<![CDATA[Formal thinking requires analytical skills to evaluate whether a statement is true or false. However, researchers have found that some students complete the mathematical proof process using intuitive thinking. Students who studied mathematical proof in their early semesters often struggle to construct structural proofs intuitively. Therefore, this study aims to explore students' thought processes in conducting mathematical proofs, transitioning from intuitive reasoning to deductive reasoning, and achieving correct conclusions. The research employs a qualitative descriptive method, validated by experts in mathematical proof and reasoning, all of whom have at least ten years of teaching experience in the field. The subjects of this study were two students selected based on their thought processes, ranging from intuitive to deductive reasoning, with both providing correct and incorrect answers. Students who struggle with this transition tend to rely on institutional and evaluative assurances. In contrast, those who successfully navigate the transition are able to integrate evaluative, empirical, and a priori warrants into their reasoning. This research suggests that all parties involved in mathematical proof need to pay careful attention to each stage of the reasoning process to ensure accuracy.]]>
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