By Dalton Hopper (Centre College) and Amanda Ellis (University of Kentucky)
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With the rapid growth of generative AI tools, it is important to understand how we, as educators, can leverage AI to enhance student learning. In Mathematical Statistics, we have noticed that many students are uncomfortable with proof writing. Students often struggle with taking next steps (or even beginning the process at all) usually out of fear of doing unnecessary work or being wrong. We believe that AI can help students become more comfortable with the proof writing process. Thus, we developed Proof AI-d assignments to be implemented in a Mathematical Statistics course. Each Proof AI-d assignment provides students with statements/theorems that need proved, along with a partially filled-in proof outline that is missing key steps. Each missing step has a guiding question that is designed to direct students' thinking in a productive way. The students' primary tasks are to fill in the missing steps before using ChatGPT and then refine their outline into a polished proof using ChatGPT as a coach. Students are provided examples of questions they can and cannot ask ChatGPT. Evidence of efficacy was assessed via Reflections (part of each assignment), a survey (administered after all assignments are complete), and institutional course evaluations. This was implemented at a small, private liberal arts college with typical class sizes ranging from 6-30 students. Mathematical Statistics is a 300-level course that serves as an elective for Mathematics majors and a requirement for students pursuing a Statistics minor.