# Capacity Building Series

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7 Below are some examples of prompts and questions that may be posed by teachers and/or by students during the activation phase; depending on the context, they may also be appropriate during other parts of the lesson. It is helpful to consider the purpose of the question or prompt. Possible purpose: Understand the mathematical task and its context What information are you/we going to use to solve this problem? Possible purpose: Establish connections, Activate prior knowledge What other problem have you/we solved that is similar to this one? Let s record all that you/we know about. What do these two have in common? What is unique about each of them? 2. DURING WORKING ON IT, ACTION During this part of the lesson, students are working on solving a problem and communicating and representing their mathematical thinking. This phase of the lesson provides multiple observational assessment opportunities, which may be captured as anecdotal or digital records. As students work to make sense of the mathematical ideas embedded in the problem, both teachers and students use questions to develop and clarify their mathematical thinking. Solving the problem during the planning phase helps teachers to anticipate some of the challenges that students may encounter and informs their questioning. By listening closely to students as they discuss their emerging solutions, teachers occasionally pose questions and use the information they glean to inform their in-themoment instructional decisions. This information may also be used as assessment-forlearning data for planning purposes, including the planning of questions for lesson consolidation. Both correct and incorrect solutions can be probed, since questioning promotes the thinking necessary to build, construct and consolidate understanding. At times, however, questioning may not be appropriate, since the students need time to persevere through their thinking without interruption. For ideas on how to plan good questions... Teachers and mathematics leaders identify the difference between planning a good problem question and the kind of ongoing questioning that draws out and encourages students thinking and moves them forward mathematically. Both are essential to unravelling student mathematical thinking. For support in planning: Differentiating Mathematics Instruction literacynumeracy/inspire/research/ different_math.pdf Below are examples of prompts and questions that teachers and students may pose in order to probe and provoke mathematical thinking. In modelling and charting good questioning, teachers equip students to be able to ask good questions of each other. Possible purpose: Clarify reasoning and understanding How do you/we know? What does this part represent in your/our solution? How do you know your/our answer is reasonable? Possible purpose: Focus on communication What could you/we add to your/our solution to make it clearer for the reader? How can you/we represent your/our thinking? Possible purpose: Make a conjecture What would happen if...? Would this work every time? Can you/we think of any examples that don t work? 3. AFTER CONSOLIDATION, HIGHLIGHTS AND SUMMARY, AND PRACTICE In this phase of the three-part lesson, the teacher strategically coordinates student sharing of their solutions to the lesson problem, using a mathematical instructional strategy like bansho, math congress or a gallery walk. During consolidation, teachers and students ask questions that help to summarize the mathematical ideas embedded in the class solutions. They support students in establishing explicit connections 7

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