Productive Mathematical Discussions: Working at the Confluence of Effective Mathematics Teaching Practices Core Mathematics Partnership Building Mathematical Knowledge and High-Leverage Instruction for Student Success

The Five Practices in Geometry: Focus on Selecting, Sequencing, and Connecting Tuesday, July 26, 2016 10:30 – 12:00 Read and discuss Chapter 5 – 45 minutes Selecting, Sequencing, and Connecting exercise - 45 minutes

Facilitate meaningful mathematical discourse Establish math goals to focus learning Implement tasks that promote reasoning and problem solving Build procedural fluency from conceptual understanding Facilitate meaningful mathematical discourse Elicit and use evidence of student thinking Pose purposeful questions Use and connect mathematical representations Support productive struggle in learning mathematics Effective Mathematics Teaching Practices “Building a Teaching Framework” 07.03.2016

Five Practices for Orchestrating Productive Discussions anticipating likely student responses to challenging mathematical tasks; monitoring students’ actual responses to the tasks (while students work on the tasks 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; and connecting different students’ responses and connecting the responses to key mathematical ideas.

Read and Discuss Take 20 minutes to read (or re-read) Chapter 5 in Smith & Stein (2011). What are the important considerations as a teacher in selecting and sequencing responses to share in the whole-class discussion? How can a teacher best prepare for connecting student responses? How do selecting, sequencing, and connection support the development of students’ identities as mathematical learners?

The Drawing Parallelograms Task Consider Part 1 of the Drawing Parallelograms Task (from the task packet, Grades 4-5). Drawing from yesterday’s posters, identify the responses you would like to share in a discussion of Part 1 of the task. Organize your work using the six cells of the table in the task – what responses would you like to share for each section? Try to limit yourself to no more than two ideas to share from each of the cells Identify at least four connecting questions you would like to ask students during the discussion that do the following: Connect to important aspects of properties of quadrilaterals in general that you would like students to be focused on Makes comparisons both among and between the three types of parallelograms Make a poster that summarizes your group’s decisions.

Wrapping up What aspects of orchestrating productive discussions do you feel the most able to engage in starting in the fall? What do you want to learn more about?

Core Mathematics Partnership Project Disclaimer Core Mathematics Partnership Project University of Wisconsin-Milwaukee, 2013-2016   This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.