Investigation of model building performances of prospective middle school mathematics teachers in the context of problem posing and solving

This study aims to examine the model-creating performances of prospective middle school mathematics teachers in teaching fractions in the context of problem posing and solving and to determine their views on using models. The study group of the study consists of 54 senior teacher candidates studying in the primary school mathematics teaching program of a state university. In the selection of the participants, the appropriate sampling method and criterion sampling methods from the purposeful sampling methods were used together. The data collection tools used in this study are Problem Posing Tasks (PPT), Problem Solving Tasks (PST), Model Building Tasks (MBT) and Opinion Form (OF). Problem posing tasks were created by the researchers in order to examine the problem posing skills of the participant teacher candidates regarding situations involving different fraction schemes and fraction operations. Problem solving tasks are aimed at solving the problems that the participant teacher candidates posed in PPT and they are expected to solve the problems by choosing one of the circle model, rectangle model, number line model and set model within this task. Model Building Tasks were used as a complementary data collection tool that assisted and complemented the research. MBT aims to reveal how prospective teachers use each of the circle model, rectangle model, number line model and set model in situations related to different fraction schemes and fraction operations. Opinion form was prepared by the researchers in order to reveal the opinions of teacher candidates on using models in teaching fractions. In this research process, Descriptive and content analysis methods were used in the analysis of the data obtained from the research. An inductive approach was followed in the content analysis. According to the results obtained from the research, it was observed that the teacher candidates could not perform successfully in almost half of the situations involving different fraction schemes and fraction operations in both the problem posing and problem solving process. Therefore, it can be said that the teacher candidates could not perform fully adequately in the problem posing and problem solving using models processes and that they have some conceptual knowledge deficiencies related to fractions. As a result of the research, it was observed that the teacher candidates could not perform successfully in the partitive fraction scheme, iterative fraction scheme, subtraction with fractions and division with fractions tasks in both the problem posing and problem solving using models processes. Apart from this, the teacher candidates showed the lowest performance in the division with fractions task. When the performances of the teacher candidates in the problem posing, problem solving and model creation tasks were examined mutually, the situation observed at the highest rate was the situation where all tasks were successfully completed. In the following cases, the prospective teachers failed to pose problems and left other tasks blank or all tasks blank. These findings were interpreted as the performance in the problem posing process and the performance in other situations were not independent of each other. When the findings obtained from the opinion form were examined, it was seen that the teacher candidates' thoughts on using models in teaching fractions were positive and that they generally had the idea that models supported conceptual learning, helped to concretize abstract concepts and ensured permanent learning. When different models were considered, the teacher candidates stated that they preferred the rectangle model the most, followed by the number line model, set model-circle model, respectively. It was seen that most of the teacher candidates preferred continuous models to discrete models and thought that discrete models were difficult to understand and confusing.