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| The Author | |
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| About SEDL | |
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| About This Book | |
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| Introduction | |
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| Julian's Story | |
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| Rationale and Purpose | |
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| Who Benefits from This Book? xxii | |
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| The Problem with Math Is English (and a Few Other Things) | |
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| Why Language and Symbolism? | |
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| What We Are Teaching | |
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| Turning the tide: A Sampling of Approaches | |
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| Mathematics Is About Relationships | |
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| Connecting the Pieces and Looking Ahead | |
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| Why a Language Focus in Mathematics? | |
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| The Convergence of Mathematics and English: More Than Just Vocabulary | |
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| Problems Based on the English Language | |
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| A Number of Problems with Number | |
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| Language and Symbolism in Traditional Instruction | |
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| Shortcomings of Traditional Instruction | |
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| More Language and Symbolism Issues: Adding Fuel to the Fire | |
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| Tell Me Again Why the Language Focus in Math? | |
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| So What Does Conceptual Understanding Look Like? | |
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| It Starts with Definitions | |
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| Making Connections in Math: Beyond Connecting Dots | |
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| The Interpretation and Translation Of Math | |
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| Conclusion | |
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| The Order of Operations: A Convention or a Symptom of What | |
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| Ails Us? | |
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| The Roots of the Rules | |
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| The Natural Order: A Mathematical Perspective | |
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| Conclusion: A Conceptual Understanding of the Order of Operations | |
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| Using Multiplication as a Critical Knowledge Base | |
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| Understanding Key Definitions and Connections | |
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| Interpreting Multiplication | |
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| Using The Power of the Distributive Property | |
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| Feeling Neglected: The Units in Multiplication | |
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| Conclusion: Small Details, Huge Impact | |
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| Fractions: The ''F Word'' in Mathematics | |
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| Defining Fractions: Like Herding Cats | |
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| The Fraction Kingdom | |
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| Interpreting Fractions | |
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| Conclusion | |
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| Operations with Fractions | |
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| Adding and Subtracting Fractions | |
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| Multiplying Fractions | |
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| Dividing Fractions | |
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| Conclusion | |
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| Unlocking the Power of Symbolism and Visual Representation | |
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| Symbolism | |
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| Visual Representation | |
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| The Power of Interpretation: Three Perspectives of Trapezoids | |
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| Conclusion | |
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| Language-Focused Conceptual Instruction | |
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| Language Focus: Beyond the Definitions | |
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| The Secrets to Solving Word Problems | |
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| Suggested Instructional Strategies | |
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| Conclusion | |
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| Mathematics: It's All About Relationships! | |
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| Language and Symbolism: Vehicles for Relationship Recognition | |
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| Relationships and Fractions | |
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| Proportional Reasoning | |
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| Relationships: Important Considerations | |
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| Relationships: Making Powerful Connections | |
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| Conclusion | |
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| The Perfect Non-Storm: Understanding the Problem and Changing the System | |
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| A Systemic Issue | |
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| Math Makeover | |
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| Conclusion | |
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| Bibliography | |
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| Index | |