But Why Does It Work?

Table of Contents

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)