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 Anticipating and Monitoring
Monday, July 25, 2016
10:30 – 12:00
Read and discuss Chapter 4 – 45 minutes
Anticipating and Monitoring 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 4 in Smith & Stein (2011).
What are the important considerations as a teacher in anticipating student thinking?
What are the important considerations in being prepared to monitor students as they work?
How do anticipating and monitoring connect to issues of access and equity for students?

6. The Drawing Parallelograms Task
Consider Part 1 of the Drawing Parallelograms Task (from the task packet, Grades 4-5).
With your small group, identify an appropriate mathematical goal for the implementation and discussion of the task.
Use the Anticipating and Monitoring sheet to draw and describe the types of student thinking that you might anticipate students will engage in as they work on the task. Be sure to include misconceptions and ”incomplete” thinking.
For each solution strategy, write at least two assessing and advancing questions for each.
After you have brainstormed ideas together, create a poster that summarizes your work.

7. Drawing Parallelograms
1. Draw two examples and two non-examples of each quadrilateral using these definitions. 

Parallelogram: A quadrilateral with 2 pairs of parallel sides.
Rectangle: A parallelogram with 4 right angles.
Rhombus: A parallelogram with 4 sides of equal length.
Parallelogram
Rectangle
Rhombus
Two Examples:
Two Non-Examples:

8. Gallery Walk
Browse the posters with Anticipated Solutions and Monitoring Questions for the Drawing Parallelograms task. What do you notice? What do you wonder? (Use sticky notes to comment.) What solution strategies would you like to take back to your group?

9. Tomorrow we will…
Make use of the anticipated student solutions and monitoring questions to engage in a selecting and sequencing activity.
Discuss the practice of connecting mathematical ideas.
Make connections to issues of identity, access, and equity.
(You may wish to preview or pre-read Chapter 5 in Smith and Stein.)

10. 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.