<![CDATA[Mathematical critical thinking is a fundamental twenty-first-century competency that underpins informed decision-making, complex problem-solving, and creative reasoning. Nevertheless, accumulating empirical evidence indicates that students’ mathematical critical thinking remains insufficient, particularly in learning circle geometry, which requires conceptual understanding, deductive reasoning, generalization, and mathematical proof, while the deductive dimension of critical thinking has received relatively limited scholarly attention. Accordingly, this study aimed to operationalize and examine six indicators of mathematical critical thinking, such as deduction, interpretation, analysis, inference, evaluation, and explanation, identify students’ highest and lowest levels of achievement across these indicators, map their response patterns, error types, and misconceptions, and investigate the strategies and obstacles they encountered when solving circle-related problems. A sequential explanatory mixed-methods design was employed involving 193 eighth-grade students from a public junior high school in Padang, West Sumatra, Indonesia. Quantitative data were collected using a six-item expert-validated essay test and analyzed descriptively, followed by semi-structured interviews with three students representing high-, moderate-, and low-achievement groups to provide explanatory qualitative insights. The findings revealed generally inadequate mathematical critical thinking with considerable inter-student variation. Interpretation emerged as the strongest indicator, whereas deduction and analysis demonstrated the weakest performance. Students consistently exhibited misconceptions, including failure to recognize the diameter as a special chord, reliance on numerical examples without generalization, weak evaluation of calculation-based claims, and limited ability to articulate procedural reasoning explicitly. These findings underscore the importance of strengthening students’ conceptual understanding of circle properties and relationships, systematically fostering deductive reasoning, proof, and generalization, and designing assessment tasks that require rigorous mathematical justification and explicit reasoning.]]>
