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Problem is a topic, event or activity, which no memorized or specified rules are known regarding its solution. Problem posing is a crucial component for mathematics discipline and problem solving is the situation of elimination of confusion in human mind. In this sense, the problem sentence of the study was determined as; 'What are Problem Solving and Posing Behaviours of Prospective Primary Mathematics Teachers about the 'Sets' Subject and Their Experiences and Difficulties Encountered During this Process?'. The purpose of this study is to analyze problem solving and posing behaviours of prospective primary mathematics teachers about the sets subject and to determine the experiences and difficulties that can be seen during these processes. The study was carried out with 56 sophomore students who study at Kocaeli University, Department of Teaching Primary Mathematics. The data was obtained using a data collection form which was prepared by the researchers. The data were analyzed and interpreted in three steps using the content analysis method including i) free problem posing and solving, ii) the experiences that can be seen during problem solving and posing processes, iii) solution recommendations relating to the difficulties (if any) that can be experienced during problem posing and solving processes. It was determined that 53 students could pose problems about the Sets subject suitable to Primary Second Grade level and also they were able to solve these problems. It was seen that 41 students had difficulties in adjusting the degree of difficulty of the problem, not being able to have the full subject knowledge and matching the primary school level during problem posing process. And it was determined that 12 students expressed that they did not experience any difficulties and did not make any solution recommendations. Based on the findings, it was concluded that students could display free problem posing skills but they could not solve the problems according to problem solving steps. This situation can be explained with the fact that the students have not studied problem posing and solving before. It was determined that students had difficulties in matching the primary school level and in adjusting the degree of difficulty of the problem and they believed that they could overcome these difficulties by gaining experience in time. This situation can explained with the fact that since students are sophomore, they do not perceive themselves as real teachers.

The aim of this study is to analyze the role of meta-cognition while solving indefinite integral problems. In this study, there are particularly three objectives to be obtained. These are; i) observe meta-cognitive behaviors of prospective mathematics teachers while solving problems, ii) determine the importance of meta-cognition in problem solving and iii) determine challenges, typical errors and points to be considered for solving indefinite integral problems. The study is a qualitative research. Data collection tools are; i) Problems Form (PF) and ii) Meta-Cognitive Skills Questionnaire (MSQ). In this context, this study was completed by 60 prospective mathematics teachers. All prospective mathematics teachers are sophomore students at a university. Data collection tools were filled by the prospective mathematics teachers in 50 minutes. Collected data were analyzed descriptively. The analysis of the problem which were solved by the prospective mathematics teachers and the examination of completed questionnaires are to provide an understanding for the meta-cognitive aspects of solving indefinite integral problems. In conclusion, the challenges faced by prospective mathematics teachers that are subject to recall, choose incorrect solution and not knowing where to start in problem solving. The common mistakes are incorrect solutions and calculation errors. On the other hand, the point that should be considered in the problem solving is to choose a strategy.

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