Developing a Contextualization of Students’ Mathematical Problem Solving

This 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