Extricating justification scheme theory in middle school mathematical problem solving

During cognitive interviews, twenty middle grades students reasoned about their solutions to four contextualized problems. The Problem Solving Justification Scheme (PSJS) was used as our theoretical lens and the basis for our analysis. The PSJS scheme was modified from the work of Harel & Sowder (1998) making it more broadly applicable and accounting for research developments in the cognitive sciences. We use student interview excerpts to define the four major categories of Mechanistic, Authoritarian, Language, and Visual of the PSJS and to elaborate on the various sub-levels. Analysis of cognitive interview transcripts revealed that both successful and unsuccessful students used combinations of justification schemes in determining their mathematical solutions. The major difference between successful and unsuccessful students was the ability to correctly select a representational aspect of the problem that triggered a correct solution strategy.