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By The Staff of Natioal Council of Teachers of Mathematics

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Extra resources for Journal for Research in Mathematics Education Vol. 33, No. 2 March 2002

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Too often, students have few experiences in comparing different concrete models for fractions and have little opportunity to communicate their solutions to problems. Equivalence is taught as a procedure disconnected from representation, and the role of the unit is addressed inadequately, if at all. The Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) and the Principles and Standards for School Mathematics (NCTM, 2000) provide teachers with suggestions for improving initial fraction instruction in Grades 3–5.

1982). Each new manipulative model was introduced as a translation from one model to another. For example, the teacher would show 2/3 or some other fraction with fraction circles and ask students to show that same fraction with chips. The students then described how both models represented the fraction, noting similarities and differences between the models. Strengths and limitations of each model were discussed with students, and in later lessons, students had opportunities to choose specific models for a variety of problem situations and to justify their choices.

A. & Wilson, L. D. (1995). Issues related to the development of an authentic assessment system for school mathematics. In T. A. ). Reform in school mathematics and authentic assessment (pp. 1–18). New York: SUNY Press. , & MacNamara, A. (1993). Teacher assessment of mathematics Attainment Target 1 (MA1). British Journal of Curriculum and Assessment, 4(1), 16–19. Ruthven, K. (1987). Ability stereotyping in mathematics. Educational Studies in Mathematics, 18, 243–253. Saxe, G. , Franke, M. , & Crockett, M.

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