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:
I try to never spend more than 10 minutes of a 50 minute class on consolidation (usually aiming for less than that). Middle school students and students with attentional challenges do not have the bandwidth for a class discussion that lasts longer than that. This forces me to be pretty strategic about what we discuss and does mean we can't talk about every interesting thing that comes up in class. Something that is especially interesting but that doesn't fit into the 10-minute time frame can be moved to a warm-up question for the next day.
- Involve other students in discussing a group's work
I almost never have the students whose work is being discussed share their process since listening passively is not that engaging for the rest of the class. The students who did the work often know what they meant and why they did what they did and gloss over those parts. To involve everyone else, I usually first ask everyone in the class to quietly study the group's work we are looking at and give a small thumbs up when they finish reading it (props to @mpershan for this lovely teacher move). I then ask for volunteers to explain a few key parts (if there aren't many volunteers, I will first have students take turns explaining each step of the work with a partner), asking follow up questions, like "Why did they do ... here?," "What would they have done if the problem instead asked for...?" Other ways to involve more of the class is to ask for students who can restate what someone has said. This can give students who need more processing time an opportunity to participate and gives everyone the opportunity to hear big ideas a few times. This does mean that students have to show clear work so that it's understandable by others so that is definitely something I emphasize a lot. - Give students something to do during/after consolidation
Related to the point above, many students struggle with listening/talking for an extended period of time. My students engage more readily when given opportunities to discuss with a partner, write something down in their notes, or do a related problem using the method we just discussed. I often have them grab a mini-whiteboard so that everyone can write down their answer to a discussion question or solve a related problem similar to the one we just discussed. If the energy level is low, I have students find a partner to discuss with who is not standing next to them to build in a bit more movement.
- Focus on connections and similarities/differences when looking at multiple pieces of student work
Consolidation often involves connecting different approaches or comparing related, but different problems. I have found it helpful to sequence the student work I want to discuss in such a way that we only focus on the step by step work of the first group. It can get repetitive if we go through each group's work in the same way. For the second or third piece of work, I ask students instead to identify what this group did the same or differently from the first group and hypothesize why they made those choices. Students can vote on their favorite method or say which method they would use in which situation and why.
- Set norms for class discussion
Something we have worked on all year is how to participate in academic discussions. This involves lots of modeling and practicing showing interest in a speaker with body language, eye contact, nodding along if things make sense, and looking quizzical when they don't. Every consolidation is an opportunity for students to practice these skills and give each other feedback. I have found it helpful to be very explicit about the behavior I am looking students to exhibit during class discussions and treat it as a skill that can be practiced and improved upon.
Please share your best tips for helping students consolidate and participate in class discussions centered on student work!! This has been the most challenging aspect of running a problem-based math class for me and I'd love to learn more.
