Coexistence Of Mathematical Reasoning And Cognitive Offloading: A Longitudinal Case Study Of One Student's Chatbot Use Across A Term Of Proof-Based Mathematics

Source abstract

Students use generative artificial intelligence chatbots for proof explanation, error checking, and exam preparation in mathematics, with documented effects on both learning and study habits. Less is known about how these uses develop in students' self-directed study across a full academic term. We followed one postgraduate student who studied proof-based mathematics at a research-intensive university using a Claude project configured with Anthropic's study template across an eleven-week teaching term and a revision period. We coded all 196 chat exchanges from twelve sessions with a scheme of prompt and response types and conducted a semi-structured interview after the course. Our findings are threefold. First, the student used the chatbot productively for concept explanation, proof construction, and error correction, treating it as less intimidating than approaching teaching staff. Second, she reported becoming quicker to turn to the chatbot for help, while the chatlogs showed continued mathematical questioning and verification. Third, the chatbot's Socratic configuration failed to match the student's needs in many exchanges, producing cascades of questions that sometimes failed to address her mathematical objections and withholding worked solutions during exam revision when no solutions were available for comparison. Following the same student across the term shows changes in her study purposes alongside continued mathematical checking and recurring difficulties with the chatbot's questioning.