Table of Contents
Preface ix
Acknowledgments xi
1 Teaching for Thinking 1
Teaching for Mathematical Thinking 1
Teaching Practices to Foster Mathematical Thinking 6
Reflect on Your Reading 13
2 The Power of Reasoning Routines 15
What Are Reasoning Routines? 15
How Do Reasoning Routines Create a Math Thinking Learning Environment? 19
Five Essential Strategies 22
Chapter Summary 39
Reflect on Your Reading 40
3 Decide and Defend: A Reasoning Routine to Support Constructing Arguments and Critiquing Reasoning 41
What Does It Mean to "Construct and Critique"? 42
An Overview of the Decide and Defend Reasoning Routine 47
Decide and Defend in Action 55
Planning and Implementing Decide and Defend 64
Reflect on Your Reading 70
4 Contemplate Then Calculate: A Reasoning Routine to Support Structural Thinking 71
What Does It Mean to "Think Structurally"? 72
An Overview of the Contemplate Then Calculate Reasoning Routine 79
Contemplate Then Calculate in Action 86
Planning and Implementing Contemplate Then Calculate 92
Reflect on Your Reading 100
5 Design Your Own Reasoning Routine 101
Finding Your Inspiration 101
A Six-Step Process for Creating a Reasoning Routine 103
Starting with a Task Type or a Common Lesson Format 134
Reflect on Your Reading 135
6 Making the Essential Strategies a Routine Part of Your Practice 137
Learning to Use the Essential Strategies Effectively 137
Working on Essential Strategies Inside a Reasoning Routine 160
Working on Essential Strategies with Colleagues and Coaches 161
Some Final Thoughts 166
References 167