Analysis of High School Students' Critical Mathematical Thinking Processes Reviewed From The Perspective of Students' Self-Efficacy

Critical thinking is an essential competency in twenty-first-century mathematics education because it enables students to analyze, evaluate, and solve mathematical problems systematically. This study aimed to analyze the mathematical critical-thinking processes of high school students across different self-efficacy levels. The study used a qualitative descriptive approach and purposively selected three Grade 10 students representing high, medium, and low self-efficacy from an initial group of 36 students. Data were collected through a mathematical critical thinking test, a self-efficacy questionnaire, and semi-structured interviews, and were analyzed using the interactive model of data reduction, data display, and conclusion drawing. The findings revealed distinct critical thinking processes across the three self-efficacy levels. The participant representing the high self-efficacy category demonstrated systematic analysis, independent inference, reflective evaluation, coherent explanation, and effective self-regulation. Likewise, participants in the medium and low self-efficacy categories exhibited distinct critical thinking processes with different reasoning patterns. Theoretically, these findings suggest that self-efficacy is reflected in the progression of mathematical critical thinking across problem-solving stages. Higher self-efficacy was associated with more independent, reflective engagement across analysis and inference, evaluation, explanation, and self-regulation. In contrast, lower self-efficacy was associated with greater procedural dependence and less sustained reasoning and self-monitoring. Given the qualitative nature of the study and the use of three case participants, these findings describe observed patterns rather than generalizable differences among students with different levels of self-efficacy. Keywords: Mathematical Critical Thinking; Self-Efficacy; Mathematical Problem Solving; Critical Thinking Processes; Arithmetic Sequences and Series