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Papers / Artículos

Understanding mathematical learning disabilities as developmental difference: a fine-grained analysis of one student’s partitioning strategies for fractions / Las discapacidades para el aprendizaje de las matemáticas como diferencia en el desarrollo: un análisis detallado de las estrategias de una estudiante al partir enteros para obtener fracciones

Pages 812-857 | Received 30 Sep 2015, Accepted 09 May 2016, Published online: 05 Sep 2016

References / Referencias

  • Andersson, U. (2010). Skill development in different components of arithmetic and basic cognitive functions: Findings from a 3-year longitudinal study of children with different types of learning difficulties. Journal of Educational Psychology, 102, 115–134. doi:10.1037/a0016838
  • Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113, 447–455. doi:10.1016/j.jecp.2012.06.004
  • 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
  • Confrey, J., Maloney, A. P., Nguyen, K. H., & Rupp, A. A. (2014). Equipartitioning, a foundation for rational number reasoning: Elucidation of a learning trajectory. In A. P. Maloney, J. Confrey, K. H. Nguyen, A. P. Maloney, J. Confrey, & K. H. Nguyen (Eds.), Learning over time: Learning trajectories in mathematics education (pp. 61–96). Charlotte, NC: IAP Information Age Publishing.
  • Empson, S. B. (1999). Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom. Cognition and Instruction, 17, 283–342. doi:10.1207/S1532690XCI1703_3
  • Empson, S. B., & Turner, E. (2006). The emergence of multiplicative thinking in children’s solutions to paper folding tasks. The Journal of Mathematical Behavior, 25, 46–56. doi:10.1016/j.jmathb.2005.11.001
  • Engle, R. A., Conant, F. R., & Greeno, J. G. (2014). Progressive refinement of hypotheses in video-supported research. In R. Goldman, R. Pea, B. Barron, & S. J. Derry (Eds.), Video research in the learning sciences (pp. 239–254). Mahwah, NJ: Erlbaum.
  • Fletcher, J. M., Lyon, G. R., Fuchs, L. S., & Barnes, M. A. (2007). Learning disabilities: From identification to intervention. New York, NY: Guilford Press.
  • Geary, D. C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363–383. doi:10.1016/0022-0965(90)90065-G
  • 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. doi:10.1016/j.jecp.2004.03.002
  • Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five year prospective study. Journal of Educational Psychology, 104, 206–223. doi:10.1037/a0025398
  • Ginsburg, H. P. (1997). Entering the child’s mind: The clinical interview in psychological research and practice. New York, NY: Cambridge University Press.
  • Grobecker, B. (2000). Imagery and fractions in students classified as learning disabled. Learning Disability Quarterly, 23, 157–168. doi:10.2307/1511143
  • Hiebert, J., & Tonnessen, L. H. (1978). Development of the fraction concept in two physical contexts: An exploratory investigation. Journal for Research in Mathematics Education, 9, 374–378. doi:10.2307/748774
  • Hunt, J. H., & Empson, S. B. (2015). Exploratory study of informal strategies for equal sharing problems of students with learning disabilities. Learning Disability Quarterly, 38, 208–220. doi:10.1177/0731948714551418
  • Lamon, S. J. (1996). The development of unitizing: Its role in children’s partitioning strategies. Journal for Research in Mathematics Education, 27, 170–193. doi:10.2307/749599
  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 629–667). Charlotte, NC: Information Age Publishing.
  • Lewis, K. E. (2011). Toward a reconceptualization of mathematical learning disabilities: A focus on difference rather than deficit (Doctoral dissertation). Retrieved from ProQuest Dissertations and Theses database (UMI No. 3555785).
  • Lewis, K. E. (2014). Difference not deficit: Reconceptualizing mathematical learning disabilities. Journal for Research in Mathematics Education, 45, 351–396. doi:10.5951/jresematheduc.45.3.0351
  • Lewis, K. E., & Fisher, M. B. (2016). Taking stock of 40 years of research on mathematical learning disability: Methodological issues and future directions. Journal for Research in Mathematics Education, 47, 338–371.
  • Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21, 16–32. doi:10.2307/749454
  • Mazzocco, M. M. M., Devlin, K. T., & McKenney, S. J. (2008). Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined. Developmental Neuropsychology, 33, 318–344. doi:10.1080/87565640801982403
  • Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development, 82, 1224–1237. doi:10.1111/j.1467-8624.2011.01608.x
  • Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115, 371–387. doi:10.1016/j.jecp.2013.01.005
  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author.
  • National Mathematics Advisory Panel. (2008). Foundations for success: Final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education.
  • Piaget, J., Inhelder, B., & Szeminska, A. (1960). Child’s conception of geometry. New York, NY: Basic Books Inc.
  • 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
  • Pothier, Y., & Sawada, D. (1983). Partitioning: The emergence of rational number ideas in young children. Journal for Research in Mathematics Education, 14, 307–317. doi:10.2307/748675
  • Schoenfeld, A. H. (2010). Reflections of an accidental theorist. Journal for Research in Mathematics Education, 41, 104–116.
  • Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., … Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23, 691–697. doi:10.1177/0956797612440101
  • Steffe, L. P. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking & Learning, 6, 129–162. doi:10.1207/s15327833mtl0602_4
  • Swanson, H. L. (2007). Cognitive aspects of math disabilities. In D. B. Berch, & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 133–146). Baltimore, MD: Paul H. Brookes.
  • Swanson, H. L., & Jerman, O. (2006). Math disabilities: A selective meta-analysis of the literature. Review of Educational Research, 76, 249–274. doi:10.3102/00346543076002249
  • Vygotsky, L. S. (1929/1993). Introduction: Fundamental problems of defectology. In R. W. Rieber, & A. S. Carton (Eds.), The collected works of L. S. Vygotsky, Volume 2: The fundamentals of defectology (pp. 29–51). London: Plenum Press.
  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
  • Werstch, J. V. (1985). Vygotsky and the social formation of mind. Cambridge, MA: Harvard University Press.

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