An investigation of eighth grade students' skills at geometry problem posing

The aim of this research is to investigate the eighth grade students' skills at geometry problem posing in different problem posing situations, to examine these skills in terms of gender, parental education status, general academic success, mathematics course success and self-efficacy beliefs toward geometry and to reveal what the students' views on problem posing and the difficulties they encounter during problem posing. For this aim, a mix method was used in which qualitative and quantitative methods were used together as a research method. The research sample consisted of 151 students who were studying in the eighth grade. There were also interviews with 8 students. The "Geometry Problem Posing Test", consisting of a total of 6 open-ended questions, including free, semi-structured and structured problem posing situations developed by the researcher, was used as a data collection tool. The Geometry Problem Posing Test was prepared about the sub-learning domains of triangles and congruent-similarity in the domain of geometry and measurement learning in the eighth grade teaching program. "Self-Efficacy Scale Toward Geometry" developed by Cantürk-Günhan and Başer (2007) was used to determine self-efficacy beliefs toward geometry of the students. In addition, "Personal Information Form" and "Interview Form for Problem Posing" were used as data collection tools. An analytical rubric, developed by Özgen, Aydın, Geçici and Bayram (2017), was used for the analysis of the problems that students posed. In this rubric, there are seven evaluation criteria. Analysis of the quantitative data was conducted using t-test, one-way analysis of variance and regression analysis in direction of sub-problems. Qualitative data were analyzed using descriptive analysis and content analysis. One of the results obtained in the research is that the students who participated in the research have a slightly low success in the geometry problem posing. Students have stated that it is difficult to write the appropriate numbers about problem for this situation. One of the reason of this situation is that the students think about the solution of the problem and they are foreign to problem posing activities. In addition, it has been determined that students have more difficulty in structured problem posing situations according to criteria in the rubric. In this research, it was found that the students' geometry problem posing test scores did not show difference significantly in terms of gender, but they showed difference significantly in terms of parents' educational status. It was determined that students' geometry problem posing test scores show a significant difference according to both general academic success and mathematics success. It has also been found that students' self-efficacy beliefs toward geometry are a significant predictor of geometry problem posing skills. In addition, all the students interviewed stated that it would be useful to make problem posing activities in mathematics courses.