Concept images and misconceptions of mathematics teacher candidates on the subject of triangles

In this study, it is aimed to investigate the concept images and misconceptions of preservice middle school mathematics teachers about triangles. In this study, which was designed with a qualitative research approach, a holistic multiple case study was used. The participants of the research are 55 preservice middle school mathematics teachers studying at a state university in the spring term of the 2021-2022 academic year. While the convenience sampling method was used in the selection of the relevant university, the criterion sampling method was used in the selection of the candidates studying at this university. In order to determine the concept images, eight items of the test prepared by Şengül-Akdemir (2017) and two items prepared by the researcher were used. In order to determine the misconceptions of the candidates about triangles, all the items in the inventory of identifying the misconceptions developed by Kaya (2018) and four items prepared by the researcher were used. In this case, a measurement tool consisting of 27 items, 12 of which is open-ended and 15 of which is multiple-choice, was applied to the candidates. Candidates were expected to explain their answers to both open-ended questions and multiple-choice questions. Even if the answers given to the multiple-choice questions are correct, since it is thought that there may be errors in the meaning of the concept, the candidates were asked to explain the multiple-choice items in this study. In this context, the open-ended responses of the candidates to both tests were examined in detail by content analysis method. As a result of the analysis, it was determined that the candidates primarily focused on non-mathematical expressions in the definitions of triangles. In addition, it has been seen that the candidates have common misconceptions about triangle inequality, elements of triangle, equilateral triangle and isosceles triangle distinction and similarities. It is thought that candidates with misconceptions may encounter difficulties in making sense of the continuation concepts.