I think a lot about room design. Nowadays, everyone in my room sits in a 6-kid pod like this:
The groups at the front of the room are a tad different, but you get the idea. This design facilitates what I want most, kids talking. To optimize it, I need to have a handle on who sits with who. Developing group chemistry is half of what makes the table system successful. In previous years, the kids are in a random arrangement for six weeks. I observe who works well with who, who seems to be displaced from their friends, and adjust it. At the semester, I give them options: choose a person or choose a table. I take their suggestions and make a third chart that lasts the rest of the year. This also gives them an anonymous way of communicating big time conflicts, if they exist.
In Calculus, I want these students exposed to more of their class. When I took Calculus, there were 12 of us. I sat in the same seat the entire year. Yes, I knew the names of everyone. But it would be tough to tell you when I got to interact with them. My groups are in a similar situation. The overwhelming majority have had classes together for years and years. They all know who is who. But could they learn more than that?
Enter moving buddies. You, dear Calculus student, get to choose a permanent partner. They will travel with you on your adventures through the room, meeting and working with exciting new people. I had them write down partner choices on an index card, a few had no preference, and I had to settle a couple disputes.
Each rotation lasts two weeks. This will continue for the rest of the semester. We'll do it again next semester, but some fiddling may be required if someone drops. Without getting too crazy with combinations, I did a bunch of random sorts and then made some edits until every pair of buddies visited at least 3 unique locations. I tried to make sure a set of 4 didn't travel together either. If you track a kids' movement, they'll sit with over half the class in the cycle.
I expect any payoff will take a long time to develop. But it beats sitting still.