1. 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

2. 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

3. 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”

4. 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.

5. 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?

6. 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.

7. 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?

8. Core Mathematics Partnership Project
Disclaimer
Core Mathematics Partnership Project
University of Wisconsin-Milwaukee,
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.