PRE-FRACTIONAL MIDDLE SCHOOL STUDENTS’ ALGEBRAIC REASONING
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2012-11
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Proceedings of the Thirty-fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
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Abstract
To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of 3 different multiplicative concepts participated. This paper reports on the 6 students with the most basic multiplicative concept, who were also pre- fractional in that they had yet to construct the first genuine fraction scheme. These students’ emerging iterating operations facilitated their algebraic activity, but the lack of a disembedding operation was a significant constraint in developing algebraic equations and expressions.
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Algebra and Algebraic Thinking, Cognition, Rational Numbers
Citation
Hackenberg, A. J., & Lee, M. Y. (2012). Pre-fractional middle school students’ algebraic reasoning. In Van Zoest, L., Lo, J.-J., & Kratky, J. L. (Eds.), Proceedings of the Thirtyfourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) [CD-ROM] (pp. 943-950). Kalamazoo, MI: Western Michigan University.
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