The Great Seventh Grade Pie Eating Contest

Thursday was a day of firsts for me. It was the first time I taught two lessons in a row, the first time I had students work in groups, the first inductive lesson that I taught, and the first time I used cold calling, a questioning strategy that Anne introduced to us in class the other day. It was a good lesson, despite the fact that I had some unexpected twists, and I think there are a bunch of ways for me to learn from what happened in that class.

The Objective

The primary objective was for students to add and subtract mixed numbers. The secondary objectives were for students to improve their social skills by working in groups, for students to take responsibility for their own education and the education of their peers, and for students to feel like they themselves are capable of determining the rules of math without having these rules explained to them.

The Task

I divided the students into two teams, and told them to imagine that they had just finished a pie eating contest. I gave each student a slip of paper with a mixed number - representing the number of pies that student had eaten - and I asked each group to find the total number of pies that their group had eaten, so that we could determine which group had eaten more pie. Then, I told them that the winner of the contest would be the group that was best able to explain how it found its answer to the other group. They were introduced to mixed numbers the day before, but never told how to add them. I told them the winner of the contest would be the team taht was best able to explain its answer. As an added twist, I threw in the cold calling idea and told them taht I would pick one student at random from each group to explain how they came to their answers. I told them it was their responsibility to make sure everyone in their group understood and was able to explain their solution.

The Result

Both groups were able to find the answer, with some, sometimes substantial prompting. The prompting was often more about how to work in a group than about how to actually do the math, so I think in the future I need to give out more instructions about how to work in a group before I get them started. The biggest problem I had with the structure of the exercise was that one group finished much, much quicker than the other, despite the fact that when I had chosen the groups the night before, I had tried to split the kids up as evenly as possible, both in terms of math intuition and group-working skill. To the group that finished first I gave a bonus problem to keep them busy, which worked decently enough, and at least kept them quiet and academically occupied while the other group finished.
Both groups found the answer in different ways, which was exactly what I had hoped for. It was also obvious that knowing they woudl be chosen randomly to explain forced them to try to teach each other, but when it came time for the randomly chosen students to do their explaining, the results were less than impressive, and it was clear, at least for one groups, that they weren't sure what they were doing.
Overall, though, I feel like the lesson was a success. I made sure to remind them that they all figured out how to add mixed numbers themselves and emphasized that I never taught them how to do these kinds of problems. Sometimes, although I wanted them to struggle through the problem, the struggle seemed to be too much for them, and I felt like I was losing a lot of the kids to frustration.
The other problem I had was time. The lesson spilled over into the next period, so it was a good thing I was teaching both; however I rushed through the material I had planned for the second lesson (multiplying and dividing mixed numbers) and I ended class with the feeling that the students weren't really clear on any of it. Like my mentor teacher said afterwards, "It's better to teach one thing well than several things poorly."
As for the cold-calling, it kept everyone involved and kept everyone interested not only in the problem but in their classmates' understanding of it, which was great, but I ended up calling on students who clearly struggled to explain the material in front of the class. If I were to teach the same lesson again tomorrow, I would keep the cold calling, but I'm not sure how I could have helped the process along so that everyone really developed a good understanding of what was going on. I could allow a second person to help explain if the first couldn't, but that would remove a lot of the incentive for the group to make sure that everyone gets it.