Under- and over-estimation: A bi-directional mapping process between symbolic and non-symbolic representations of number?

Experimental Psychology

Volumn 58, Issue 1, 2011, Pages 39-49

  Crollen, Virginie ^a   Castronovo, Julie ^a,b   Seron, Xavier ^a,c  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b UNIVERSITY OF LEEDS   (United Kingdom)

^c CLINIQUES UNIVERSITAIRES SAINT LUC   (Belgium)

Author keywords

Mapping process; Numerical estimation; Over estimation; Under estimation

Indexed keywords

ADULT; ARTICLE; COGNITION; DECISION MAKING; FEMALE; HUMAN; MALE; MATHEMATICS; PHYSIOLOGY; REACTION TIME;

ADULT; COGNITION; FEMALE; HUMANS; JUDGMENT; MALE; MATHEMATICS; REACTION TIME;

EID: 78651092652     PISSN: 16183169     EISSN: None     Source Type: Journal    
DOI: 10.1027/1618-3169/a000064     Document Type: Article

References (58)

1. Allik, J., & Tuulmets, T. (1991). Occupancy model of perceived numerosity. Perception & Psychophysics, 49, 303-314.
2. Bevan, W., & Turner, E. (1964). Assimilation and contrast in the estimation of number. Journal of Experimental Psychology, 67, 458-462.
3. Buckley, P. B., & Gillman, C. B. (1974). Comparison of digit and dot patterns. Journal of Experimental Psychology, 103, 1131-1136
4. Campbell, J. I. D., & 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.
5. Castronovo, J., & Seron, X. (2007). Numerical estimation in blind subjects: Evidence of the impact of blindness and its following experience. Journal of Experimental Psychology: Human Perception and Performance, 33, 1089-1106.
6. Cipolotti, L., & Butterworth, B. (1995). Toward a multiroute model of number processing: Impaired number transcoding with preserved calculation skills. Journal of Experimental Psychology, 124, 375-390.
7. Cipolotti, L., Butterworth, B., & Denes, G. (1991). A specific deficit for numbers in a case of dense acalculia. Brain, 114, 2619-2637.
8. 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.
9. Cohen Kadosh, R. (2008). Numerical representation: Abstract or nonabstract? The Quarterly Journal of Experimental Psychology, 61, 1160-1168.
10. Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A., & Goebel, R. (2007). Notation-dependent and independent representations of numbers in the parietal lobes. Neuron, 53, 307-314.
11. Cohen Kadosh, R., & Walsh, V. (2009). Numerical representation in the parietal lobes: Abstract or not abstract? Behavioral and Brain Sciences, 32, 313-328.
12. Cordes, S., Gelman, R., Gallistel, C. R., & Whalen, J. (2001). Variability signatures distinguish verbal from non-verbal counting for both large and small numbers. Psychonomic Bulletin and Review, 8, 698-707.
13. Dagenbach, D., & McCloskey, M. (1992). The organization of arithmetic facts in memory: Evidence from a brain-damaged patient. Brain and Cognition, 20, 345-366.
14. Dehaene, S. (1992). Varieties of numerical abilities. Cognition,44, 1-42.
15. Dehaene, S. (1997). The number sense. New York: Oxford University Press.
16. Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.
17. Dehaene, S. (2003). The neural basis of the Weber-Fechner law: A logarithmic mental number line. Trends in Cognitive Sciences, 7, 145-147.
18. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.
19. Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219-250.
20. Dehaene, S., Izard, V., & Piazza, M. (2005). Control over nonnumerical parameters in numerosity experiments. Unpublished manuscript. Available: www.unicog.org.
21. Dehaene, S., Izard, V., Spelke, E., & Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science, 30, 1217-1220.
22. Delazer, M., & Benke, T. (1997). Arithmetic facts without meaning. Cortex, 33, 697-710.
23. Durgin, F. H. (1995). Texture density adaptation and the perceived numerosity and distribution of texture. Journal of Experimental Psychology: Human Perception and Performance, 21, 149-169.
24. Frith, C. D., & Frith, U. (1972). The solitaire illusion: An illusion of numerosity. Perception & Psychophysics, 11, 409-410.
25. Gallistel, C. R., & Gelman, R. (1992). Pre-verbal and verbal counting and computation. Cognition, 44, 43-74.
26. Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4, 59-65.
27. Ginsburg, N. (1980). The regular-random numerosity illusion: Rectangular patterns. The Journal of General Psychology, 103, 211-216.
28. Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496-499.
29. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the "Number Sense": The approximate number system in 3-, 4-, 5-, 6-year-olds and adults. Developmental Psychology, 44, 1457-1465.
30. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665-668.
31. Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children's mathematics achievement. Journal of Experimental Child Psychology, 103, 17-29.
32. Holloway, I. D., Price, G. R., & Ansari, D. (2010). Common and segregated neural pathways for the processing of symbolicand nonsymbolic numerical magnitude: An fMRI study. Neuroimage, 49, 1006-1017.
33. Indow, T., & Ida, M. (1977). Scaling of dot numerosity. Perception & Psychophysics, 22, 265-276.
34. Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106, 1221-1247.
35. Kaufman, L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. American Journal ofPsychology, 62, 498-525.
36. 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.
37. Krueger, L. E. (1972). Perceived numerosity. Perception & Psychophysics, 11, 5-9.
38. Krueger, L. E. (1982). Single judgments of numerosity. Perception & Psychophysics, 31, 175-182.
39. Krueger, L. E. (1984). Perceived numerosity: A comparison of magnitude production, magnitude estimation, and discrimination judgments. Perception & Psychophysics, 35, 536-542.
40. Krueger, L. E. (1989). Reconciling Fechner and Stevens: Toward a unified psychophysical law. Behavioral and Brain Sciences, 12, 251-320.
41. Lipton, J. S., & Spelke, E. (2005). Preschool children's mapping of number words to non-symbolic numerosities. Child Development, 76, 978-988.
42. Mandler, G., & Shebo, B. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General, 111, 1-22.
43. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519-1520.
44. Mundy, E., & Gilmore, C. K. (2009). Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology, 103, 490-502.
45. Pesenti, M., Thioux, M., Samson, D., Bruyer, R., & Seron, X. (2000). Number processing and calculation in a case of visual agnosia. Cortex, 36, 377-400.
46. 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.
47. Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499-503.
48. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237-243.
49. Stevens, S. S. (1953). On the brightness of lights and the loudness of sounds. Science, 118, 576.
50. Stevens, S. S. (1955). The measurement of loudness. Journal of the Acoustical Society of America, 27, 815-829.
51. Stevens, S. S (1957). On the psychophysical law. Psychological Review, 64, 153-181.
52. Stevens, S. S. (1966). Matching functions between loudness and ten other continua. Perception & Psychophysics, 1, 5-8.
53. Stevens, S. S., & Greenbaum, H. (1966). Regression effect in sychophysical judgment. Perception &chophysics, 1,439-446.
54. Teghtsoonian, R. (1973). Range effects in psychophysical scaling and a revision of Steven's law. The American Journal of Psychology, 86, 3-27.
55. Teghtsoonian, R., & Teghtsoonian, M. (1978). Range and regression effects in magnitude scaling. Perception & Psychophysics, 24, 305-314.
56. Van Oeffelen, M. P., & Vos, P. G. (1982). A probabilistic model for the discrimination of visual number. Perception & Psychophysics, 32, 163-170.
57. Verguts, T., Fias, W., & Stevens, M. (2005). A model of exact small-number representation. Psychonomic Bulletin & Review, 12, 66-80.
58. Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Non-verbal counting in humans: The psychophysics of number representation. Psychological Science, 10, 130-137.