Examination of the concept of translation and rotation in the plane on prospective teachers with different thinking structures according to the RBC abstract model

Individual differences in thinking structures are revealed by the fact that people are inherently different from one another. Individuals' thinking structures were classified as analytical, harmonic, or geometric by Krutetskii based on their problem-solving abilities. In addition, the process of formation of information in the mind is shaped according to thinking structures. Because knowledge creation in the mind cannot be observed, the RBC abstraction model was developed to analyze the level of information formation based on individual actions. The aim of this study is to examine the information formation processes of prospective mathematics teachers with different thinking structures. In this context, the case study design, which is one of the qualitative research methods, was used as a research method. The sample consists of 97 prospective teachers who took the analytical geometry course in the primary school mathematics teaching and mathematics teaching program in a state university in the 2021-2022 academic year. The test prepared by the researcher was applied to the prospective teachers in order to examine the process of forming information about translation and rotation transformations in the plane. In addition, the Mathematics Process Tool test was applied to determine the thinking structures of prospective mathematics teachers. According to the study's findings, prospective mathematics teachers had the most harmonic thinking structure and the least geometric thinking structure. According to the findings, teacher candidates struggle to generate meaningful information during the problem-solving process.