Introduction

• Content of the Book
• Classroom Examples: Text and Video
• The Lesson Sequences on Mathematical Argument

Chapter 1 Mathematical Argument in the Elementary Grades: What and Why?

• The What: Representation-Based Argument
• Examples of Mathematical Argument
• Why Linger on Mathematical Argument?

Chapter 2 Elementary Students as Mathematicians

• The Mathematician's Process
• Facilitating a Community of Student Mathematicians
• Why Should Students Act Like Mathematicians?

Chapter 3 The Teaching Model

• Introducing the Lesson Sequence
• Phase I: Noticing Regularity
• Phase II: Articulating a Claim
• Phase III: Investigating Through Representations
• Phase IV: Constructing Arguments
• Phase V: Comparing Operations
• What Students Gain

Chapter 4 Using the Lesson Sequences: What the Teacher Does

• Phase I: Noticing Regularity
• Phase II: Articulating a Claim
• Phase III: Investigating Through Representations
• Phase IV: Constructing Arguments
• Phase V: Comparing Operations

Chapter 5 Mathematical Argument in the Elementary Classroom: Impact on Students and Teachers

• Mathematics Content and Practices
• Applying New Understanding in Students' Regular Math Work
• Participation and Confidence Among the Range of Learners
• Mathematical Argument: An Opportunity for Teacher Learning About Fundamental Mathematics

Appendix A Same Sum, Same Difference (Whole Numbers)

• Goals for Students
• Sequence Overview

Appendix B Changing a Number in Addition of Multiplication (Whole Numbers)

• Goals for Students
• Sequence Overview

Online Lesson Sequences

• Sequence 1: Core Ideas of Addition and Subtraction (Whole Numbers)
• Sequence 2: Changing a Number in Addition or Subtraction (Whole Numbers)
• Sequence 3: Same Sum, Same Difference (Whole Numbers)
• Sequence 4: Core Ideas of Multiplication and Division (Whole Numbers)
• Sequence 5: Changing a Number in Addition or Multiplication (Whole Numbers)
• Sequence 6: Factors, Products, and Fractions (Whole Numbers and Fractions)
• Sequence 7: Same Product, Same Quotient (Whole Numbers)
• Sequence 8: Multiplication, Division, and Powers of Ten (Wholes Numbers and Decimals)