Empowering Mathematical Problem-Posing Pedagogy with Generative AI: A Theoretical Framework and Case Study

In the era of artificial intelligence, fostering creativity, critical thinking, and problem-solving skills has become increasingly important, particularly in mathematics education. Problem-posing pedagogy is recognized as an effective approach to achieving these educational goals. However, teachers often face challenges in task design, creating effective prompts, and managing classroom interactions. This study proposes a novel theoretical framework powered by Generative AI (GAI) to address these challenges. The framework consists of four interconnected stages: Design, Simulate, Engage, and Refine. By leveraging GAI, teachers can generate personalized tasks, anticipate classroom dynamics, and dynamically adjust teaching strategies. A case study demonstrates the framework's potential to enhance student engagement and improve problem-posing activities. Despite its promising potential, the framework requires further empirical validation and optimization through real-world application. Future research will explore the integration pathways of GAI in mathematical problem-posing pedagogy.