<![CDATA[Abstract: This research aimed to describe the thinking process in proof problem solving using direct, contraposition, and contradiction methods in 2nd semester mathematic education students of Nusantara PGRI University of Kediri with (1) high, (2) moderate, and (3) low learning achievements. The research method employed was qualitative approach. Subject of research was selected using purposive sampling technique, consisting of 6 2nd-semester mathematic education students: 2 students with high, 2 with moderate, and 2 with low learning achievements. Data collection was carried out using interview based on proof problem solving assignment. Data validation was carried out using time triangulation, and the valid data was analyzed using data reduction, data display, and conclusion drawing. The result of research showed that: (1) The thinking process of students with high learning achievement. The proof problem solving in direct contraposition, and contradiction ways. In entry phase, the subjects understood the problem by writing antecedent as they know and consequence to be proved. In finishing phase, the subjects explained antecedent into premise correctly and completely, did algebraic operation to connect consequence to premise, in order to prove the consequence. In review phase, the subjects check their answer and were sure with their answer after seeing the process and proof result. (2) The thinking process of students with moderate learning achievement. The proof problem solving in direct, contraposition, and contradiction ways. In entry phase, the subjects understood the problem by writing antecedent as they know and consequence to be proved. In finishing phase, the subjects explained antecedent into premise correctly, did algebraic operation with summing procedure and distributive property to connect consequence to premise in order to prove the consequence. In review phase, the subjects did not check their answer and were sure with their answer when their proved. (3) The thinking process of students with low learning achievement. The proof problem solving in direct, contraposition, and contradiction ways. In entry phase is the same, the subjects understood the problem by writing antecedent as they know and consequence to be proved. In finishing phase, the subjects explained antecedent into premise difficultly, did algebraic operation with summing procedure and distributive property to connect consequence to premise using number example, thereby could not prove the consequence. Then in review phase, the subjects did not check their answer and were sure with their answer after seeing their proof result.Keywords: Thinking Process, Problem Solving, Proof, Learning Achievement ]]>
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