Symbolic estrangement: Evidence against a strong association between numerical symbols and the quantities they represent

Journal of Experimental Psychology: General

Volumn 141, Issue 4, 2012, Pages 635-641

  Lyons, Ian M ^a   Ansari, Daniel ^b   Beilock, Sian L ^a  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Comparison; Number; Quantity; Representation; Symbols

Indexed keywords

ADULT; ARTICLE; ASSOCIATION; COMPARATIVE STUDY; HUMAN; MATHEMATICAL PHENOMENA; NEUROPSYCHOLOGICAL TEST; PATTERN RECOGNITION; PHYSIOLOGY; PSYCHOMOTOR PERFORMANCE;

ADULT; ASSOCIATION; HUMANS; MATHEMATICAL CONCEPTS; NEUROPSYCHOLOGICAL TESTS; PATTERN RECOGNITION, VISUAL; PSYCHOMOTOR PERFORMANCE; YOUNG ADULT;

EID: 84872708971     PISSN: 00963445     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0027248     Document Type: Article

References (47)

1. Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278-291. doi:10.1038/nrn2334
2. Ansari, D., Lyons, I. M., van Eimeren, L., & Xu, F. (2007). Linking visual attention and number processing in the brain: The role of the temporoparietal junction in small and large symbolic and nonsymbolic number comparison. Journal of Cognitive Neuroscience, 19, 1845-1853. doi:10.1162/jocn.2007.19.11.1845
3. Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016-1031. doi:10.1111/j.1467-8624.2008.01173.x
4. Buckley, P. B., & Gillman, C. B. (1974). Comparisons of digits and dot patterns. Journal of Experimental Psychology, 103, 1131-1136. doi:10.1037/h0037361
5. Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14, 534-541. doi:10.1016/j.tics.2010.09.007
6. Chen, Q., & Verguts, T. (2010). Beyond the mental number line: A neural network model of number-space interactions. Cognitive Psychology, 60, 218-240. doi:10.1016/j.cogpsych.2010.01.001
7. Crutch, S. J., & Warrington, E. K. (2010). The differential dependence of abstract and concrete words upon associative and similarity-based information: Complementary semantic interference and facilitation effects. Cognitive Neuropsychology, 27, 46-71. doi:10.1080/02643294.2010.491359
8. Damian, M. F. (2004). Asymmetries in the processing of Arabic digits and number words. Memory & Cognition, 32, 164-171. doi:10.3758/BF03195829
9. Deacon, T. (1997). The symbolic species: The co-evolution of language and the human brain. London, England: Norton.
10. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.
11. Dehaene, S. (2008). Symbols and quantities in parietal cortex: Elements of a mathematical theory of number representation and manipulation. In P. Haggard & Y. Rossetti (Eds.), Sensorimotor foundations of higher cognition: Attention and Performance 22 (pp. 527-574). New York, NY: Oxford University Press.
12. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.
13. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506. doi:10.1080/02643290244000239
14. Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P., & Orban, G. A. (2003). Parietal representation of symbolic and nonsymbolic magnitude. Journal of Cognitive Neuroscience, 15, 47-56. doi:10.1162/089892903321107819
15. Gebuis, T., & Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141, 642-648. doi:10.1037/a0026218
16. Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., & Verguts, T. (2010). Verbal-spatial and visuospatial coding of number-space interactions. Journal of Experimental Psychology: General, 139, 180-190. doi:10.1037/a0017688
17. Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115, 394-406. doi:10.1016/j.cognition.2010.02.002
18. Goldfarb, L., Henik, A., Rubinsten, O., Bloch-David, Y., & Gertner, L. (2011). The numerical distance effect is task dependent. Memory & Cognition, 39, 1508-1517. doi:10.3758/s13421-011-0122-z
19. Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008, October 2). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665-668. doi:10.1038/nature07246
20. Holloway, I. D., & Ansari, D. (2010). Developmental specialization in the right intraparietal sulcus for the abstract representation of numerical magnitude. Journal of Cognitive Neuroscience, 22, 2627-2637. doi:10.1162/jocn.2009.21399
21. Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106, 1221-1247. doi:10.1016/j.cognition.2007.06.004
22. Kranczioch, C., Debener, S., Schwarzbach, J., Goebel, R., & Engel, A. K. (2005). Neural correlates of conscious perception in the attentional blink. NeuroImage, 24, 704-714. doi:10.1016/j.neuroimage.2004.09.024
23. Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105, 395-438. doi:10.1016/j.cognition.2006.10.005
24. Luck, S. J., & Vogel, E. K. (1997, November 20). The capacity of visual working memory for features and conjunctions. Nature, 390, 279-281. doi:10.1038/36846
25. Lyons, I. M., & Ansari, D. (2009). The cerebral basis of mapping nonsymbolic numerical quantities onto abstract symbols: An fMRI training study. Journal of Cognitive Neuroscience, 21, 1720-1735. doi:10.1162/jocn.2009.21124
26. Lyons, I. M., & Beilock, S. L. (2009). Beyond quantity: Individual differences in working memory and the ordinal understanding of numerical symbols. Cognition, 113, 189-204. doi:10.1016/j.cognition.2009.08.003
27. Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121, 256-261. doi:10.1016/j.cognition.2011.07.009
28. Mandler, G., & Shebo, B. J. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General, 111, 1-22. doi:10.1037/0096-3445.111.1.1
29. McCrink, K., & Spelke, E. S. (2010). Core multiplication in childhood. Cognition, 116, 204-216. doi:10.1016/j.cognition.2010.05.003
30. Merten, K., & Nieder, A. (2009). Compressed scaling of abstract numerosity representations in adult humans and monkeys. Journal of Cognitive Neuroscience, 21, 333-346. doi:10.1162/jocn.2008.21032
31. Nieder, A. (2009). Prefrontal cortex and the evolution of symbolic reference. Current Opinion in Neurobiology, 19, 99-108. doi:10.1016/j.conb.2009.04.008
32. Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185-208. doi:10.1146/annurev.neuro.051508.135550
33. Opfer, J. E., & Siegler, R. S. (2007). Representational change and children's numerical estimation. Cognitive Psychology, 55, 169-195. doi:10.1016/j.cogpsych.2006.09.002
34. Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116, 33-41. doi:10.1016/j.cognition.2010.03.012
35. 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. doi:10.1016/j.neuron.2004.10.014
36. Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human interparietal cortex. Neuron, 53, 293-305.
37. Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004, October 15). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499-503. doi:10.1126/science.1102085
38. Pylyshyn, Z. W. (2001). Visual indexes, preconceptual objects, and situated vision. Cognition, 80, 127-158. doi:10.1016/S0010-0277(00)00156-6
39. Raymond, J. E., Shapiro, K. L., & Arnell, K. M. (1992). Temporary suppression of visual processing in an RSVP task: An attentional blink? Journal of Experimental Psychology: Human Perception and Performance, 18, 849-860. doi:10.1037/0096-1523.18.3.849
40. Revkin, S. K., Piazza, M., Izard, V., Cohen, L., & Dehaene, S. (2008). Does subitizing reflect numerical estimation? Psychological Science, 19, 607-614. doi:10.1111/j.1467-9280.2008.02130.x
41. Santens, S., & Gevers, W. (2008). The SNARC effect does not imply a mental number line. Cognition, 108, 263-270. doi:10.1016/j.cognition.2008.01.002
42. Santens, S., Roggeman, C., Fias, W., & Verguts, T. (2010). Number processing pathways in human parietal cortex. Cerebral Cortex, 20, 77-88. doi:10.1093/cercor/bhp080
43. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237-250. doi:10.1111/1467-9280.02438
44. van Dijck, J. P., Gevers, W., Lafosse, C., Doricchi, F., & Fias, W. (2011). Non-spatial neglect for the mental number line. Neuropsychologia, 49, 2570-2583. doi:10.1016/j.neuropsychologia.2011.05.005
45. Verguts, T., & Fias, W. (2004). Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience, 16, 1493-1504. doi:10.1162/0898929042568497
46. Wagner, J. B., & Johnson, S. C. (2011). An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition, 119, 10-22. doi:10.1016/j.cognition.2010.11.014
47. Wiese, H. (2003). Iconic and non-iconic stages in number development: The role of language. Trends in Cognitive Sciences, 7, 385-390. doi:10.1016/S1364-6613(03)00192-X