1. 5 Practices for Orchestrating productive math discussions
Caroline Loomis
Secondary Mathematics TOSA
San Juan USD

2. Mathematical Discourse
Social interaction provides us with the opportunity to use others as resources, to share our ideas with others, and to participate in the joint construction of knowledge.
- Margaret S. Smith and Mary Kay Stein 2011

3. NCTM on Discourse
Mathematical discourse includes:
Purposeful exchange of ideas through classroom discussion
Use of verbal, written, and visual communication.

4. CA Framework on Discourse

5. Mathematical Discourse
“Research tells us that complex knowledge and skills are learned through social interaction.”
- Vygotsky 1978; Lave and Wenger 1991

6. Mathematical Discourse
What does it look like in your classroom?

8. Mathematical Discourse

9. Five Practices that Promote Discourse
Anticipating student response prior to the lesson
Monitoring students’ work (written and verbal) on a task
Selecting particular students to present their mathematical work
Sequencing students’ responses in a specific order for discussion
Connecting different students’ response and connecting the responses to key mathematical ideas

10. Goals for lesson: Make connections between the different representations and generalize the pattern to write a rule.

12. Characteristics of a Discourse-rich environment
What are teachers doing?
What are students doing?
Engaging students in purposeful sharing
Presenting and explaining ideas
Selecting and sequencing student approaches and solution strategies
Listening carefully to and critiquing the reasoning of peers
Facilitating discourse among students
Seeing to understand the approaches used by peers
Ensuring progress toward mathematical goals
Identifying how different approaches to solving a task are similar or different

13. Promoting Mathematical Discourse
If students should…
have opportunities to talk with, respond to, and question each other…
engage in these opportunities in ways that can support mathematical learning for the classroom community…
Then we should…

15. Principles To Action
“Students who learn to articulate and justify their own mathematical ideas, reason through their own and others’ mathematical explanations, and provide a rationale for their answers develop a deep understanding that is critical to their future success in mathematics and related fields.” Carpenter, Franke, and Levi (2003, p. 6),

16. Resources
5 Practices for Orchestrating Productive mathematics Discussions – Margaret Smith and Mary Kay Stein NCTM 2011 Principals to Action – NCTM 2014 Framework for moving towards discourse – Hufferd-Ackles, Fuson and Sherin 2004 Accellerating Oral Language with Academic Conversations -- Jeff Zwiers California Mathematics Framework 2016