The Scenario and Their Questions
1. Can we determine the final number of regions given the dimensions of the original rectangle? (i.e. 5 in the example)
2. Can we determine the number of different sized regions given the dimensions of the original rectangle? (i.e. 2 in the example...3x3 and 1x1)
3. Can we determine the size of the final square to be colored in given the dimensions of the original rectangle? (i.e. 1x1 in the example)
4. Are prime numbers somehow important as dimensions of the original rectangle?
5. What happens with both dimensions of the original rectangle are odd? When both are even? When one is even and one is odd?
Groupwork and Status Treatments
1. Before we did anything else, I started by reviewing group norms...
- Everyone participates and everyone's ideas are valued
- Share and explain your ideas
- Listen to understand the ideas of others
- Ask and respect questions
- Help without telling others how to think
...and we spent five minutes at the end of the session by having participants journal about how they (personally) did in adhering to group norms. They identified things they did well and things they did not.
2. Before launching the scenario, I passed out grid paper with only this on it...
3. During their group work time, I identified what (from my perspective) seemed to be lower status group members. I looked for ways each of these members was helping the group to function well and highlighted them publicly as we wrapped up the group work phase.
1. One participant said that, upon receiving the dilemma, was extremely underwhelmed. Her statement during our meta-debrief was something like, "I was expecting something significant and profound." But, she said during the course of the session she and her group became extremely interested in one of their questions. By the end of the session their group was high-fiving each other over their solution....over rectangles and squares. It left me wondering what sparked this excitement for them. The freedom to pose their own question? To pursue one they found interesting? I'm not sure.
2. One participant commented that she had a very difficult time with the session because she felt like she didn't have enough time to think to herself. We talked a little bit about my decision to not give too much individual time so that, when coming back together as a group, nobody has a finished idea to share...only the beginnings of one. But her point is a good one and something I struggle with as a teacher. It gives me a lot to think about.
All in all, it was a fun investigation.