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Mathematics

Leading a discussion

Mathematics
In a group discussion, the teacher and all of the 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, and interpreting. The teacher and a wide range of students contribute orally, listen actively, and respond to and learn from others’ contributions.
Mathematics

Eliciting and interpreting

Mathematics
Teachers pose questions or tasks that provoke or allow students to share their thinking about specific academic content in order to evaluate student understanding, guide instructional decisions, and surface ideas that will benefit other students. To do this effectively, a teacher draws out a student’s thinking through carefully-chosen questions and tasks and considers and checks alternative interpretations of the student’s ideas and methods.
Mathematics

Implementing norms and routines for discourse

Mathematics
Each discipline has norms and routines that reflect the ways in which people in the field construct and share knowledge. These norms and routines vary across subjects but often include establishing hypotheses, providing evidence for claims, and showing one’s thinking in detail. Teaching students what they are, why they are important, and how to use them is crucial to building understanding and capability in a given subject. Teachers may use explicit explanation, modeling, and repeated practice to do this.
Mathematics

Explaining and modeling content

Mathematics
Explaining and modeling are practices for making a wide variety of content, academic practices, and strategies explicit to students. Depending on the topic and the instructional purpose, teachers might rely on simple verbal explanations, sometimes with accompanying examples or representations. In teaching more complex academic practices and strategies, such as an algorithm for carrying out a mathematical operation or the use of metacognition to improve reading  comprehension, teachers might choose a more elaborate kind of explanation that we are calling “modeling.” Modeling includes verbal explanation, but also thinking aloud and demonstrating.