Chapter 1, “Mathematical Argument in the Elementary Grades: What and Why?,” introduces the major content of the book—the focus on mathematical argument, why that’s important, and the choice of operations as a context for work on mathematical argument for elementary students. The chapter introduces the concept of “productive lingering” on important mathematics. Chapter 2, “Elementary Students as Mathematicians,” describes how students engage in “new to them” mathematics and how their work parallels the process by which professional mathematicians create mathematical ideas. Chapter 3, “The Teaching Model,” presents the teaching model for engaging students in mathematical argument, describes the five phases in detail, and presents classroom examples to illustrate how each phase engages students in important mathematical ideas and practices. Chapter 4, “Using the Lesson Sequences: What the Teacher Does,” details where the teacher focuses her attention, the decisions she makes in response to students’ thinking, and the actions she takes as the class goes through the fives phases of the teaching model. Chapter 5, “Mathematical Argument in the Elementary Classroom: Impact on Students and Teachers,” summarizes evidence from student assessments and classroom observations about what students in our collaborating classrooms learned about mathematics content and practices, what was gained in participation and confidence, and how students applied their learning about mathematical argument in their regular math classes.
Chapters 1 through 4 also include video- and text-based examples drawn from the classrooms of our collaborating teachers; mathematical investigations for you to develop your own mathematical thinking and to become familiar with the mathematics content students in the examples are working on; and sets of focus questions about selected examples and about each chapter as a whole.
— Introduction, xii-xiii
