- In their book, "Using the Five Practices for Orchestrating Productive Mathematics Discussions," Margaret Smith and Mary Stein outline a framework to support intentional planning for all aspects of a daily math lesson. Which allows educators to facilitate the consolidation of the lesson in a more purposeful and targeted manner. These foundational five steps are; first, anticipating likely student responses to worthwhile mathematical tasks including the models, strategies and possible misconceptions used. Second, monitoring students actual responses to the tasks. Third, selecting particular student work samples to be presented by students during the whole class discussion. Fourth, sequencing the student responses that will be shared in a specific order. And fifth, connecting students' responses to underlying mathematical ideas. The five practices enable educators to transform student tasks into learning experiences while also minimizing the amount of improvisation and on spot decisions that an educator needs to make about the kinds of support a student needs and how best to deliver it. By focusing on key aspects of student thinking and demonstrated skills and understanding from within that lesson's context, educators can set the stage for a consolidation that avoids the show and tell kind of consolidation that we often see. And instead connects key math ideas and learning takeaways as we consolidate learning and prepare for tomorrow's learning goals. In this way, the consolidation becomes an orchestrated discussion that uses student responses to advance the mathematical understanding of the whole class and hopefully engages more of your students in the consolidation phase with a more precise and useful sharing of student learning. In order to support the use of the five practices, a planner or template can be used to help educators organize their own thinking as well as track student solutions throughout the monitoring phase of the task. This support will also guide the selecting, sequencing and connecting components of the strategy. While monitoring students, examples of student strategies, misconceptions and even the use of models or manipulatives that students use to support their thinking and problem solving can be written down. This allows educators to select and sequence which strategies will be a focus during the consolidation, who might share it and in what order. First of all, you will need time to make this decision. Plan a 10 minute independent activity that students can do when the problem solving time is finished. While you look over your notes and the student work to select and sequence which student strategies will be shared. It's important that you select a low entry point for the consolidation. Having a student explain a sophisticated strategy that most of the class has not yet come to use or understand does not further the math learning of the class on the whole. Aim for the majority of students when you select and sequence student solutions to focus on during the consolidation. You can always have one-to-one conversations with students during the monitoring phase or after the consolidation. Meeting with a small group of students after to give them feedback about other strategies, will be important for their consolidation of learning too. Your choice of strategy or problem solving method is paramount. Often more important than the choice of who will share. With that being said, if several students have used the same strategy, you could choose a student that you feel would personally benefit from the opportunity as a positive experience. It's highly recommended that you include student voice as it will almost certainly improve the buy-in and attention of your students when you consolidate. Consolidation should not simply be a teacher's voice reviewing key learning and effective strategies. The purpose is to consolidate student learning in a timely way that highlights key ideas observed which will support students in their current mathematical understanding as we connect to the learning goals going forward. Taking pictures of a small part of the student work that you would like them to speak to during the consolidation can be helpful. When an entire chart paper showing all student work is displayed, students will often revert back to sharing the whole story of their math for that lesson. You could also circle the strategy or key idea right on their paper as a way of ensuring that you remember which aspect you wanted them to explain during the consolidation. Finally, be clear about what you want a student to share, asking a question like, "Can you please tell us why you chose to blank?" Or "I noticed that you decided to blank here, can you let us know a little bit more about that?" If you simply ask a student to share their work or explain what they did, you will get a show and tell, and often lengthy response. Ultimately, the five practices can support the consolidation of your math lesson by minimizing the amount of on the spot decisions you'll need to make during that lesson by clearly focusing on specific math ideas, to further group math understanding and by allowing students to build on the ideas and strategies of others.