What is Mathematical Practices

Oral student contributions are important for learning mathematics, but without a written record of students' reasoning, revising is difficult or impossible. While writing makes revising possible, research needs to theoretically frame what to revise, how to revise, and how to support revisions. The chapter addresses the question: How can the academic literacy in mathematics framework inform research and practice on mathematical writing? The examples illustrate how that framework provides a complex view of language and a focus on mathematical practices to frame research and practice on mathematical writing and revising. The chapter considers why student writing and revising are important and describes how both research and instruction can emphasize mathematical practices. The examples focus on explanatory and argumentative writing and several mathematical practices central to revising explanations or arguments: generating conjectures, connecting representations, justifying claims, constructing arguments, and attending to precision.