Learning to Craft and Critically Evaluate Prompts: The Role of Generative AI (ChatGPT) in Enhancing Pre-service Mathematics Teachers' TPACK and Problem-Posing Skills

Abstract

The use of generative AI (Chat GPT) for the process of posing mathematical problems was introduced to 15 pre-service teachers (henceforth referred to as "teachers") in a re-training program aimed at teaching advanced secondary school mathematics. After solving mathematical problems, they were given an assignment to pose and refine additional problems in accordance with the curriculum requirements by giving "prompts" to the AI environment and refining them as needed. In this paper, we focus on the qualitative analysis of three key stages experienced by the teachers: writing the initial prompt to request assistance from ChatGPT to improve the problem; the response provided by ChatGPT; and the teachers' reflections on how they utilized ChatGPT's recommendations to update and refine their problem. This analysis reveals that the chat's responses and the teachers' reactions to them made several key contributions to improving mathematical problems, particularly by enhancing the clarity of the problem and increasing its challenge and complexity. Additionally, it improved mathematical precision and showed how it could be linked to real-world applications, thereby increasing student engagement. The chat also encouraged inquiry-based thinking and provided guidance for helping struggling students. Overall, these contributions significantly enhanced the quality of the mathematical problems and improved their TPACK (theoretical, pedagogical, and content knowledge).