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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 50minutes. 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.

The aim of this study is to evaluate free problem posing studies of prospective mathematics teachers about Ratio and Proportion Subject’, to determine the difficulties faced by the prospective teachers during problem posing process and to elicit suggestions regarding the experienced difficulties. For this purpose a data form was created by the researchers. This data form has three parts which were; i) The task of posing free problems, ii) The difficulties faced during problem posing processand iii) Suggestions for solutions of the difficulties. The data form was applied to 114 prospective primary mathematics teachers. During the analysis of the data regarding the first part of the data form, the following criteria were considered; i) Problem text (language and expression), ii) The compatibility of the problem with the mathematical principles, iii) The type/structure of the problemand iv) The solvability of the problem. In the analysis of the data obtained from the second and third parts of the form, content analysis was conducted and the program which is called as NVivo 10 was used. In conclusion, it was concluded that prospective mathematics teachers posed clear and understandable problems which were compatible with the mathematical principles in the form of exercise type and which can be solved by students. The difficulties faced during problem posing process determined as; lack of experience, lack of the content knowledge, not recognizing the cognitive levels of the students, lack of curriculum knowledge and difficulties in writing problem texts. The solutions which were suggested in the scope of this study were as the following; emphasizing problem solving and posing studies, in depth analysis of the curriculum, teaching special teaching methods in details and resorting to resources during problem posing process.

Problem posing means either posing new problem situations in terms of given conditions or re-formulating an already written problem. In this study, the aim is to evaluate problems written by prospective mathematics teachers about ratio and proportion subjects in terms of criteria specified according to problem posing methods. According to this purpose, ‘Problem Posing Form about Ratio and Proportion Subject’ including questions for determining the tasks of free problem posing, semi-structured problem posing, structured problem posing and for determining which one is the most challenging problem posing task, was developed by the researchers. The data form was applied to 45 sophomore students who are studying in Kocaeli University, Teaching Primary School Mathematics department. The data collected throughout this study was evaluated by considering; i) Problem text (language and expression), ii) The compatibility of the problem with the mathematical principles, iii) The type/structure of the problemand iv) The solvability of the problem. In conclusion, it was concluded that prospective mathematics teachers posed clear and understandable problems which are compatible with the mathematical principles in the form of activity and which can be solved by students. The challenging sides of problem posing appeared as the hesitation on posing problems which are suitable to students’ levels, the difficulty in remembering the subject clearly and not having sufficient information about problem posing.

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 purpose of this study is to analyze the role of meta-cognition while solving function problems and to develop suggestions for classroom practice. Especially, the first of three objectives to be attained is to monitor meta-cognitive behaviors of prospective teachers, who study at the department of “teaching mathematics at primary schools”, while solving problems; the second is to evaluate the importance of meta-cognition in solving problems; and the third is to analyze typical errors, challenges, successes and strategies chosen for solving function problems. The analysis of the questionnaires filled out by students, as well as students' solutions related to the problems, provide an understanding for the meta-cognitive aspects of solving function problems.

The main purpose of this study is to reveal the thoughts that prospective teachers studying at the department of teaching mathematics at primary schools possess with respect to the concept of ‘Mathematics' through metaphors. The study was carried out with 106 female and 44 male students, total of 150 prospective teachers, who study at Kocaeli University Educational Faculty, Department of Teaching Mathematics at Primary Schools, during the fall semester in the 2011-2012 academic year. The data for the study was obtained by having students complete the blanks in the sentence ‘Mathematics is like…….; Because…….’. The study had a descriptive nature, since it is an attempt to reveal an existing situation as it is. The metaphors developed by the participant prospective teachers on the concept of ‘mathematics’ were analyzed and interpreted by using qualitative research methods under the positive, negative and conceptual categories. In this context, the perceptions of prospective teachers studying at the department of teaching mathematics at primary schools regarding the concept of mathematics provide different perspectives.