Orchestrating Productive Mathematical Discussionss CPM National Conference 2012
Read and React “Ensuring that students have the opportunity to reason mathematically is one of the most difficult challenges that teachers face. A key component is creating a classroom in which discourse is encouraged and leads to better understanding. Productive discourse is not an accident, nor can it be accomplished by a teacher working on the fly, hoping for serendipitous student exchange that contains meaningful mathematical ideas.” Frederick Dillion
Think – Pair - Share • What do you do to plan a lesson? • To what extent does the cognitive demand of the lesson that you are using affect the level of planning in which you engage?
Lesson Structure • Lesson Opener • Explore – Students engaging in solving problems • Discuss and Summarize– This is the time in class when powerful learning and conversation occur. • Maintaining balance between the discipline of the mathematics and student authorship
Analyzing the case of David Crane • As you read the case, look for the balance between the mathematical goals of the lesson being clear and students authorship.
Five Practices • Anticipating • likely student responses to challenging mathematical tasks; • Monitoring • student’s actual responses to the tasks (while students work on the task in pairs or small groups); • Selecting • particular students to present their mathematical work during the whole-class discussion;
Sequencing • The student responses that will be displayed in a specific order; • Connecting • Different students’ responses and connecting the responses to key mathematical ideas
Foundation – Goal of lesson • Selecting the mathematical goal that is essential for every student should know and understand about math as a result of the lesson.
Rabbit Problem • Determine the learning goal for this lesson • Anticipate • Envision how students might mathematically approach this problem. • Record the various solution methods on the sample recording tool
In what sequence would you want the various solutions to occur? • What opportunities are there to make connections in order to highlight the mathematical goal?
Calling Plan Case Study • Mathematical Goals – Students should • Recognize that there is a point of intersection between two unique non parallel linear equations that represents where the two functions have the same x- and y- values • Understand that the two functions “switch positions” a the point of intersection • Make connections between the multiple representations and identify the slope and y-intercept in each representational form
Next Steps • How might I incorporate this into my practice? • What seems reasonable for how often I will use the Five practices in my planning? • Where do I want to start?
References 5 Practices for Orchestrating Mathematics Discussions by Margaret Smith & Mary Kay Stein Published by National Council of Teachers of Mathematics 2011