Predictors of early numeracy: Is there a place for mistakes when learning about number?

British Journal of Developmental Psychology

Volumn 25, Issue 4, 2007, Pages 543-558

  Muldoon, Kevin P ^a   Lewis, Charlie ^b   Berridge, Damon ^b  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36448939765     PISSN: 0261510X     EISSN: None     Source Type: Journal    
DOI: 10.1348/026151007X174501     Document Type: Article

References (34)

1. Agresti, A., & Caffo, B. (2000). Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. American Statistician, 54, 280-288.
2. Baroody, A. (1992). The development of preschooler's counting skills and principles. In J. Bideaud, C. Meljac, & J.-P. Fischer (Eds.), Pathways to number: Children's developing numerical abilities (pp. 99-126). Hillsdale, NJ: Lawrence Erlbaum and Associates.
3. Bialystok, E. (1992). Symbolic representation of letters and numbers. Cognitive Development, 7, 301-316.
4. Briars, D., & Siegler, R. S. (1984). A featural analysis of preschooler's counting knowledge. Developmental Psychology, 20, 607-618.
5. Cowan, R. (1987a). When do children trust counting as a basis for relative number judgments? Journal of Experimental Child Psychology, 43, 328-345.
6. Cowan, R. (1987b). Assessing children's understanding of one-to-one correspondence. British Journal of Developmental Psychology, 5, 149-153.
7. Cowan, R., & Biddle, S. (1989). Children's understanding of one-to-one correspondence in the context of sharing. Educational Psychology, 9, 133-140.
8. Cowan, R., Dowker, A., Christakis, A., & Bailey, S. (1996). Even more precisely assessing children's understanding of the order irrelevance principle. Journal of Experimental Child Psychology, 62, 84-101.
9. Davis, G. E., & Pitkethly, A. (1990). Cognitive aspects of sharing. Journal for Research in Mathematics Education, 21, 145-153.
10. Flavell, J. H. (1970). Developmental studies of mediated memory. In H. W. Reese & L. P. Lipsitt (Eds.), Advances in child development and behavior (Vol. 5, pp. 181-211). New York: Academic Press.
11. Fluck, M., & Henderson, L. (1996). Counting and cardinality in English nursery pupils. British Journal of Educational Psychology, 66, 501-517.
12. Freeman, N., Antonucci, C., & Lewis, C. (2000). Representation of the cardinality principle: Early conception of error in a counterfactual test. Cognition, 74, 71-89.
13. Frydman, O., & Bryant, P. (1988). Sharing and understanding of number equivalence by young children. Cognitive Development, 3, 323-339.
14. Fuson, K. C. (1988). Children's counting and concepts of number. New York: Springer-Verlag.
15. 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.
16. Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121-151.
17. Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
18. Gelman, R., & Meek, E. (1983). The notion of principle: The case of counting. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum.
19. Hughes, M. (1986). Children and number. Oxford: Blackwell.
20. Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52, 130-169.
21. LeFevre, J., Smith-Chant, B. L., Fast, L., Skwarchuk, S., Sargla, E., Arnup, J. S., et al. (2006). What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2. Journal of Experimental Child Psychology, 93,285-303.
22. McCullagh, C. E., & Searle, S. R. (2000). Generalized, linear and mixed models. New York: Wiley.
23. Miller, K. (1984). Child as the measurer of all things: Measurement procedures and the development of quantitative concepts. In C. Sophian (Ed.), Origins of cognitive skills (pp. 193-228). Hillsdale, NJ: Erlbaum.
24. Mix, K. S. (1999). Similarity and numerical equivalence: Appearances count. Cognitive Development, 14, 269-297.
25. Muldoon, K., Lewis, C., & Freeman, N. H. (2003). Putting counting to work: Preschoolers' understanding of cardinal extension. International Journal of Educational Research, 39, 695-718.
26. Muldoon, K. P. (2003). Modelling young children's number skills: The roles of procedural proficiency and error-detection in the development of arithmetical problem solving. Unpublished doctoral thesis.
27. Muldoon, K. P., Lewis, C., & Towse, J. (2005). Because it's there! Why children count, rather than infer, corresponding sets. Cognitive Development, 20, 472-491.
28. Pepper, K. L., & Hunting, R. P. (1998). Preschoolers' counting and sharing. Journalfor Research in Mathematics Education, 29, 164-183.
29. Piaget, J. (1952). The child's conception of number. London: Routledge and Kegan Paul.
30. Porter, J. (1999). The attainment of pupils with severe learning difficulties on a simple counting and error detection task. Journal of Applied Research in Intellectual Disabilities, 12, 87-99.
31. Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical thinking (pp. 75-109). Hove: Psychology Press.
32. Siegler, R. S. (1995). How does change occur: A microgenetic study of number conservation. Cognitive Psychology, 28, 225-273.
33. Sophian, C. (1997). Beyond competence: The significance of performance for conceptual development. Cognitive Development, 12, 281-303.
34. Wynn, K. (1990). Children's understanding of counting. Cognition, 36, 155-193.