An exploration of critical thinking stages of junior high school students in solving contradictory mathematical problems

Abstract

Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical problems. A qualitative descriptive design was employed, involving two eighth-grade students from SMP Negeri 01 Sumber Pucung, Malang, who were selected based on their skeptical responses to illogical mathematical tasks. Data were collected through open-ended tests and interviews, then analyzed to capture reasoning patterns and problem-solving strategies. The findings revealed three distinct stages of mathematical critical thinking: (1) Initial Stage (interpretation), where anomalies are sensed; (2) Tracing Stage (analysis), where contradictions are identified; and (3) Global View Stage (evaluation and inference), where holistic reasoning and alternative solutions are proposed. Subject 1 demonstrated conceptual awareness, cognitive flexibility, and evaluative rigor, while Subject 2 showed procedural accuracy but limited inferential precision. These findings suggest that contradictory problems can serve as effective instructional tools for balancing procedural and conceptual reasoning. Practical implications highlight the need for integrating contradictory problems into mathematics instruction to promote metacognitive reflection. Future research should expand participant diversity, employ longitudinal and experimental designs, and explore affective dispositions influencing students’ critical engagement.