Acuity of the approximate number system and preschoolers' quantitative development

Developmental Science

Volumn 17, Issue 4, 2014, Pages 492-505

  van Marle, Kristy ^a   Chu, Felicia W ^a   Li, Yaoran ^a   Geary, David C ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHILD DEVELOPMENT; COGNITION; EXECUTIVE FUNCTION; FEMALE; HUMAN; INDIVIDUALITY; INTELLIGENCE; INTELLIGENCE TEST; LEARNING; MALE; MATHEMATICS; NEUROPSYCHOLOGICAL TEST; PRESCHOOL CHILD; SCHOOL; THEORETICAL MODEL;

CHILD DEVELOPMENT; CHILD, PRESCHOOL; COGNITION; EXECUTIVE FUNCTION; FEMALE; HUMANS; INDIVIDUALITY; INTELLIGENCE; INTELLIGENCE TESTS; LEARNING; MALE; MATHEMATICS; MODELS, THEORETICAL; NEUROPSYCHOLOGICAL TESTS; SCHOOLS;

EID: 84904652576     PISSN: 1363755X     EISSN: 14677687     Source Type: Journal    
DOI: 10.1111/desc.12143     Document Type: Article

References (62)

1. Beck, D.M., Schaefer, C., Pang, K., & Carlson, S.M. (2011). Executive function in preschool children: test-retest reliability. Journal of Cognition and Development, 12, 169-193.
2. Blatchford, R., Burke, J., Farquhar, C., Plewis, I., & Tizard, B. (1987). Associations between pre-school reading related skills and later reading achievement. British Educational Research Journal, 13, 15-23.
3. Bonny, J.W., & Lourenco, S.F. (2013). The approximate number system and its relation to early math achievement: evidence from the preschool years. Journal of Experimental Child Psychology, 114, 375-388.
4. Brainerd, C.J. (1979). The origins of the number concept. New York: Praeger.
5. Brannon, E.M., & Van de Walle, G.A. (2001). The development of ordinal numerical competence in young children. Cognitive Psychology, 43, 53-81.
6. Briars, D., & Siegler, R.S. (1984). A featural analysis of preschoolers' counting knowledge. Developmental Psychology, 20, 607-618.
7. Bugden, S., & Ansari, D. (2011). Individual differences in children's mathematical competence are related to the intentional but not the automatic processing of Arabic numerals. Cognition, 118, 32-44.
8. Bull, R., Espy, K.A., & Wiebe, S.A. (2008). Short-term memory, working memory, and executive functions in preschoolers: longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33, 205-228.
9. Bullock, M., & Gelman, R. (1977). Numerical reasoning in young children: the ordering principle. Child Development, 48, 427-434.
10. Bynner, J. (1997). Basic skills in adolescents' occupational preparation. Career Development Quarterly, 45, 305-321.
11. Carey, S. (2004). Bootstrapping and the origins of concepts. Daedalus, 133, 59-68.
12. Carlson, S. M. (2012). Executive Function Scale for Preschoolers Test Manual. Institute of Child Development, University of Minnesota, Minneapolis, MN.
13. Chu, F., vanMarle, K., & Geary, D.C. (2013). Quantitative deficits of preschool children at risk for mathematical learning disability. Frontiers in Developmental Psychology, 4, 195. doi: 10.3389/fpsyg.2013.00195
14. Clark, C.A.C., Pritchard, V.E., & Woodward, L.J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46, 1176-1191.
15. Clark, C.A., Sheffield, T.D., Wiebe, S.A., & Espy, K.A. (2013). Longitudinal associations between executive control and developing mathematical competence in preschool boys and girls. Child Development, 84(2), 662-677.
16. De Smedt, B., & Gilmore, C.K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108, 278-292.
17. Duncan, G.J., Dowsett, C.J., Claessens, A., Magnuson, K., Huston, A.C., Klebanov, P., Pagani, L.S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428-1446.
18. Feigenson, L., Carey, S., & Hauser, M. (2002). The representations underlying infants' choice of more: object-files versus analog magnitudes. Psychological Science, 13, 150-156.
19. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307-314.
20. Fuson, K.C. (1988). Children's counting and concepts of number. New York: Springer-Verlag.
21. Gallistel, C.R. (2007). Commentary on Le Corre & Carey. Cognition, 105, 439-445.
22. Gallistel, C.R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43-74.
23. Gallistel, C.R., & Gelman, R. (2000). Non-verbal numerical cognition: from reals to integers. Trends in Cognitive Sciences, 4, 59-65.
24. Gallistel, C.R., & Gelman, R. (2005). Mathematical cognition. In K. Holyoak & R. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (Vol. 23, pp. 559-588). Cambridge: Cambridge University Press.
25. Geary, D.C. (1995). Reflections of evolution and culture in children's cognition: implications for mathematical development and instruction. American Psychologist, 50, 24-37.
26. Geary, D.C. (2011). Cognitive predictors of achievement growth in mathematics: a five year longitudinal study. Developmental Psychology, 47, 1539-1552.
27. Geary, D.C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22, 23-27.
28. Geary, D.C., Bow-Thomas, C.C., & Yao, Y. (1992). Counting knowledge and skill in cognitive addition: a comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54, 372-391.
29. Geary, D.C., Hoard, M.K., Nugent, L., & Bailey, H.D. (2013). Adolescents' functional numeracy is predicted by their school entry number system knowledge. PLoS ONE, 8 (1), e54651. doi: 10.1371/journal.pone.0054651
30. Gelman, R., & Gallistel, C.R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
31. Ginsburg, H.P., & Baroody, A.J. (2003). Test of early mathematical ability (3rd edn.). Austin, TX: Pro-Ed.
32. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the 'number sense': the approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457-1465.
33. Halberda, J., Mazzocco, M., & Feigenson, L. (2008). Individual differences in nonverbal number acuity correlate with maths achievement. Nature, 455, 665-669.
34. Huntley-Fenner, G., & Cannon, E. (2000). Preschoolers' magnitude comparisons are mediated by a preverbal analog mechanism. Psychological Science, 11, 147-152.
35. Invernizzi, M., Sullivan, A., Meier, J., & Swank, L. (2004). PreK teacher's manual: Phonological awareness and literacy screening. Charlottesville, VA: University of Virginia.
36. Jordan, N.C., Kaplan, D., Ramineni, C., & Locuniak, M.N. (2009). Early math matters: kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850-867.
37. 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.
38. LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B.L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: longitudinal predictors of performance. Child Development, 81, 1753-1767.
39. Levine, S.C., Huttenlocher, J., & Jordan, N. (1992). Development of calculation abilities in young children. Journal of Experimental Child Psychology, 53, 72-93.
40. Libertus, M.E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with math abilities. Developmental Science, 14(6), 1292-1300.
41. Locuniak, M.N., & Jordan, N.C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41, 451-459.
42. Lourenco, S.F., Bonny, J.W., Fernandez, E.P., & Rao, S. (2012). Nonsymbolic number and cumulative area representations contribute to shared and unique variance to symbolic math competence. Proceedings of the National Academy of Sciences, USA, 109, 18737-18742.
43. Lyons, I.M., Ansari, D., & Beilock, S.L. (2012). Symbolic estrangement: evidence against a strong association between numerical symbols and the quantities they represent. Journal of Experimental Psychology: General, 141, 635-641.
44. Lyons, I.M., & Beilock, S.L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121, 256-261.
45. Mazzocco, M., Feigenson, L., & Halberda, J. (2011a). Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS One, 6(9), e23749.
46. Mazzocco, M.M.M., Feigenson, L., & Halberda, J. (2011b). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development, 82, 1224-1237.
47. Nieder, A. (2009). Prefrontal cortex and the evolution of symbolic reference. Current Opinion in Neurobiology, 19, 99-108.
48. Preacher, K.J., & Hayes, A.F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879-891.
49. Ritchie, S.J., & Bates, T.C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychological Science, 24, 1301-1308.
50. Rousselle, L., & Noël, M.-P. (2007). Basic numerical skills in children with mathematical learning disabilities: a comparison of symbolic vs. non-symbolic number magnitude processing. Cognition, 102, 361-395.
51. Sarnecka, B.W., & Carey, S. (2008). How counting represents number: what children must learn and when they learn it. Cognition, 108, 662-674.
52. SAS Institute (2004). Statistical analysis system 7.5. Cary, NC: Author.
53. Siegler, R.S., & Robinson, M. (1982). The development of numerical understandings. In H.W. Reese & L.P. Lipsett (Eds.), Advances in child development and behavior, Vol. 16 (pp. 242-312). New York: Academic Press.
54. Spelke, E.S. (2000). Core knowledge. American Psychologist, 55, 1233-1243.
55. Starkey, P. (1992). The early development of numerical reasoning. Cognition, 43, 93-126.
56. vanMarle, K. (2013). Different mechanisms underlie infants' representation of small and large numbers in an ordinal choice task. Journal of Experimental Child Psychology, 114, 102-110.
57. vanMarle, K., Aw, J., McCrink, K., & Santos, L.R. (2006). How capuchin monkeys (Cebus apella) quantify objects and substances. Journal of Comparative Psychology, 120(4), 416-426.
58. vanMarle, K., & Wynn, K. (2001, April). Preschoolers' detection of magical events. Poster presented at the biannual conference of the Society for Research in Child Development (SRCD) in Minneapolis, MN.
59. vanMarle, K., & Wynn, K. (2011). Tracking and quantifying objects and non-cohesive substances. Developmental Science, 14, 502-515.
60. Wechsler, D. (2002). Wechsler Preschool and Primary Scale of Intelligence-III. San Antonio, TX: The Psychological Corporation, Harcourt Brace & Co.
61. Wynn, K. (1990). Children's understanding of counting. Cognition, 36, 155-193.
62. Wynn, K. (1992). Children's acquisition of the number words and the counting system. Cognitive Psychology, 24, 220-251.