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Do You See What I See? Deepening Teachers’ Understanding of Linear Equations through Student Interviews

Authors: Tamara Pearson; Kelli Nipper; Catherine Matos;

Do You See What I See? Deepening Teachers’ Understanding of Linear Equations through Student Interviews

Abstract

Many teachers have trouble transitioning their students between natural recursive thinking about the data and algebraic notation for representing linear functions (Zazkis & Liljedahl, 2002). In this study, we interviewed eighteen middle school students to see how they used prior instruction to think about a geometric pattern and construct its corresponding linear equation. All students were given the same task to complete and were questioned about their thinking during the interview. We found that the recording of pattern recognition plays a substantial part in helping students recognize and write explicit patterns. By having students decompose the total perimeter into how they saw the pattern growing, students were more successful in making the connection to the numeric representation of growth. In addition, they were better able to explain how they set up the equation, and the connection of each part of the equation to the original pattern. As teachers work with their students in developing a conceptual understanding of linear equations, it is critical that students are exposed to geometric patterns. The results of this study will help mathematics teacher educators better prepare teachers to develop their students’ develop rich and connected mathematical understanding. References: Zazkis, R. & Liljedahl, P. (2002a, March). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379-402. Zazkis, R. & Liljedahl, P. (2002b). Arithmetic sequence as a bridge between conceptual fields. Canadian Journal of Science, Mathematics and Technology Education, 2(1), 93-120.

Keywords

conceptual knowledge, QA1-939, Theory and practice of education, linear equations, generalization, LB5-3640, Mathematics, teacher education

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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