Last spring I attended MCTM’s pre-conference. Yeap Ban Har spoke about how Singapore empowered students to learn from each other, communicate mathematically and be able to think beyond the answer. I have used group work for years. Johnson and Johnson’s materials in the 80’s. And for the last 15 yrs., Elizabeth Cohen’s Designing Groupwork. I’ve stayed committed but that ‘sweet light’ of total engagement and increased learning seemed to elude me. Until this year.
I’ve used Sara Van der Werf’s 100 numbers activity before (See Saravanderwerf.com). You give the students one piece of paper and they work together. They really get into it and lean into the work. But this year I followed Sara’s suggestion and took pictures of them working, discussed it and hung up the pictures. That primed the pump but what really got the water flowing was the transfer to doing all of our math this way. And having it be the first math that they do when they come into the room.
A problem is on the screen and the students are given one blank sheet of paper. They then all work together to solve the problem. No dance and pony show to get them excited about it. No scaffolding to lead them down the path I want. Just the math and a piece of paper. Everyone is expected to contribute and everyone is to be ready to share. And, the class becomes responsible for their learning by determining whether answers are correct and questioning each other to support their decisions.
One of the biggest challenges, as in all group work, is having group worthy problems. A group worthy problem is one where there are multiple approaches, strategies to use. It takes thinking and discussion to decide what the group should do. Ideally, there is an initial reaction of, ‘What?’ This really helps students appreciate, enjoy and even celebrate their solution when it comes. The learning is in the struggle, not the answer. More on that another day.
Writing group worthy problems takes time. Bonnie (my grade alike partner, whose name I now have permission to use) and I meet often. We read the standard, look at the recommended material from the district, search the net and then usually rewrite something. It is time consuming but it is so worth it. Student discourse and ownership of the class is increasing. More on that later.
One of my favorite problems this year was when we gave students a picture of a triangular prism with dimensions and volume provided. There were two questions. 1. Why is this called a triangular prism? 2. Why is — the volume? Instead of being given a formula and being told to practice, which is not group worthy, students had to analyze, use prior knowledge, test out ideas and convince each other.
At the end of the quarter I asked students to write about what they like about math/math class. Overwhelmingly students said group work and math making sense. Yes, a lot of work but so worth it.