Unveiling interaction patterns between students and generative <scp>AI</scp> teachable agent: Focusing on students' agency and <scp>AI</scp> agents' authority

With the growing integration of artificial intelligence (AI) in education, conversational AI agents are increasingly used to support student learning. This study examines how interactions with AI teachable agents are temporally associated with students' agency and how these associations relate to students' learning outcomes. Analysing 7188 discussion threads containing over 117,000 text utterances, we explore the relationship between AI authority and student agency using classification and regression models. Findings reveal that AI authority is significantly associated with subsequent student agency levels; however, increased student agency does not lead to changes in AI authority. Sequential interaction analysis shows that students initially demonstrate higher agency in response to authoritative AI prompts, though this effect stabilizes over time. In addition, higher student agency is associated with more elaboration and clarification talk but also with increased off‐task discussions, which slightly hinder learning gains. These findings underscore the need for balancing structured AI guidance with opportunities for student autonomy. This research contributes critical insights into designing AI‐assisted learning environments that foster both engagement and effective learning outcomes.