Components of Mathematical Problem Solving Competence and Mediation Effects of Instructional Strategies for Mathematical Modeling

Abstract

This study is aimed at investigating the relationships between the components of problem solving skills (four procedural components and modeling competence) and the impact of instructional strategies (collaborative learning and problem posing) on students’ mathematical modeling competence. A survey on students’ mathematical problem solving competence, that was comprised of 40 items, was administered to 1,224 students in Korea and their responses were analyzed quantitatively (exploratory factor analysis, confirmatory factor analysis, and path analysis). The results indicated that students’ competencies regarding procedural components of mathematical problem solving positively affected their mathematical modeling competence. Additionally, instructional strategies utilizing collaborative learning and problem posing mediated and synergized the effect in terms of procedural components of mathematical problem solving and mathematical modeling competence. The study also discusses its contributions to and implications for mathematics educators and teachers.