An Exploratory Study of the Factors Related to Successful Mathematical Problem Solving on Non-routine Unconstrained Tasks

Abstract

A main goal of mathematics educators is to guide students in becoming better problem solvers; however, the recipe for successful problem solving is complex due to the varying factors that play a role in the problem solving process (Schoenfeld, 1992). There is a limited amount of research that examines problem solving when students work on non-routine problems outside of the classroom; therefore, the goal of this study is to use secondary data analysis to discover what factors (Schoenfeld, 1992) relate to problem solving on non-routine unconstrained tasks of students in the middle grades. Identifying the factors that relate to successful unconstrained non-routine problem solving can help mathematics teachers and policy makers make more informed decisions about curriculum and instruction in order to enhance problem solving aptitude. Using Schoenfeld’s (1992) theoretical framework for mathematical behavior, the following question set the groundwork for the current study: What resource (computational skills and heuristics), control (self-regulation), and belief/affect factors (demographics, motivation, and anxiety) both individually and collectively relate to unconstrained non-routine mathematical problem solving? The research question is answered in a series of three stages that examines how the factors relate to a) problem correctness, b) correct problem set-up, and c) problem completion. Results suggest that higher levels of self-regulation, and SES status predict problem completion; higher self-regulation, ability beliefs, and SES predict correctly setting-up the problem; and higher levels of anxiety and stronger computational skills predict solving the problem correctly. Reasons for the patterns of results are discussed, as well as suggestions for future research to extend on the current findings.