Investigation of middle school pre-service elementary mathematics teachers' problem-posing skills in the dynamic geometry software environment

The purpose of this study is to examine the skills of pre-service elementary mathematics teachers in problem-posing activities in a dynamic geometry software environment. A holistic multiple-case qualitative research method was used in the study. The participants of the study consisted of six pre-service teachers studying in the fourth year of the elementary mathematics teaching department at a state university in the spring semester of the 2024-2025 academic year. Problem-posing activities created by the researcher using GeoGebra, a dynamic geometry software program, GeoGebra files, clinical interviews, and audio and screen recordings were used as data collection tools. To better analyze pre-service teachers ' GeoGebra supported problem-posing activities, the problem-posing activities were conducted in three stages. First, pre-service teachers were asked to use GeoGebra's features in the activity or to discover and explain hidden features. In the second stage, pre-service teachers were asked to pose new problems related to the given activity. In the third stage, pre-service teachers were asked to talk about how they solved the problems they posed. In the evaluation of the problems posed by the pre-service teachers, a framework developed by the researcher, based on the problem-posing activities evaluation framework developed by Semerci (2019), was used. The framework used to evaluate problem-posing activities included evaluation criteria such as question meaning, mathematical nature, closeness to life, relevance of data, data availability, linguistic and semantic complexity, availability of the problem's solution, the problem's story, and the problem's dynamism. The study concluded that pre-service teachers had difficulty with all problem-posing activities. Additionally, pre-service teachers stated that they felt more comfortable and wrote easier problem statements during free problem-posing activities because there were no topic restrictions. It was determined that pre-service teachers made fewer errors in the free problem-posing type. All pre-service teachers were found to have more difficulty with semi-structured problem-posing activities than with free problem-posing activities. The pre-service teachers were found to be able to pose problems more easily in structured problem-posing activities than in semi-structured ones. Furthermore, the study results suggested that pre-service teachers lacked sufficient experience in problem-posing activities using dynamic geometry software such as GeoGebra.