A mathematics learning community moves teachers toward facilitating rather than dominating discussion among students. Teachers must choose problems to support meaningful mathematical discussions.
Practice routines are critical for establishing math community. Benefits of these routines include:
Creating instructional norms
Freeing up attention to content and students
Adding the safety of predictability to intellectually risky situations
Classroom routines could include:
- Passing out materials
- Setting up the learning work areas for individual students, partners, small groups, and large groups
- Lesson outline or routine- setting up the task; independent/ small group work; and end of lesson sharing, summarizing, and making connections
- Specific procedures for introducing and playing games
- Collecting materials
Lesson preparation is a key part for teachers. A helpful framework supporting productive mathematical discussions includes:
- Anticipating – both correct and incorrect strategies that students might use to solve a problem
- Monitoring – students as they work to solve the problem making notes of strategies, representations, and conversations that may be helpful to share with the whole class.
- Selecting – Specific work samples presented in sequence to share publicly.
- Sequencing – student work to maximize the chances that the mathematical goals could be met
- Connecting – different responses so that students can understand how the same mathematical idea is embedded in different strategies (Stein, Engle, Smith & Hughes, 2008)
As members of the math community, students must participate as a mathematician by:
- Listening to understand others’ thinking
- Participating in discussions
- Sharing ideas that challenge their thinking and understanding
- Honoring private think time
- Respecting their own and others’ rights and abilities to solve problems