I'm part of a Facebook group for teachers who are implementing some components of Building Thinking Classrooms (BTC) based on the book by Peter Liljedahl. A question that comes up frequently in the group is how teachers are handling consolidation, which is the wrap up of big ideas that Peter recommends at the end of class, using student work from class as a means to summarize and help students make key connections. This is pretty similar to the final three practices in 5 Practices for Orchestrating Productive Mathematics Discussions (Selecting, Sequencing, and Connecting). We want students in all math classes to see beyond the specific problems they solved. This is especially important in a math classroom that doesn't follow the "I do, we do, you do" model since students are figuring out how to solve problems without being shown a general principle or model to follow and need to see how the work they did establishes something generalizable and useful. In both the BTC and 5 Practices approach, the teacher selects several pieces of student work, decides on what order to discuss them, and helps students make sense of this work and the big ideas of the lesson that they encompass. This is often the most challenging part of class since many students are much less interested in listening, summarizing, and comparing than in solving problems, which is inherently a more active process.
I am by no means an expert on consolidation, but it is something that I worked a lot on this year, partly because I am working with a population of students right now where the vast majority have documented learning differences and who have historically struggled with motivation in Math. These challenges are most evident when students are asked to analyze classmates' work and participate in a class discussion about the day's problems. Here are some strategies that I have found helpful for this part of class: