Investigation of middle school students' geometric problem-posing processes and problem-posing strategies

In recent years, as a result of the changes and developments in the fields of science and technology, both personal and social needs and the innovations and developments in learning and teaching methods have affected and changed the expected roles of individuals. This change and development has made it necessary to educate individuals who produce knowledge and use this knowledge in life effectively, who can solve problems and have critical thinking skills. In this context, the aim of the curriculums prepared in recent years is not only to teach the mathematics etc. as a lesson but also to educate individuals who can use the knowledge they have, who can question, think critically, solve problems and to prepare these individuals for society. Another problem encountered in the learning process is problem posing. Problem posing is the process of creating a new problem from a given situation or from a lived experience. Problem posing is closely related to problem-solving skills and contributes to the development of problem-solving skills. For this reason, many countries have included problem posing in mathematics education programs. Our country has also gained its share from these developments and has included problem posing in the education programs prepared in recent years. When examining both national and international literature, it is seen that most of the problem posing studies in mathematics education are gathered in certain topics such as problem-posing skills, classification of posed problems. Although there are studies about the problem posing processes and strategies in the literature, it is seen that most of these studies are centred upon the field of algebra and numbers learning, they are generally made with teacher and teacher candidates, and the studies done at the secondary school level are only carried out on a single grade level. On the other hand, it is seen that there are some problem posing studies in the field of geometry learning, but they are few. When these studies are examined, it is understood that most of the studies are problem posing studies which are done with dynamic geometry software. In the literature, it is seen that there is no study covering the whole of the secondary school levels in the field of geometry learning and revealing the problem posing processes and problem posing strategies of students. For this reason, in the research we investigated the problem posing processes and the strategies of middle school students on geometry learning, one of the most important areas of the mathematics. In the research, from qualitative research methods a special case study was used as a method. In the research, a clinical interview was conducted in order to examine the students' process of posing geometry problem and to determine the problem posing strategies. The study was carried out with 160 students from 14 different secondary schools and different grades in Kucukcekmece district of Istanbul. The data of the study was collected by "Problem Posing Activities" and "Interview Form". In the analysis of the data obtained from the research, descriptive analysis and content analysis from qualitative data analysis techniques were used. In accordance with the evidence of the research, it was determined that students used thirteen different problem posing strategies while posing problems. The most frequently used problem posing strategies used by the students were the Daily Life Adaptation Strategy and the Drawing a Figure and Posing the Problem According to this Figure Strategy; whereas the problem posing strategies that the students used the least were the Backward Checkout Strategy and the Emotional Approach Strategy. In the research, it was determined that the students were following the certain steps of problem posing while posing the problem. Students' use of the steps mentioned in the problem posing process varies depending on whether they use some steps or not. This leads to differences in the problem posing process of students. Four types of students are mentioned in this research. In the research, the most important reasons for most of the secondary school students' having trouble in posing mathematically sufficient problems while posing geometry problems are shown as; students' having little experience or no experience; not knowing what the problem meant and the perception they have about problem solving. Based on these results of the research, suggestions for the development of geometry problem posing skills of secondary school students were presented.