Özet:

The purpose of this study is to determine the pre-service teachers' proofs on the relations of triangles in the middle school mathematics curriculum, as well as their knowledge of the teaching of these relations and the difficulties that students may face. 45 pre-service teachers attending a state university participated in the qualitative investigation. Four open-ended questions were used to obtain data for each of the five relations. The gathered data were evaluated using the "Mathematical Knowledge for Teaching" model and content analysis. The findings demonstrated that pre-service teachers' content knowledge about triangle relations was not adequate and there were deficiencies in their pedagogical content knowledge. It was discovered that in general, pre-service teachers were unable to effectively explain the mathematical representations of triangle relations and employed the notations improperly. It has been noticed that the majority of pre-service teachers were unable to give proof. When evaluating the pre-service teachers' teaching knowledge, it was established that they were able to organize student-centered instruction and provide a variety of activities for each of the students, but the steps of the teaching process were not clearly articulated. It has been found out that majority of pre-service teachers offer generic information about the difficulties that students may encounter, but do not emphasize the content-specific difficulties that may be encountered.

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