Psychological models for the development of mathematical understanding: rational numbers and functions

By R. Case, M. Kalchman, Joan Moss. 2001

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An integrated theory of whole number and fractions development. (2011, unknown): “Consistent with these predictions, Kalchman, Moss, and Case (2001) found that an instructional program that emphasized fraction magnitudes was highly effective in promoting understanding of rational numbers, including decimals and percentages as well as fractions.”
How Students Learn: Science in the Classroom. (2005, background): “Cambridge, MA: MIT Press. Brown, A.L., Bransford, J.D., Ferrara, R.A., and Campione J.C. (1983). Learning, remembering, and understanding. In J.H. Flavell and E.M Markman (Eds.), Handbook of child psychology: Cognitive development volume 3 (pp. 78-166). New York: Wiley. Bruner, J. (1960). The proces”
An effective metacognitive strategy: learning by doing and explaining with a computer-based Cognitive Tutor (2002, result): “Finally, our emphasis on visual and verbal knowledge integration is consistent with other successful instructional interventions that have been fundamentally designed to help students connect visual intuitions and more formal verbal knowledge (Griffin et al., 1994; Kalchman et al., 2001).”