Abstract
We provide evidence that student representations can serve different purposes in the context of classroom problem solving. A strategy used expressly to solve a problem might be represented in one way, and in another way when the problem is generalized or extended, and yet in another way when the solution strategy is explained to peers or a teacher. We discuss the apparent long-term memory implications this has regarding the preferences that students have for their original versus later developed representations, and how these preferences relate to the use of representational flexibility in classroom settings.
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Notes
The material contained herein is based upon work supported by the U.S. National Science Foundation (NSF) under grant numbers 0138806 (The Newark Public Schools Systemic Initiative in Mathematics) and ESI-0333753 (MetroMath: The Center for Mathematics in America’s Cities). Any opinions, findings and conclusions or recommendations are those of the authors and do not necessarily reflect the views of the NSF, Rutgers University or the Newark Public Schools.
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The authors would like to thank the editor and three anonymous reviewers for a number of invaluable suggestions.
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Warner, L.B., Schorr, R.Y. & Davis, G.E. Flexible use of symbolic tools for problem solving, generalization, and explanation. ZDM Mathematics Education 41, 663–679 (2009). https://doi.org/10.1007/s11858-009-0190-8
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DOI: https://doi.org/10.1007/s11858-009-0190-8