We had breakfast, two morning problem solving sessions, lunch, and an afternoon problem solving session. The topics we explored today were pentominoes and divisibility, cryptography, and something called polygon differencing.
My goal with this post is to share a couple of my take-aways from today. We had to take a pre-workshop survey, and one of the questions asked about what we felt were our strengths and weaknesses as a mathematics teacher. I listed teaching students to problem solve as a weakness. With this in mind, I kept a page of ideas throughout the course of the day.
One of my favorite things we did was de-brief after the first session on pentominoes. We were asked to take out a sheet of paper and answer two questions.
1. What characteristics describe a good group member?
2. What characteristics describe a good problem solver?
We took our answers to these questions, shared them in our groups, and then compiled a top 3 list for our group. Then, we compiled our group lists into a set of norms.
Since I am planning to have students work in groups this coming school year, I think I'd like to do some problem solving activities the first few days and develop a set of norms at the same time. These norms could then be posted for students to reference throughout the school year.
Now, I just need to figure out what sorts of problems I want to pose to my students.
Round Robin Strategy
Another thing I quickly took note of as soon as we did it so I wouldn't forget was a round robin strategy for sharing within our groups. The facilitator provided us with our first problem and told us to work on it independently for 10 minutes. No discussing with tablemates at all. Then, after the timer went off, she announced that we were going to do a round robin. How she approached the round robin really appealed to me. Instead of asking everyone to share what they had come up with, she asked each person to go around the circle and (in less than a minute) share how he/she had originally approached the problem. We weren't supposed to share what we had discovered in the ten minutes we had been working on the problem. We were only supposed to share our initial thoughts. It was very interesting to hear where everyone in the group had started. This provided insights into how others were thinking that normally wouldn't be shared because they weren't polished/proved/or even right.
When I just ask students to share final answers without how they got there, I'm doing a disservice to my students. This reminds me of the book Making Thinking Visible (affiliate link) which I read in early 2013. I pulled it back out this week and started it again.
Looking forward to sharing more takeaways soon!