As an educator myself, this quarter for the first time for my course's final project, I've switched to actually asking my students to provide an "AI Authenticity Audit" of their (project-relevant) chats in the construction of said projects. All my students' output over the last two years went from pre-AI level quality to boardroom-ready polish, and I'm actually more interested to see how they arrive at an outcome rather than the final output itself - focusing on their questioning, curating, editing, and iterating process. Didn't think we'd get to somewhere like this so soon, but here we are. Strange, but I'm trying it out.
IMO this kind of thing adds work and stress for the best students. If I'd been faced with something like this while I was in school I would have felt the need to basically curate a parallel construction AI discussion, knowing it would be judged. I understand the theory that, in the age of AI, the prompts are more interesting than the outputs, but I'm not convinced this is the way.
Things like the Denmark approach (and/or in-person written responses) seem like a better direction. Treat take-home writing the same as we've treated take-home math questions - as useful practice (for those who choose to actually engage with it), but not a significant input to grading.