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Proof of geometry is a topic that involves mathematical reasoning abilities and relates to perseverance involving hard work, the spirit of achievement, and self-confidence. The current important problem that occurs at this time is that students who are future teachers of mathematics still experience difficulties in compiling proofs, especially those who are not challenged to work hard. This qualitative research explores mathematics teacher candidates' reasoning abilities and perseverance in proving geometric theorems. Therefore, the research design used a case study. There were three participants in this study, and they were student prospective mathematics teachers' s taking geometry courses. Data were collected through working documents, open questionnaires, and semi-structured interviews and were analyzed using iterative techniques consisting of data condensation, data exposure, and verification. The study's results showed that students' prospective teachers did not prioritize proof in solving geometry problems, even though they worked hard to solve the problems independently until they were finished. The students' perseverance also impacts their mathematical reasoning in proving geometric theorems. Students with more hard work values tend to have more reasoning values. The results of this study have implications that there needs to be an effort from the teacher to get used to giving proof questions to support students' perseverance and mathematical reasoning abilities.
Geometry theorem Mathematical reasoning Perseverance Proof
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