A 3-year longitudinal study of children's comprehension of counting: Do they recognize the optional nature of nonessential counting features?
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2015
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Elsevier Science
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Escudero, A., Rodríguez, P., Lago, M. O., & Enesco, I. (2015). A 3-year longitudinal study of children's comprehension of counting: Do they recognize the optional nature of nonessential counting features?. Cognitive Development, 33, 73-83. https://doi.org/10.1016/j.cogdev.2014.05.003
Abstract
This 3-year longitudinal study examines developmental changes in children's ability to differentiate essential from nonessential counting features. Kindergarteners watched a computer-presented detection task which included three kinds of counts: correct conventional, erroneous and pseudoerrors (with and without statements of cardinal values for the sets). Children had to judge the correctness of those counts and justify their responses. Our data showed that children's explanations provided additional information and thus increased reliability of the assessment. Children were better at detecting erroneous counts than pseudoerrors and at detecting pseudoerrors with cardinal value than pseudoerrors without it. Group analysis showed that children's performance improved with age but analysis of individual differences qualified this result by identifying individual differences in developmental patterns. This study thus provides a more detailed picture of the developmental trajectories of children's comprehension of essential and nonessential counting aspects
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This investigation was funded by Ministry of Education and Science of Spain (SEJ2006-12642).
Referencias bibliográficas:
• Briars, D., & Siegler, R. S.(1984). A featural analysis of preschoolers’ counting knowledge. Developmental Psychology, 20, 607–618. http://dx.doi.org/10.1037/0012-1649.20.4.607
• Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Hove, UK: Psychology Press.
• Dowker, A. (2008). Individual differences in numerical abilities in preschoolers. Developmental Science, 11(5), 650–654. http://dx.doi.org/10.1111/j.1467-7687.2008.00713.x
• Escudero, A. (2012). Erroneous and unusual counts: A longitudinal analysis of the comprehension of counting skills (doctoral thesis). Madrid, Spain: Complutense University. Retrieved from http://eprints.ucm.es/20000/
• Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. http://dx.doi.org/10.1037/a0025510
• 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. http://dx.doi.org/10.1016/0022-0965(92)90026-3
• Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77, 236–263. http://dx.doi.org/10.1006/jecp.2000.2561
• Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choice 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. http://dx.doi.org/10.1016/j.jecp.2004.03.002
• Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard Press.
• Gelman, R., & Meck, E. (1983). Pre-schoolers’ counting: Principles before skills. Cognition, 13, 343–359. http://dx.doi.org/10.1016/0010-0277(83)90014-8
• Gelman, R., & Meck, E. (1986). The notion of principle: The case of counting. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 29–57). Hillsdale, NJ: Erlbaum.
• Hallett, D., Nunes, T., Bryant, P., & Thorpe. (2012). Individual differences in conceptual and procedural fraction understanding: The role of abilities and school experience. Journal of Experimental Child Psychology, 112, 469–486. http://dx.doi.org/10.1016/j.jecp.2012.07.009
• Jordan, J. A., Mulhern, G., & Wylie, J.(2009). Individual differences in trajectories of arithmetical developmentin typically achieving 5-to 7-years-olds. Journal of Experimental Child Psychology, 103, 455–468. http://dx.doi.org/10.1016/j.jecp.2009.01.011
• Kamawar, D., LeFevre, J., Bisanz, J., Fast, L., Skwarchuck, S., Smith-Chant, B., et al. (2010). Knowledge of counting principles: How relevant is order irrelevance? Journal of Experimental Child Psychology, 105, 138–145. http://dx.doi.org/10.1016/j.jecp.2009.08.004
• Laupa, M., & Becker, J. (2004). Coordinating mathematical concepts with the demands of authority: Children’s reasoning about conventional and second-order logical rules. Cognitive Development, 19, 147–168. http://dx.doi.org/10.1016/j.cogdev.2003.11.001
• LeFevre, J., Smith-Chant, B., Fast, L., Skwarchuk, S., Sargla, E., Arnup, J., 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. http://dx.doi.org/10.1016/j.jecp.2005.11.002
• Luchins, A. S., & Luchins, E. H. (1950). New experimental attempts at preventing mechanization in problem solving. Journal of General Psychology, 42, 279–297. http://dx.doi.org/10.1080/00221309.1950.9920160
• McNeil, N. M. (2007). U-Shaped development in math: 7-Year-olds outperform 9-year-olds on equivalence problems. Developmental Psychology, 43(3), 687–695. http://dx.doi.org/10.1037/0012-1649.43.3.687
• McNeil, N. M., & Alibali, M. W. (2005). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 1–17. http://dx.doi.org/10.1111/j.1467-8624.2005.00884.x
• Rodríguez, P., Lago, M. O., Enesco, I., & Guerrero, S. (2013). Children’s understanding of counting: Kindergarten and Primary school children’s detection of errors and pseudoerrors. Journal of Experimental Child Psychology, 114, 35–46. http://dx.doi.org/10.1016/j.jecp.2012.08.005
• Sarnecka, B.W., & Carey, S.(2008). How counting represents number:What children mustlearn and when they learn it. Cognition, 108, 662–774.
• Saxe, G. B., Becker, J., Sadeghpour, M., & Sicilian, S. (1989). Developmental differences in children’s understanding of number word conventions. Journal for Research in Mathematics Education, 20(5), 468–488.