Symbolic number: The integration of magnitude and spatial representations in children aged 6 to 8 years

Frontiers in Psychology

Volumn 2, Issue JAN, 2011, Pages

  White, Sonia L J ^a,b   Szucs, Dénes ^a   Soltész, Fruzsina ^a  

^a University of Cambridge   (United Kingdom)

^b QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Magnitude representation; Numerical stroop paradigm; Spatial representation; Spatial numerical association of response codes effect; Symbolic representation

Indexed keywords

EID: 84867084249     PISSN: None     EISSN: 16641078     Source Type: Journal    
DOI: None     Document Type: Article

References (58)

1. Berch, D. B., Foley, E. J., Hill, R. J., and Ryan, P. M. (1999). Extracting parity and magnitude from Arabic numerals: developmental changes in number processing and mental representation. J. Exp. Child Psychol. 74, 286-308.
2. Booth, J. L., and Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Dev. Psychol. 41, 189-201.
3. Boucart, M., and Humphreys, G. W. (1994). Attention to orientation, size, luminance, and color: attention failure within the form domain. J. Exp. Psychol. Hum. Percept. Perform. 20, 61-80.
4. Bryce, D., Szucs, D., Soltész, F., and Whitebread, D. (2011). The development of inhibitory control: an averaged and single-trial lateralized readiness potential study. Neuroimage 57, 723-732.
5. Carey, S. (1985). Conceptual Change in Childhood. Cambridge, MA: MIT Press.
6. Case, R., and Griffin, S. (1990). "Child cognitive development: the role of central conceptual structures in the development of scientific and social thought," in Developmental Psychology: Cognitive, Perceptuo-Motor, and Neuropsychological Perspectives, ed. C. A. Hauert (Amsterdam: Elsevier Science), 193-230.
7. De Smedt, B., Verschaffel, L., and Ghesquiere, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. J. Exp. Child Psychol. 103, 469-479.
8. Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. London: Allen Lane, The Penguin Press.
9. Dehaene, S., Bossini, S., and Giraux, P. (1993). The mental representation of parity and number magnitude. J. Exp. Psychol. 122, 376-396.
10. Dehaene, S., and Cohen, L. (1995). Towards an anatomical and functional model of number processing. Math. Cogn. 1, 83-120.
11. Dehaene, S., Dehaene-Lambertz, G., and Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends Neurosci. 21, 355-361.
12. Dennis, S. (1992). "Stage and structure in the development of children's spatial representations," in The Mind's Staircase: Exploring the Conceptual Underpinnings of Children's Thought and Knowledge, ed. R. Case (Hillsdale, NJ: Erlbaum), 229-246.
13. Ebersbach, M., Luwel, K., Frick, A., Onghena, P., and Verschaffel, L. (2008). The relationship between the shape of the mental number line and familiarity with numbers in 5to 9year old children: evidence for a segmented linear model. J. Exp. Child Psychol. 99, 1-17.
14. Feigenson, L., Spelke, E., and Carey, S. (2002). Infants discrimination of number versus continuous extent. Cogn. Psychol. 44, 33-66.
15. Fias, W., and Fischer, M. H. (2005). "Spatial representation of numbers," in Handbook of Mathematical Cognition, ed. J. I. D. Campbell (New York: Psychology Press), 43-54.
16. Fischer, M. H., Castel, A. D., Dodd, A. D., and Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nat. Neurosci. 6, 555-556.
17. Fuson, K. C., and Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first-and second-grade place-value and multidigit addition and subtraction. J. Res. Math. Educ. 21, 80-206.
18. Geary, D. C. (1994). Children's Mathematical Development: Research and Practical Applications. Washington: American Psychological Association.
19. Gebuis, T., Cohen Kadosh, R., and de Haan, E. (2009). Automatic quantity processing in 5-year olds and adults. Cogn. Process. 10, 133-142.
20. Gelman, R., and Gallistel, C. R. (1978). The Young Child's Understanding of Number. NewYork: Harvard University Press.
21. Girelli, L., Lucangeli, D., and Butterworth, B. (2000). The development of automaticity in accessing number magnitude. J. Exp. Child Psychol. 76, 104-122.
22. Griffin, S. (2004). Building number sense with number worlds: a mathematics program for young children. Early Child. Res. Q. 19, 173-180.
23. Griffin, S. (2005). "Fostering the development of whole-number sense: teaching mathematics in the primary grades, "in How Students Learn: History, Mathematics and Science in the Classroom, eds M. S. Donovan and J. D. Bransford (Washington, DC: The National Academies Press), 257-308.
24. Griffin, S., and Case, R. (1996). Evaluating the breadth and depth of training effects when central conceptual structures are taught. Monogr. Soc. Res. Child Dev. 61, 83-102.
25. Griffin, S., Case, R., and Capodilupo, A. (1995). "Teaching for understanding: the importance of central conceptual structures in the elementary mathematics curriculum," in Teaching for Transfer: Fostering Generalization in Learning, eds A. McKeough, I. Lupert, and A. Marini (Hillsdale, NJ: Erlbaum), 121-151.
26. Henik, A., and Tzelgov, J. (1982). Is three greater than five: the relation between physical and semantic size in comparison tasks. Mem. Cognit. 10, 389-395.
27. Holloway, I. D., and Ansari, D. (2008). Domain-specific and domain-general changes in children's development of number comparison. Dev. Sci. 11, 644-649.
28. Holloway, I. D., and Ansari, D. (2009). Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement. J. Exp. Child Psychol. 103, 17-29.
29. Kaufmann, L., and Nuerk, H. C. (2006). Interference effects in a numerical Stroop paradigm in 9to 12-yearold children with ADHD-C. Child Neuropsychol. 12, 223-243.
30. Landerl, K., and Kölle, C. (2009). Typical and atypical development of basic numerical skills in elementary school. J. Exp. Child Psychol. 103, 546-565.
31. Moyer, R. S., and Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature 215, 1519-1520.
32. Mussolin, C., and Noël, M.-P. (2007). The nonintentional processing Arabic numbers in children. J. Clin. Exp. Neuropsychol. 29, 225-234.
33. Okamoto, Y., and Case, R. (1996). Exploring the microstructure of children's central conceptual structures in the domain of number. Monogr. Soc. Res. Child Dev. 61, 27-58.
34. Piaget, J. (1952). The Child's Conception of Number. NewYork:Norton.
35. Resnick, L. B. (1983). "A developmental theory of number understanding," in The Development of Mathematical Thinking, ed. H. P. Ginsburg (New York: Academic), 110-153.
36. Resnick, L. B. (1989). Developing mathematical knowledge. Am. Psychol. 44, 162-169.
37. Rousselle, L., and Noël, M. P. (2007). Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs. non-symbolic number magnitude processing. Cognition 102, 361-395.
38. Rousselle, L., and Noël, M. P. (2008). The development of automatic numerosity processing in preschoolers: evidence from numerosityperceptual interference. Dev. Psychol. 44, 544-560.
39. Rubinsten, O., Henik, A., Berger, A., and Shahar-Shalev, S. (2002). The development of internal representations of magnitude and their association with Arabic numerals. J. Exp. Child Psychol. 81, 74-92.
40. Schneider, M., Grabner, R. H., and Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: their interrelations in grades 5 and 6. J. Educ. Psychol. 101, 359-372.
41. Schwarz, W., and Ischebeck, A. (2003). On the relative speed account of number-size interference in comparative judgments of numerals. J. Exp. Psychol. Hum. Percept. Perform. 29, 507-522.
42. Sekuler, R., and Mierkiewicz, D. (1977). Children's judgments of numerical inequalities. Child Dev. 48, 630-633.
43. Shaki, S., Fischer, M. H., and Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychon. Bull. Rev. 16, 328-331.
44. Siegler, R. S., and Booth, J. L. (2004). Development of numerical estimation in young children. Child Dev. 75, 428-444.
45. Siegler, R. S., and Opfer, J. E. (2003). The development of numerical estimation: evidence for multiple representations of numerical quantity. Psychol. Sci. 14, 237-243.
46. Siegler, R. S., and Robinson, M. (1982). "The development of numerical understanding, "in Advances in Child Development and Behaviour, Vol. 16, eds H. W. Reese and L. P. Lipsitt (New York: Academic), 242-312.
47. Soltész, F., Szücs, D., and Szücs, L. (2010). Relationships between magnitude representation, counting and memory in 4to 7-year-old children: A developmental study. Behav. Brain Funct. 6, 1-14.
48. Soltész, F., White, S., and Szücs, D. (2011). Event-related brain potentials dissociate the developmental time-course of automatic numerical magnitude analysis and cognitive functions during the first three years of primary school. Dev. Neuropsychol. 36, 682-701.
49. Szücs, D., and Soltész, F. (2007). Eventrelated potentials dissociate facilitation and interference effects in the numerical Stroop paradigm. Neuropsychologia 45, 3190-3202.
50. Szücs, D., Soltész, F., Jarmi, E., and Csepe, V. (2007). The speed of magnitude processing and executive functions in controlled and automatic number comparison in children: an electro-encephalography study. Behav. Brain Funct. 3, 1-20.
51. Szucs, D., Soltész, F., Bryce, D., and Whitebread, D. (2009). Real-time tracking of motor response activation and response competition.
52. Tzelgov, J., and Ganor-Stern, D. (2005). "Automaticity in processing ordinal information," in Handbook of Mathematical Cognition, ed. J. I. D. Campbell (New York: Psychology Press), 55-66.
53. Tzelgov, J., Meyer, J., and Henik, A. (1992). Automatic and intentional processing of numerical information. J. Exp. Psychol. Learn. Mem. Cogn. 18, 166-179.
54. van Dijck, J.-P., and Fias, W. (2011). A working memory account for spatial-numerical associations. Cognition 119, 114-119.
55. van Galen, M., and Reitsma, P. (2008). Developing access to number magnitude: a study of the SNARC effect in 7to 9-year-olds. J. Exp. Child Psychol. 101, 99-113.
56. van Opstal, F., Gevers, W., de Moor, W., and Verguts, T. (2008). Dissecting the symbolic distance effect: comparison and priming effects in numerical and nonnumerical orders. Psychon. Bull. Rev. 15, 419-425.
57. van Opstal, F., and Verguts, T. (2011). The origins of the numerical distance effect: the same-different task. J. Cogn. Psychol. 23, 112-120.
58. Xu, F., and Spelke, E. S. (2000). Large number discrimination in 6-monthold infants. Cognition 74, B1-B11.