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Articles

Strategic development of multiplication problem solving: Patterns of students' strategy choices

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Pages 159-170 | Received 06 Jan 2014, Accepted 02 Jun 2015, Published online: 19 Aug 2016

References

  • Alibali, M. W., Phillips, K. M., & Fischer, A. D. (2009). Learning new problem-solving strategies leads to changes in problem representation. Cognitive Development, 24, 89–101.
  • Ambrose, R., Baek, J. M., & Carpenter, T. P. (2003). Children's invention of multidigit multiplication and division algorithms. In A. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructive adaptive expertise (pp. 305–336). Mahwah, NJ: Erlbaum.
  • Ashlock, R. B. (2002). Error patterns in computation: Using error patterns to improve instruction (8th ed.). Upper Saddle River, NJ: Merrill Prentice Hall.
  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29, 15–46.
  • Bottge, B., Butler, M., Choo, S., & Gassaway, L. (2013, April). Detecting error patterns and improving fraction computation. Presented at the Annual Convention of the Council for Exceptional Children, San Antonio, TX.
  • Common Core State Standards Initiative. (2012). Common Core State Standards for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
  • Dayton, C. M. (1998). Latent analysis scaling. Thousand Oaks, CA: SAGE.
  • de la Torre, J., & Douglas, J. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika, 73, 595–624.
  • Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D., & Hamlett, C. L. (2009). The effects of strategic counting instruction, with and without deliberate practice, on number combination skill among students with mathematics difficulties. Learning and Individual Differences, 20, 89–100.
  • Fuchs, L. S., Powell, S. R., Seethaler, P. R., Cirino, P. T., Fletcher, J. M., Fuchs, D., & Hamlett, C. L. (2010). The effects of strategic counting instruction, with and without deliberate practice, on number combinations skill among students with mathematics difficulties. Learning and Individual Differences, 20, 89–100. doi:10.1016/j.lindif.2009.09.003.
  • Fuchs, L. S., Powell, S. R., Seethaler, P. M., Fuchs, D., Hamlett, C. L., Cirino, P. T., & Fletcher, J. M. (2010). A framework for remediating number combination deficits. Exceptional Children, 76, 135–156.
  • Geary, D. C., Hoard, M. K., & Byrd-Craven, J. (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.
  • Hancock, G. R., & Samuelsen, K. M. (2008). Advances in latent variable mixture models. Charlotte, NC: IAP.
  • Hagenaars, J. A., & McCutcheon, A. L. (Eds.). (2002). Applied latent class analysis. Cambridge, UK: Cambridge University Press.
  • Harel, G., & Confrey, J. (Eds.). (1994). The development of multiplicative reasoning in the learning of mathematics. Albany, NY: SUNY Press.
  • Huang, G. H., & Bandeen-Roche, K. (2004). Building an identifiable latent class model with covariate effects on underlying and measured variables. Psychometrika, 69, 5–32.
  • Hunt, J. H., & Vasquez, E. (2014). Effects of ratio strategies intervention on knowledge of ratio equivalence for students with learning disability. The Journal of Special Education, 48, 180–190.
  • Kouba, V. L. (1989). Children's solution strategies for equivalent set multiplication and division word problems. Journal for Research in Mathematics Education, 20, 147–158.
  • Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124, 83–97.
  • Lewis, K. E. (2010). Understanding mathematical learning disabilities: A case study of errors and explanations. Learning Disabilities: A Contemporary Journal, 8(2), 9–18.
  • Magidson, J., & Vermunt, J. K. (2004). Latent class models. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 175–198). Thousand Oaks, CA: Sage.
  • McCrink, K., & Spelke, E. S. (2010). Core multiplication in childhood. Cognition, 116(2), 204–216.
  • Muthén, L. K., & Muthén, B. O. (2012). Mplus user's guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • National Mathematics Advisory Panel. (2008). Foundation for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
  • Nitko, A. J., & Brookhart, S. M. (2011). Educational assessment of students. (6th ed.). Boston, MA: Pearson Education.
  • Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14, 535–569.
  • Piaget, J. (1951). Psychology of intelligence. London, England: Routledge and Kegan Paul.
  • Piaget, J. (1965). The child's conception of number. New York, NY: Norton.
  • Sherin, B., & Fuson, K. (2005). Multiplication strategies and the appropriation of computational resources. Journal for Research in Mathematics Education, 347–395.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.). New York, NY: McGraw-Hill.
  • Siegler, R. S. (1988a). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development, 59, 833–851.
  • Siegler, R. S. (1988b). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258–275.
  • Siegler, R. S. (2000). The rebirth of children's learning. Child Development, 71, 26–35.
  • Siegler, R. S. (2005). Children's learning. American Psychologist, 60, 769–778.
  • Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), The origins of cognitive skills (pp. 229–293). Hillsdale, NJ: Erlbaum.
  • Vermunt, J. K., & Magidson, J. (2002). Latent class cluster analysis. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 89–106). New York, NY: Cambridge University Press.
  • Zhang, D., Ding, Y., Barrett, E.D., Xin, Y. P., & Liu, R.-D. (2014b). A comparison of strategic development of multiplication skills in low-, average- and high- achieving students. The European Journal of Psychology of Education, 29(2), 195–214.
  • Zhang, D., Hsu, H. Y., Katsiyannis, A., Barrett, D. E., & Ju, S. (2011). Adolescents with disabilities in the juvenile justice system: Patterns of recidivism. Exceptional Children, 77, 283–298.
  • Zhang, D., Stecker, P.M., Huckabee, S., & Miller, R. (in press). Students’ strategic development for middle school students struggling with fractions: assessment and intervention. The Journal of Learning Disabilities.
  • Zhang, D., Xin, Y., Harris, K., & Ding, Y. (2014a). Improving multiplication strategic development in children with math difficulties. Learning Disability Quarterly, 37, 15–30.
  • Zhang, D., Xin, Y. P., & Si, L. (2013). Transition from intuitive to advanced strategies in multiplicative reasoning for students with math disabilities. The Journal of Special Education, 47(1), 50–64.
  • Zhou, X., Booth, J. R., Lu, J., Zhao, H., Butterworth, B., Chen, C., & Dong, Q. (2011). Age-independent and age-dependent neural substrate for single-digit multiplication and addition arithmetic problems. Developmental Neuropsychology, 36, 338–352.

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