An investigation of mathematical thinking styles of middle school students with the opinions of teachers and pre-service teachers on this subject

The present study was conducted to investigate the views of mathematics teachers and pre-service teachers on the prediction of mathematical thinking skills of middle school students. In this process, types of mathematical thinking of middle school students were also investigated. The study is designed as a case study, a qualitative research design, based on an in-depth and detailed analysis. The study group was selected to represent all groups that could be participants in the study with maximum variation sampling method. Thus, the study was initially conducted with 96 middle students. Then, the study was conducted with 6 first, second, third and fourth pre-service mathematics teachers attending primary education mathematics teaching department and 6 middle school mathematics teachers. In the study, four non-routine problems, each related to a mathematical thinking sub-dimension, were used in order to determine the mathematical thinking types and predictions of mathematics teachers, pre-service teachers and middle school students. Detailed solutions to the problems were obtained as written documents. Furthermore, semi-structured interviews on problems were conducted with mathematics teachers and pre-service teachers using an interview form. The interview data was obtained as audio recordings, and these recordings were then transcribed. During the interviews, the researcher's observation notes were also collected separately and examined. In the present study, conducted to investigate mathematical thinking of middle school students, mathematics teachers and pre-service teachers in detail, content analysis, a qualitative analysis method, was utilized. In the study, it was determined that the middle school students completed the solution of the problem without considering all possible solutions and only providing a few examples in the assumption component of mathematical thinking. Similarly, in the problem of customization, it was determined that the students generally attempted to solve the problem by assigning certain values. In the scope of assumption and customization problems, it was observed that teachers and pre-service teachers could not predict the strategies used by the students adequately. In the problem of verification and persuasion component, although it was observed that a small percentage of the students attempted to apply different cases, majority of the students attempted to apply previously learned formulas. When the predictions of teachers and pre-service teachers on verification and persuasion component are examined, it was concluded that pre-service teachers expressed the solution methods stated by the students more when compared to the teachers. About the generalization problem, it was determined that the students used the 5 solution strategies. Analysis of the predictions of teachers and pre-service teachers demonstrated that the teachers commented the least and first pre-service teachers commented the most. It was found that the theoretical knowledge levels of pre-service teachers were adequate when compared to teachers, while in practice, the teachers were more successful. Recommendations were made based on the study results. As a result of research, it is thought that it would be useful to perform various activities in order to predict the mathematical thinking styles of the students during the professions of the teachers and during their undergraduate education. Keywords: Mathematical Thinking, Assumption, Customization, Verification and Persuasion, Generalization, Non-routine Problems, Problem Solving, Middle School Students, Pre-service Teacher, Mathematics Teacher.