Background and Context: Question and inquiry are integral parts of knowledge seeking and learning. Despite their importance, students tend not to ask enough questions in the classroom. However, studies have shown that students interact extensively with generative AI systems for learning and problem solving. Objective: In this paper, we seek to better understand the types of questions that students ask AI systems, and how those questions evolve during problem solving and across tasks. Method: We use the Graesser et al. taxonomy to classify students' inquiries into 18 types. We develop a few-shot learning approach to automatically classify students' interactions with AI into these categories. We use this system to analyze 830 interactions of CS2 students across two programming tasks. Findings: Our results suggest that a small subset of question types accounts for the majority of student inquiries, and that the types of questions students ask change substantially as the task progresses.

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