Abstract
Purpose: This study aims to identify and describe the characteristics of students’ retractive thinking in solving differential equation problems. The research focuses on how students recognize errors, evaluate solution procedures, and revise their mathematical reasoning during the problem-solving process. Methods: This qualitative study employed a case study design involving eight mathematics education students who had completed a Differential Equations course. Participants were selected through purposive sampling. Data were collected using think-aloud protocols, semi-structured interviews, and documentation of students’ written work. Data were analyzed through data condensation, data display, and conclusion drawing, supported by triangulation and member checking to ensure credibility. Findings: The findings reveal three main characteristics of retractive thinking. First, students demonstrate error recognition, shown by their ability to identify inconsistencies in their solution steps during or after problem solving. Second, students exhibit procedural re-examination, where they return to earlier steps to verify formulas and computational processes. Third, students apply solution revision strategies, ranging from correcting algebraic errors to restructuring entire solution procedures. However, retractive thinking is not consistently supported by conceptual understanding, as many revisions remain procedural rather than conceptual. This indicates a gap between procedural fluency and conceptual awareness in differential equation problem solving. Research Implications: The findings suggest the importance of integrating metacognitive strategies in teaching differential equations, particularly activities that promote self-monitoring, error analysis, and reflective revision. These strategies can strengthen students’ retractive thinking abilities. However, this study is limited by its small sample size and case study design, which restrict generalization. The findings are therefore context-bound and intended to provide analytical insight rather than statistical generalization. Originality: This study contributes to the literature by specifically identifying and describing retractive thinking characteristics in the context of differential equation problem solving, offering a process-oriented perspective beyond procedural error analysis