I’ve been mapping out Unit 1 more specifically, and I feel I may have partially resolved my own query about spending more than one day on the same problem (in a way that incorporates some of the commenters from my first post!).
Many of the weeks are set up the following way now (after Kogut and I got some time to talk during our awesome retreat).
Monday: Community building, week set-up, and launching of several problems
Tuesday: Students continue working on the several problems.
Wednesday: Students wrap-up their work on several problems, choose one to make into a product (paper, video, pamphlet, flipbook, etc).
Thursday: Peer-feedback and revision on the product.
Friday: Year-long project, Unit project, summarizing, big picture, community building again etc.
So on Monday-midday Wednesday, students will have some number of problems (3-6 or so) that they can spend their time on. Then Wednesday and Thursday, students will choose a problem to spend more time on, making their work more formal and complete.
How does this help resolve my earlier question? First, this system means that a student controls how much time s/he spends on each problem earlier in the week — if someone gets into a problem, they can stick with it or if they want to do a bunch of problems in slightly less depth, they can do that too. Further, if a student does multiple problems on Monday-Wednesday, they will have to spend more time with one of them, but will get to choose which one it is and will get to work on it in a creative way. Hopefully all this will mostly lead to meaningful engagement with problems, whether in passing or in depth and will remove the angst of my trying to get the whole class to dive deeper on the same problem in the same way at the same time.