Exploring Junior High School Students’ Mathematical Problem-Solving Abilities in Linear Equations Based on Cognitive Style

Abstract

This study explores junior high school students’ mathematical problem-solving abilities in the topic of linear equations based on their cognitive styles. A qualitative case study design was employed involving 13 ninth-grade students from SMP Negeri 6 Watubangga, Southeast Sulawesi, Indonesia. Students’ cognitive styles were identified using the Matching Familiar Figures Test (MFFT), resulting in the classification of nine impulsive and four reflective students. Four participants, consisting of two impulsive and two reflective students with moderate mathematical ability, were purposively selected for in-depth analysis. Data were collected through a mathematical problem-solving test on linear equations, semi-structured interviews, and documentation. Data analysis followed the interactive model of Miles, Huberman, and Saldaña, including data condensation, data display, and conclusion drawing and verification. Students’ problem-solving performance was analyzed using Polya’s four-stage framework: understanding the problem, devising a plan, carrying out the plan, and looking back. The findings revealed clear differences between impulsive and reflective students across the problem-solving stages. Impulsive students tended to respond quickly but often failed to identify relevant information, develop systematic solution plans, and verify their answers, resulting in procedural and computational errors. In contrast, reflective students demonstrated more organized and systematic problem-solving processes, carefully selecting strategies and reviewing their work before reaching conclusions. These findings highlight the importance of considering cognitive styles when designing adaptive mathematics instruction to enhance students’ problem-solving abilities.