STUDENTS’ MEANINGS FOR EXTENSIVE QUANTITATIVE UNKNOWNS
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Proceedings of the Thirty-ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
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A series of three design experiments was conducted with middle school students to investigate relationships between students’ rational number knowledge and algebraic reasoning. After the first experiment a change was made in the investigation of students’ construction of extensive quantitative unknowns. Students were asked to represent in pictures and equations the values for an unknown height measured in two different, multiplicatively-related measurement units. The work of 13 students operating at two levels of multiplicative reasoning was analyzed to identify differences and similarities. Students operating at the lower level of reasoning required substantial support to construct unknowns with implicit quantitative relationships, while students operating at the higher level of reasoning constructed unknowns with explicitly embedded units.
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Hackenberg, A. J., Aydeniz, F., Jones, R., & Borowksi, R. (2017). Students’ meanings for extensive quantitative unknowns. In Galindo, E. & Newton, J. (Eds.), Proceedings of the Thirty-ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 311-314). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
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