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Mathematics Education Research Journal

, Volume 29, Issue 1, pp 1–23 | Cite as

Pre-service middle school mathematics teachers’ evaluations of discussions: the case of proof by contradiction

  • Esra Demiray
  • Mine Işıksal Bostan
Original Article
First Online:

Abstract

The purposes of this study are to investigate whether pre-service middle school mathematics teachers evaluate discussions in the cases regarding proof by contradiction correctly, to what extent they explain their correct evaluations by referring to proof by contradiction, and the reasons of their misinterpretations of discussions in the cases regarding proof by contradiction. Data were collected from pre-service middle school mathematics teachers enrolled in a state university in Ankara, Turkey, by asking them to evaluate discussions in two cases related to proof by contradiction. In data analysis, descriptive statistics and item-based analysis were employed. The results of the study indicated that pre-service middle school mathematics teachers are successful in evaluating discussions in the cases regarding proof by contradiction. In terms of year level, it was found that the percentage of the second year students’ correct answers was the lowest in both cases. Moreover, the first year students were the most successful group in the first case, and the third year students were the most successful group in the second case. Nearly half of the students explained their correct answers by referring to proof by contradiction in the first case while the percentage of students who explained their correct answers by mentioning proof by contradiction in the second case was considerably low. When incorrect answers of pre-service middle school mathematics teachers were analyzed, two reasons of their misinterpretations of discussions were emerged as “misunderstanding of the assumption” and “perceiving proof as unnecessary”.

Keywords

Mathematical proof Proof methods Proof by contradiction Pre-service middle school mathematics teachers 
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© Mathematics Education Research Group of Australasia, Inc. 2016

Authors and Affiliations

  1. 1.Faculty of EducationHacettepe UniversityAnkaraTurkey
  2. 2.Faculty of EducationMiddle East Technical UniversityAnkaraTurkey

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