How Problematic Writer-AI Interactions (Rather than Problematic AI) Hinder Writers' Idea Generation

Writing about a subject enriches writers' understanding of that subject. This cognitive benefit of writing -- known as constructive learning -- is essential to how students learn in various disciplines. However, does this benefit persist when students write with generative AI writing assistants? Prior research suggests the answer varies based on the type of AI, e.g., auto-complete systems tend to hinder ideation, while assistants that pose Socratic questions facilitate it. This paper adds an additional perspective. Through a case study, we demonstrate that the impact of genAI on students' idea development depends not only on the AI but also on the students and, crucially, their interactions in between. Students who proactively explored ideas gained new ideas from writing, regardless of whether they used auto-complete or Socratic AI assistants. Those who engaged in prolonged, mindless copyediting developed few ideas even with a Socratic AI. These findings suggest opportunities in designing AI writing assistants, not merely by creating more thought-provoking AI, but also by fostering more thought-provoking writer-AI interactions.