Extricating Justification Scheme Theory in Middle School Mathematical Problem Solving
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2012, 2012 by The Research Council on Mathematics Learning. All rights reserved. Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research developments in the cognitive sciences. During cognitive interviews, students reasoned about their solutions to four contextualized problems. We use student interview excerpts to define the four major categories of Mechanistic, Authoritarian, Language, and Visual of the justification scheme and to elaborate on the various sublevels. Analysis of cognitive interview transcripts revealed combinations of justifications leading to both successful and unsuccessful problem-solving strategies. The major difference between these strategies was the ability to correctly select a representational aspect of the problem that triggered a correct solution strategy.