From Prompting to Epistemic Proactivity: Temporal Trajectories of Student-AI Interaction in Mathematics Learning

Abstract

GenAI is increasingly used by students as learning companions, yet little is known about how they use these tools in open-ended learning settings, where the goal is not to complete a specific task but to improve understanding and making progress. This study examined Grade-9 students' dialogue with a general-purpose LLM during mathematics practice, in which students prepared a curriculum-aligned skill for a later assessment. We investigated whether students' interactions revealed forms of epistemically proactive AI use: trajectories in which they strategically use and regulate AI to advance their understanding, and whether these trajectories predicted immediate AI-free performance on the same skill. A total of 112 students worked with a web-based LLM tutor on a mathematical-modeling task; 97 completed both AI-free pre- and post-tests. Student turns were coded for self-regulated learning functions, help-seeking content, and mathematical-modeling activity; three dimensions hypothesized to capture epistemically proactive AI use in this task. Descriptively, students' interactions showed little explicit regulation and mostly involved procedural or conceptual questions. Static summaries of AI use, including whole-session prompt functions, request types, modeling stages, and behavioral diversity, did not predict post-test performance after controlling for prior knowledge. In contrast, temporal indicators were informative: students performed better when their interactions shifted from early to late phases toward a more epistemically proactive balance of conceptual or procedural help-seeking and mathematical work, rather than verification, answer-seeking, or validation. These findings suggest that productive AI-supported learning is better understood as a domain-specific trajectory of epistemic proactivity. We discuss implications for AI tutor design and classroom orchestration.