Examination of mathematical thinking skills of preservice mathematics teachers in the context of mathematical modeling

In this study, mathematical thinking skills of preservice mathematics teachers were investigated in the context of mathematical modelling. In this study, in which the qualitative research approach was adopted, the case study method was used. The research was conducted with 165 preservice mathematics teachers studying at a state university in the Central Anatolia Region in the 2021-2022 academic year. As a data collection tool, the "Mathematical Modeling Oriented Mathematical Thinking Test" consisting of 12 openended questions, three for the specializing and generalizing components of mathematical thinking, two for the conjecturing, and four open questions for the proving component, was developed and administered to the teacher candidates. The data obtained at the end of the application process, on the other hand, were evaluated according to the rubric and the answers of the candidates who could not get full points were classified and themed according to the mistakes they made. As a result of the data obtained, it was determined that the preservice teachers could not fully carry out the modeling process due to the themes of "Lack of reading comprehension" and "Lack of attention" in the questions related to the specializing component. It was determined that in the questions of the generalizing component, they could not fully carry out the modeling process due to the themes of "Wrong association between data", "Lack of attention" and "Not reaching the general". In the questions related to the conjecturing component, it was determined that they could not fully perform the modeling process due to the themes of "Lack of attention" and "Incomplete relationships between data". In addition, it was observed that the preservice teachers answered the modeling questions of the proving component, which is one of the mathematical thinking components, less than the other components. In the questions related to the proving component, it is thought that the modeling process could not be carried out completely due to the themes of "Not reaching the general", "Lack of attention", "Lack of justification", "Lack of subject matter knowledge" and "Lack of reading comprehension". As a result of these themes reached in the analysis of the data, it was suggested to the teachers and parents that attention and focus studies should be carried out in order to eliminate the lack of attention and reading comprehension in students. At the same time, the importance of using models in the modeling process was realized in line with the data obtained, and it was suggested that teachers give examples of mathematical models in the lesson and that students should be encouraged to use models in solving problems.