Mathematical Critical Thinking Skills of Students in Solving Set Theory Problems - Intan Rimawati; Siti Suprihatiningsih; Gusti Uripno; Milagros R. Baldemor (Department of Mathematics Education, Universitas Muhammadiyah Purwokerto, Indonesia, 2026)
Mathematical critical thinking is a fundamental competency that students must develop to solve complex problems effectively; however, empirical evidence consistently indicates that this ability remains underdeveloped among junior high school students in Indonesia, particularly in the domain of set theory. This study aims to describe and analyze the mathematical critical thinking skills of seventh-grade students at a public junior high school located in a rural district of West Kalimantan, Indonesia, in solving set theory problems, based on four Facione indicators: interpretation, analysis, evaluation, and inference. A descriptive qualitative design was employed, involving six students selected through purposive sampling from a class of 29 students in the 2025/2026 academic year, categorized into high, medium, and low ability groups. Data were collected through a written essay test and semi-structured interviews, then analyzed using an interactive model comprising data reduction, data display, and conclusion drawing. Results show that high-ability students fulfilled all four critical thinking indicators optimally but demonstrated a consistent limitation in verbal mathematical justification. Medium-ability students performed adequately on interpretation and analysis but encountered difficulties in evaluation and systematic inference. Low-ability students failed to meet most indicators, with the most pronounced deficits in evaluation and inference. This study contributes to the field by investigating the distribution of critical thinking profiles within a unified classroom environment. Crucially, it highlights that verbal mathematical justification represents a fundamental developmental barrier that transcends procedural competence, offering specific implications for the refinement of mathematics instruction.