Analysis of junior high school students' refractive thinking process in solving numeracy problems

The purpose of this study is to examine how junior high school students use refractive thinking to solve algebraic problems based on their mathematical skill levels, specifically high and low. Refractive thinking involves a phase where students rethink and modify their approaches to solving algebraic problems. This qualitative study employs interviews and observational methods, with participants consisting of students with both high and low mathematical abilities. The results indicate that students with high mathematical ability navigate the stages of refractive thinking more effectively, including problem identification, strategy formulation, and evaluation. These students are often able to quickly identify errors and experiment with multiple strategies to arrive at better solutions. In contrast, students with low mathematical ability struggle with problem identification and tend to persist with initial, less effective approaches. These findings highlight significant differences in the refractive thinking processes of the two groups, underscoring the need to develop instructional strategies that foster reflective thinking skills, particularly for students with lower mathematical aptitude.