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

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

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

CA Framework on Discourse

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

Mathematical Discourse What does it look like in your classroom?

Mathematical Discourse

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

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

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

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…

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),

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