Generative AI has changed how students produce writing assignments. The final artifact is no longer sufficient to understand the process through which it was produced. We introduce DraftTrace, a writing environment that jointly captures three complementary views of writing: the final product, the writing process and interactions with an integrated AI-assistant. DraftTrace reconstructs how a document develops over time and organizes these signals into submission, longitudinal, and class-level analytics for instructors. We deployed DraftTrace in a graduate NLP course with 81 students and compared their sessions with LLM-generated responses entered by automated tools and with copy-typed responses. While product measures distinguish differences in text formulation, process measures distinguish differences in how text is entered. Considering both views together helps characterize cases such as copy-typing. Interaction traces show that students use the assistant differently across stages of writing: to clarify the question at an early stage and to verify answers at a later stage. A preliminary instructor survey highlights the importance of multi-view writing analytics and their interpretability.

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