, D. C., MCCLELLAND, J. L., SEIDENBERG, M. S., & PATTERSON, K. E. (1996). Understanding normal and impaired word reading: Computational principles in quasi-regular domains. Psychological Review, 103, 56-115.
43. RATINCKX, E., BRYSBAERT, M., & FIAS, W. (2005). Naming two-digit Arabic numerals: Evidence from masked priming studies. Manuscript submitted for publication.
44. RICKARD, T. C., & BOURNE, L. E., JR. (1996). Some tests of an identical elements model of basic arithmetic skills. Journal of Experimental Psychology: Learning, Memory, & Cognition, 22, 1281-1295.
45. RICKARD, T. C., HEALY, A. F., & BOURNE, L. E., JR. (1994). On the representation of arithmetic facts: Operand order, symbol, and operation transfer effects. Journal of Experimental Psychology: Learning, Memory, & Cognition, 20, 1139-1153.
46. SEIDENBERG, M. S., & MCCLELLAND, J. L. (1989). A distributed, developmental model of word recognition and naming. Psychological Review, 96, 523-568.
47. SIEGLER, R. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258-275.
48. SOKOL, S. M., MCCLOSKEY, M., COHEN, N. J., & ALIMINOSA, D. (1991). Cognitive representations and processes in arithmetic: Inferences from the performance of brain-damaged patients. Journal of Experimental Psychology: Learning, Memory, & Cognition, 17, 355-376.
49. STAZYK, E. H., ASHCRAFT, M. H., & HAMANN, M. S. (1982). A network approach to mental multiplication. Journal of Experimental Psychology: Learning, Memory, & Cognition, 8, 320-335.
50. THELEN, E., SCHÖNER, G., SCHEIER, C., & SMITH, L. B. (2001). The dynamics of embodiment: A field theory of infant perseverative reaching. Behavioral & Brain Sciences, 24, 1-86.
51. THIBODEAU, M. H., LEFEVRE, J.-A., & BISANZ, J. (1996). The extension of the interference effect to multiplication. Canadian Journal of Experimental Psychology, 50, 393-396.
52. WHALEN, J., MCCLOSKEY, M., LINDEMANN, M., & BOUTON, G. (2002). Representing arithmetic table facts in memory: Evidence from acquired impairments. Cognitive Neuropsychology, 19, 505-522.
53. WINKELMAN, J. H., & SCHMIDT, J. (1974). Associative confusions in mental arithmetic. Journal of Experimental Psychology, 102, 734-736.
54. 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, & Cognition, 16, 83-97.