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An Investigation of pre-service middle school mathematics teachers’ achievement levels in mathematical proof and the reasons of their wrong interpretations

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2013
Demiray, Esra
The first purpose of the study is to investigate pre-service middle school mathematics teachers’ achievement levels in refutation, proof by contrapositive and proof by contradiction. The second purpose is to determine the reasons of their wrong interpretations in mentioned proof methods. The third purpose of the study is to investigate to what extent they can conduct valid proofs. As related to the third purpose, proof methods that they used in their valid proof and the reasons of conducting invalid proofs were also investigated. The participants of the study were selected through convenience sampling. Data was collected from the pre-service middle school mathematics teachers enrolled in a state university in Ankara. To address research questions, frequencies and percentages of the data for every question was used and item based in-depth analysis was employed. The results of the study indicated that pre-service middle school mathematics teachers’ achievement levels in refutation and proof by contradiction are considerably high. However, they mostly answered to contrapositive questions wrongly. The reasons of their wrong interpretations in the mentioned proof methods were also determined. The results of the open-ended proof questions revealed that more than half of the students can conduct valid proof for all of the statements. When students’ valid proof were analyzed, it was seen that mathematical induction and direct proof were mostly used. When students’ invalid proofs were analyzed, it was seen that ‘using the numbers to prove the statement’ and ‘direct restatement of the given expression’ were the common reasons of their invalid proofs.