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This article describes the development of a problem‐solving instrument intended for classroom use that addresses the Common Core State Standards for Mathematics. In this study, 137 students completed the assessment, and their responses were analyzed. Evidence for validity was collected and examined using the current standards for educational and psychological testing. Instrument validation findings regarding internal consistency reliability were high, and multiple forms of validity (i.e., content, response processes, internal structure, relationship to other variables, and consequences of testing) were found to be appropriate. The resulting instrument provides teachers and researchers with a sound tool to gather data about sixth‐grade students' problem solving in the Common Core era.

a b s t r a c tThis paper investigates how students contextualize mathematical problem solving, not the actual problems. When students attempt to solve problems, what contexts (situational, cultural, or conceptual) do they evoke to describe their experiences with problem solving? The Common Core State Standards for Mathematical Practice emphasize contextualizing and decontextualizing problems, but what does this mean in practice? Middle and high school students were asked to attempt ability-appropriate problems during semi-structured interviews in this qualitative study. Situational contexts were analyzed using representation analysis (symbolic and nonsymbolic) while cultural contexts were analyzed using linguistic analysis (metaphors). The synergy of these two analyses developed a coherent and consistent conceptual contextualization for mathematical problem solving. Secondary students conceptualized problems as containers with the given information within the problem and solutions outside the problem. Thus students' representations are a means to travel from within the problem to outside of the problem.

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving performance and performance on a unit test were analyzed. The intervention had a positive effect on students' problem-solving performance whereas the comparison group experienced no changes. ANCOVA analyses suggest that intervention students solved more problems on the posttest than their peers, but the comparison group outperformed the intervention group on the unit test.