How Self-Efficacy Shapes Mathematical Analytical Thinking: A Qualitative Study using Action-Process-Object-Schema Theory

Analytical thinking enables students to solve complex problems in a systematic and measurable manner. This study examined students' analytical thinking processes in relation to self-efficacy using the Action-Process-Object-Schema (APOS) theory. The researchers employed a qualitative method with an explanatory approach. They selected mathematics education students from Universitas Muhammadiyah Purwokerto who were enrolled in a sequence convergence course as research subjects. To collect data, the researchers used analytical thinking tests, questionnaires, and interviews. Based on the self-efficacy questionnaire, the researchers classified students into high, medium, and low self-efficacy groups. They selected one informant from each category using purposive sampling. The data analysis involved three stages: data reduction, presentation of findings, and interpretation. The analytical thinking process included collecting, differentiating, organizing, and attributing. The findings showed that students in the high and medium self-efficacy groups demonstrated strong analytical thinking skills. They successfully completed all stages—collecting, differentiating, organizing, and attributing. In contrast, students with low self-efficacy lacked adequate prior knowledge and required assistance in applying mathematical concepts and completing proofs during the organizing stage. These students gathered only limited information at the collection stage due to a poor understanding of the main problem. As a result, they could only partially complete each stage of the analytical thinking process. Keywords: analytic thinking process, APOS theory, self-efficacy.