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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 | |