Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect

Attention, Perception, and Psychophysics

Volumn 71, Issue 4, 2009, Pages 803-821

  Knops, André ^a,b,c   Viarouge, Arnaud ^a,b,c   Dehaene, Stanislas ^a,b,c,d  

^a INSERM   (France)

^b DIF   (France)

^c UNIVERSITÉ PARIS SACLAY   (France)

^d Centre de Recherche Interdisciplinaire en Biologie   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ADULT; ARTICLE; ATTENTION; DECISION MAKING; DISCRIMINATION LEARNING; FEMALE; HUMAN; LEARNING; MALE; MATHEMATICS; ORIENTATION; PATTERN RECOGNITION; PROBLEM SOLVING; PSYCHOMOTOR PERFORMANCE; REACTION TIME; SHORT TERM MEMORY; SYMBOLISM;

ADULT; ASSOCIATION LEARNING; ATTENTION; CHOICE BEHAVIOR; DISCRIMINATION LEARNING; FEMALE; HUMANS; MALE; MATHEMATICS; MEMORY, SHORT-TERM; ORIENTATION; PATTERN RECOGNITION, VISUAL; PROBLEM SOLVING; PSYCHOMOTOR PERFORMANCE; REACTION TIME; SYMBOLISM; YOUNG ADULT;

EID: 67650138991     PISSN: 19433921     EISSN: None     Source Type: Journal    
DOI: 10.3758/APP.71.4.803     Document Type: Article

References (47)

1. Barth, H., Kanwisher, N., & Spelke, E. (2003). The construction of large number representations in adults. Cognition, 86, 201-221.
2. Barth, H., La Mont, K., Lipton, J., Dehaene, S., Kanwisher, N., & Spelke, E. (2006). Nonsymbolic arithmetic in adults and young children. Cognition, 98, 199-222.
3. Beran, M. J. (2007). Rhesus monkeys (Macaca mulatta) enumerate large and small sequentially presented sets of items using analog numerical representations. Journal of Experimental Psychology: Animal Behavior Processes, 33, 42-54.
4. Brannon, E. M., & Terrace, H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282, 746-749.
5. Brannon, E. M., & Terrace, H. S. (2000). Representation of the numerosities 1-9 by rhesus monkeys (Macaca mulatta). Journal of Experimental Psychology: Animal Behavior Processes, 26, 31-49.
6. Cantlon, J. F., & Brannon, E. M. (2006). Shared system for ordering small and large numbers in monkeys and humans. Psychological Science, 17, 401-406.
7. Cordes, S., Gallistel, C. R., Gelman, R., & Latham, P. (2007). Nonverbal arithmetic in humans: Light from noise. Perception & Psycho-physics, 69, 1185-1203.
8. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.
9. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
10. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and numerical magnitude. Journal of Experimental Psychology: General, 122, 371-396.
11. Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219-250.
12. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506.
13. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970-974.
14. Fischer, M. H., Warlop, N., Hill, R. L., & Fias, W. (2004). Oculomotor bias induced by number perception. Experimental Psychology, 51, 91-97.
15. Freyd, J. (1993). Five hunches about perceptual processes and dynamic representations. In D. Meyer & S. Kornblum (Eds.), Attention and performance XIV: Synergies in experimental psychology, artificial intelligence, and cognitive neuroscience (pp. 99-119). Cambridge, MA: MIT Press.
16. Freyd, J., & Finke, R. A. (1984). Representational momentum. Journal of Experimental Psychology: Learning, Memory, & Cognition, 10, 126-132.
17. Freyd, J., & Finke, R. A. (1985). A velocity effect for representational momentum. Bulletin of the Psychonomic Society, 26, 443-446.
18. Freyd, J., & Pantzer, T. M. (1995). Static patterns moving in the mind. In S. M. Smith, T. B. Ward, & R. A. Finke (Eds.), The creative cognition approach (pp. 181-204). Cambridge, MA: MIT Press.
19. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43-74.
20. Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2007). Symbolic arithmetic knowledge without instruction. Nature, 447, 589-591.
21. Halpern, A. R., & Kelly, M. H. (1993). Memory biases in left versus right implied motion. Journal of Experimental Psychology: Learning, Memory, & Cognition, 19, 471-484.
22. Hooge, I. T., & Erkelens, C. J. (1998). Adjustment of fixation duration in visual search. Vision Research, 38, 1295-1302.
23. Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435-448.
24. Hubbard, T. L. (1995). Cognitive representation of motion: Evidence for friction and gravity analogues. Journal of Experimental Psychology: Learning, Memory, & Cognition, 21, 241-254.
25. Hubbard, T. L. (2005). Representational momentum and related displacements in spatial memory: A review of the findings. Psychonomic Bulletin & Review, 12, 822-851.
26. Hubbard, T. L., & Ruppel, S. E. (2000). Spatial memory averaging, the landmark attraction effect, and representational gravity. Psychological Research, 64, 41-55.
27. Huynh, H., & Feldt, L. S. (1976). Estimation of the box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1, 69-82.
28. Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106, 1221-1247.
29. Jacobs, A. M. (1986). Eye-movement control in visual search: How direct is visual span control? Perception & Psychophysics, 39, 47-58.
30. Kerzel, D. (2003). Attention maintains mental extrapolation of target position: Irrelevant distractors eliminate forward displacement after implied motion. Cognition, 88, 109-131.
31. Krueger, L. E. (1984). Perceived numerosity: A comparison of magnitude production, magnitude estimation, and discrimination judgments. Perception & Psychophysics, 35, 536-542.
32. McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception & Psychophysics, 69, 1324-1333.
33. McCrink, K., & Wynn, K. (2004). Large-number addition and subtraction by 9-month-old infants. Psychological Science, 15, 776-781.
34. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519-1520.
35. Nieder, A., Freedman, D. J., & Miller, E. K. (2002). Representation of the quantity of visual items in the primate prefrontal cortex. Science, 297, 1708-1711.
36. Nieder, A., & Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. Proceedings of the National Academy of Sciences, 101, 7457-7462.
37. Oldfield, R. C. (1971). The assessment and analysis of handedness: The Edinburgh Inventory. Neuropsychologia, 9, 97-113.
38. Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555.
39. Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53, 293-305.
40. Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499-503.
41. Pinhas, M., & Fischer, M. H. (2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109, 408-415.
42. Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 91, 191-205.
43. Sheliga, B. M., Riggio, L., & Rizzolatti, G. (1994). Orienting of attention and eye movements. Experimental Brain Research, 98, 507-522.
44. Shepard, R. N., Kilpatrick, D. W., & Cunningham, J. P. (1975). The internal representation of numbers. Cognitive Psychology, 7, 82-183.
45. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124-1131.
46. Verguts, T., & Fias, W. (2004). Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience, 16, 1493-1504.
47. Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1-B11.