This is just a quick post to reflect on something that went really well this past week. We have been working on a modification of the Pig Unit from IMP. In the process of investigating, we were trying to wrap our heads around this problem:

If you roll a die two times in a row, what are the chances that you will get at least one 1?
What if you roll 3 times? 4 times? "n" times?

We usually do these problems in small groups (3-6 students) but I decided to mix it up for this one. I split the class into two large groups (each of about 12) and we formed an "inner circle" and an "outer circle." The inner circle got 5 minutes to form some initial thoughts about the problem individually and then we opened it up for a whole group, collaborative sense-making. I told them they were "done" when every person in the group both agreed with and could explain their collective solution. The other half of the students (the outer circle) were partnered with someone on the inner circle and they were to be silent observers, recording the ways in which their partner was positively contributing to the group discussion. I also removed myself from contributing to their efforts in any way.

Afterwards, we talked about ways the group worked well together, ways they didn't work well together, and we identified the habits/strategies that were useful for each group. There were a lot of amazing things that happened and some really great discussion that followed. Mostly, I loved that the students had to (and did) push, challenge, and support each other in an attempt to justify their solution and prove to each other that it made sense.

I was left wondering:
1. Why doesn't this work as well with a WHOLE class discussion/collaboration? What would support that? I think this post and research might help....haven't read it yet.
2. Does this collaboration happen with small groups also? It's harder to tell when you are monitoring multiple groups.