Before or after? Beyond timing of students’ interaction with generative artificial intelligence in proving mathematical statements

Abstract In this study, we investigate how the sequence of interactions with generative Artificial Intelligence (genAI) influences undergraduate students’ mathematical proof construction. We compared two instructional approaches: Initial genAI-Independent Proving (IIP) in which students constructed their own drafts before interacting with genAI, and Initial genAI-Dependent Proving (IDP), in which students interacted with genAI proofs before drafting their own proofs. Thirty undergraduate students participated, engaging with two related proof tasks across the instructional sessions. We analyzed how students incorporated AI-generated proofs into their work. The results show that students in both conditions incorporated AI-generated proofs to a similar extent, but differed in how they engaged with genAI during the proving process. Students in the IIP condition used genAI to revisit key components of their proofs and to revise their independently constructed proofs whereas those in the IDP condition used genAI as a reference or guide in their proof-making process. Reflection survey responses indicate that while students recognized the efficiency of early genAI use in the IDP approach, they perceived the IIP structure as more beneficial for enhancing conceptual understanding. These findings suggest that how students engage with genAI might be as important as when they use it, highlighting the pedagogical importance of structuring both the timing and the role of genAI in mathematical instruction.