<![CDATA[This study aims to explore the abductive reasoning strategies used by prospective mathematics teachers in proving and refuting mathematical statements. This study used a qualitative method with a case study design. Fourteen third-year prospective mathematics teachers were involved in this study and were then grouped according to the characteristics of the type of abductive reasoning they used. Data collection techniques included tests given to all prospective mathematics teachers and interviews conducted with five prospective mathematics teachers selected based on their type of abductive reasoning. The data obtained was analyzed through stages that included data condensation, data display, and conclusion drawing. Technique triangulation was used to check the validity of the research findings. In general, it was found that the types of abductive reasoning strategies used by prospective mathematics teachers in proving included fact optimization and mistaken fact. Meanwhile, in refuting mathematical statements, there are three types of abductive reasoning used by students, consisting of fact optimization, mistaken fact, and factual error. The results of this study provide insight into how abductive reasoning contributes to formulating mathematical conjectures and can help educators design relevant learning strategies to support the improvement of students' proof and refutation abilities]]>
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