Problem posing in a dynamic geometry environment: Investigation of preservice mathematics teachers' problem posing processes

This study explores the problem-posing processes of pre-service mathematics teachers within a dynamic geometry environment, with a particular focus on how this environment were utilized during the problem-posing process. A total of twelve participants participated in the study, working collaboratively in pairs. Each pair engaged in two problem-posing tasks and was asked to pose problems utilizing GeoGebra, a dynamic geometry software tool. The problem-posing processes were examined based on the stages of a general problem-posing process model: orientation, connection, generation, and reflection. In the first stage, the central focus was on examining the problem situation in the task. In the second stage, three types of connections emerged in the development of problem ideas: structural (data-oriented), intuitive (hypothesis-oriented), and pedagogical (pedagogy-oriented). The third stage centered on the articulation of the problem idea in written form, which was analyzed within two categories: semantic and linguistic. In the final stage, participants conducted a comprehensive evaluation of the problem's structure, with their activities categorized into reflection during the problem-posing process and reflection following the posing of the problem. Moreover, the analysis of how each pair utilized components of the dynamic geometry environment was detailed in accordance with existing frameworks in the literature regarding measurement, dragging, and insertion actions. The results not only characterize the behaviors of pre-service teachers at each stage of the general problem-posing process model but also elucidate how components of the dynamic geometry environment are employed throughout these stages. This study offers recommendations for the effective integration of technology-supported problem-posing processes into mathematics instruction.