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| Preface: How to Use This Book | |
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| Acknowledgments | |
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| About the Author | |
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| The Mathematical Brain and High-Impact Teaching | |
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| Teaching Mathematics Through Differentiating Instruction | |
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| The Mathematical Brain | |
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| Brains as Prioritizing Filters | |
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| Number Sense | |
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| Multiple Intelligences: Avenues for Learning Math | |
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| Summary of Brain Research | |
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| Instructional Phases for Developing Math Skills | |
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| Teaching Strategy: Mathematical Games to Develop Number Sense | |
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| SHEMR: A Tool for High-Impact Learning in Mathematics Evaluating One's Own Instructional Planning | |
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| What's Next? | |
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| Differentiated Instruction and Response to Intervention in Mathematics | |
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| Differentiation and Response to Intervention: Refocusing Math Instruction | |
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| Teaching Phases in the Direct Instruction Lesson | |
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| Problems With Direct Instruction in a Large Class | |
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| Teaching Strategy: The Guess, Assess, and Tear Out Tactic | |
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| A Differentiated Instruction Lesson Example | |
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| Teaching Strategy: Using Guess, Assess, and Tear Out! Moving From Direct Instruction to Differentiated Instruction in Math | |
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| The Omega Group | |
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| The Mainline Instruction Group | |
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| The Beta Group | |
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| Is Further Differentiation Needed? | |
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| Anything Wrong With This Scenario? Enhancing the Differentiated Instruction Model | |
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| Guidelines for Differentiated Lesson Planning | |
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| Results of Differentiated Lessons | |
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| A Differentiated Instruction Overview: What It Is and What It Isn't | |
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| Response to Intervention in Mathematics | |
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| Case Study: A RTI for Number Sense and Early Math Skill | |
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| What's Next? | |
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| Differentiating for Primary and Elementary Math | |
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| Research on Math Readiness | |
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| Steps in Developing Early Math Skills | |
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| Teaching Strategy: A Concrete, Semi-Concrete, Abstract Learning Tactic | |
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| Using CSA in the Classroom | |
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| CSA in the Higher Grades | |
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| Summary: CSA Tactic | |
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| Teaching Strategy: The Errorless Learning Procedures | |
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| Summary: Errorless Learning | |
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| Teaching Strategy: Classwide Peer Tutoring for Differentiating in the Math Class | |
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| What's Next? | |
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| Differentiating for Deep Conceptual Understanding | |
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| High-Impact Teaching for Operations in Math | |
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| The Debate on Calculators in Elementary Mathematics | |
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| Constructivist Theory and Understanding of Mathematics | |
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| Using Cognitive Guided Visualization | |
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| Scaffolded Instruction in Math | |
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| Debate on What a Scaffold Is | |
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| Graphic Representations of Word Problem Schemas | |
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| Using a Representational Strategy | |
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| Teaching Expanded Notation and Partialing | |
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| Process Mnemonics Strategies to Teach Computation | |
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| Research Support | |
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| What's Next? | |
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| Differentiating With Learning Strategies | |
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| The Brain Research Basis for Metacognitive Theory and Tactics | |
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| Learning Strategies for Word Problems | |
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| The Schema-Based Math Strategy | |
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| Differentiated Tear Out Activities for Story Problem Schemas | |
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| What's Next? | |
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| Differentiating in the Middle Grades | |
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| Working Toward Higher-Order Thinking | |
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| Teaching Strategy: Anchored Instruction | |
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| Teaching Games in Higher Grades | |
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| The PASS Strategy | |
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| Moving On Up! Math Instruction Guidelines for Secondary Learners | |
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| Appendix | |
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| References | |
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| Index | |