It is during the Summarize phase that the teacher guides the students to reach the mathematical goals of the Problem and to connect their new understanding to prior mathematical goals and Problems in the Unit. The Summarize begins when most students have gathered sufficient data or made sufficient progress toward solving the Problem. In this phase, students present and discuss their solutions and the strategies they used to understand the Problem, organize the data, and find the solution. During the discussion, the teacher helps students enhance their conceptual understanding of the mathematics in the Problem and guides them in refining their strategies into efficient, effective, generalizable problem-solving techniques or algorithms.
Although the teacher leads the discussion in the Summarize, students play a significant role. Ideally, they pose conjectures, question each other, offer alternatives, provide reasons, refine their strategies and conjectures, and make connections. As a result of the discussion, students should become more skillful at using the ideas and techniques that come out of the experience with the Problem.
If it is appropriate, the Summarize can end by the teacher posing a question or two to check students’ understanding of the mathematical goal(s) that have been developed at this point in time. Check for Understanding questions occur occasionally in the teacher support for the Summarize. These questions help the teacher to assess the degree to which students are developing and using their mathematical knowledge.
Orchestrating a Discussion
The following questions can help the teacher prepare for orchestrating a discussion during the summary.
- How can I help the students make sense of and appreciate the variety of methods that may be used?
- How can I orchestrate the discussion so that students summarize their thinking about the Problem?
- What questions can guide the discussion?
- What concepts or strategies need to be emphasized? What ideas do not need closure at this time?
- What definitions or strategies do we need to generalize?
- What connections and extensions can be made?
- What new questions might arise and how do I handle them?
- What can I do to follow up, practice, or apply the ideas after the summary?
Reflecting on Student Learning
The following questions can be used to assess student understanding at the end of the lesson.
- What evidence do I have that students understand the Focus Question? Where did my students get stuck?
- What strategies did they use?
- What breakthroughs did my students have today?
- How will I use this to plan for tomorrow? For the next time I teach this lesson?
- Where will I have the opportunity to reinforce these ideas as I continue through this Unit? The next Unit?