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Mathematics

Leading a discussion

Mathematics
In a group discussion, the teacher and students work on specific content together, using one another’s ideas as resources. The purposes of a discussion are to build collective knowledge and capability in relation to specific instructional goals and to allow students to practice listening, speaking, interpreting, agreeing and disagreeing. The teacher and a wide range of students contribute orally, listen actively, and respond to and learn from others’ contributions. Teachers work to ensure students are positioned as competent among their peers, that patterns of interaction are respectful, and that the collective work of the group uses the strengths of and benefits each student.
Mathematics

Eliciting and interpreting

Mathematics
Teachers pose questions that create openings for students to share their thinking about specific academic content. They seek to understand student thinking, including novel points of view, new ideas, ways of thinking, or alternative conceptions. Teachers draw out student thinking through carefully chosen questions and tasks and attend closely to what students do and say. They consider and check alternative interpretations of student ideas and methods. Teachers are attentive to how students might hear their questions and to how students communicate their own thinking. Teachers use what they learn about students to guide instructional decisions, and to surface ideas that will benefit other students. By eliciting and interpreting student thinking, teachers position students as sense-makers and center their thinking as valuable.
Mathematics

Implementing norms and routines for discourse

Mathematics
Every content area has norms and practices for how people construct and share knowledge. These norms and practices vary across subjects but often include establishing hypotheses, providing evidence for claims, and explaining one’s reasoning to others. Teaching students these norms and practices, showing why they are important, and providing opportunities to use them, is crucial for building understanding and capability in a given subject. Teachers name these norms and practices as students use them, and they provide scaffolds, model, and then offer opportunities for students to use the norms and practices.
Mathematics

Explaining and modeling content

Mathematics
Explaining and modeling are practices for making a wide variety of topics, academic practices, and strategies explicit to students. Teachers determine when explaining or modeling can help to make visible to students content and practices that often remain tacit. Teachers might use simple explanations when working with straightforward content. They might choose modeling, which includes verbal explanation as well as thinking aloud and demonstrating when sharing the metacognitive process, to provide greater access to students about strategies and practices.