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A routine element of every class

Reasoning needs to be part of every mathematics lesson — a routine element of every classroom discussion.

Most dialogue in mathematics classrooms is between teachers and students. Typically, it follows the pattern of teacher question followed by student response. One way of developing students' reasoning skills is to change this pattern of interaction.

When teachers model the practice of evaluating ideas, students can learn to make thoughtful judgements about the mathematical soundness of their peers' ideas and to contribute in an environment of thoughtful, well-reasoned discussion.

Developing student-to-student dialogue takes concerted effort, but it results in orderly and respectful mathematical argument, with students taking ownership of their ideas.

A social environment where everyone listens attentively and reflectively to each other also takes effort and time to develop.

Student-to-student dialogue

Good dialogue is developed when students understand how they should contribute.

A social activity

Good mathematics teachers at all levels explicitly teach sharing and listening skills.