Some of the best days in my classroom this year were the first days of students grappling with a good (low threshold, high ceiling, high cognitive demand, content-illuminating) problem. Students were engaged, discussing, modeling, struggling, defending their thinking, etc.
Many of these problems require multiple days. By the end of the first day, students may have “gotten” parts of the problem, may have even generalized, but they weren’t (according to me) done. Many students though, despite high interest/engagement on the first day, demonstrated much less interest in returning to the same prompt.
The great thing about these good problems is how much you can do with them! So how do I teach/motivate students to sustain their interest over multiple days with the same prompt? Will discussing the value of sticking with the same problem (the why we do this) and a class norm of “you’re not done until you’ve used at least two methods and two (three?) representations” do the trick?