Explaining the steps followed by elementary mathematics teacher candidates in the process of free problem posing

Although the things that people call problems are not the same, it is important for everyone to notice these obstacles and find solutions. Because problems that we don't notice create new problems. Therefore, our daily life is negatively affected by this situation. Realizing the problems experienced, revealing the current situation and being able to create solutions to the problem makes human life easier. At this stage, courses such as mathematics create awareness about the problems in human life. When we consider the problem-making process as a meaning-making process, we can say that problem-making is a tool that helps a person reveal the way they look at certain situations. In case of realizing the problems, the importance of problem-posing activities, that is, presenting the problem, is great. Considering the importance of problem-posing in mathematics education and the necessity of implementing problem-posing activities in courses, it was also considered important to phase out this process. The aim of this research is to lay out the steps that primary school mathematics teacher candidates follow in their free problem posing processes. The research is a qualitative study conducted with 12 prospective teachers studying in the 4th grade of a university. In the research, three topics were given to prospective teachers each week and they were asked to poze free problems. This problem-posing work lasted 7 weeks. In order to understand the problem-posing processes in depth, individual interviews were conducted with teacher candidates. During the problem-posing tasks, the voice thinking procedure was performed and unsystematic observation was performed. As a result of the research, it was seen that teacher candidates went through four stages in their free problem-posing processes: "Planning the Problem to be Posed, Posing the Problem, Planning the Solution of the Posed Problem and Evaluating the Posed Problem". In addition, it has been revealed in the steps of teacher candidates towards these stages. It is thought that the steps of the free problem-posing process revealed as a result of this study will shed light on the development of problem-posing skills.