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| Preface | |
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| Activities at a Glance | |
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| About the Authors | |
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| Foundations of Student-Centered Instruction | |
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| How Children Learn and Understand Mathematics | |
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| Constructing Ideas | |
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| Understanding | |
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| Classroom Influences on Learning | |
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| Using Models in the Classroom | |
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| Teaching with Problems | |
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| Problem-Based Tasks | |
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| The Value of Teaching with Problems | |
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| A Three-Part Format for Problem-Based Lessons | |
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| Teachers' Questions about Problem-Based Teaching | |
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| Planning in a Problem-Based Classroom | |
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| Planning Problem-Based Lessons | |
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| Variations of the Three-Part Lesson | |
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| Diversity in the Classroom | |
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| Assessment in a Problem-Based Classroom | |
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| Appropriate Assessment | |
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| Rubrics and Their Uses | |
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| Diagnostic Interviews | |
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| Grading | |
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| Get Started | |
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| Developing Early Number Concepts and Number Sense | |
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| Early Counting and Number | |
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| Early Number Sense | |
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| Relationships Among Numbers 1 Through 10 | |
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| Relationships for Numbers 10 to 20 | |
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| Numbers to 100: Early Introductions | |
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| Number Sense and the Real World | |
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| Expanded Lesson | |
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| Developing Meaning for the Operations and Solving Story Problems | |
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| Addition and Subtraction | |
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| Teaching Addition and Subtraction | |
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| Problem Structures for Multiplication and Division | |
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| Teaching Multiplication and Division | |
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| More Thoughts About Children Solving Story Problems | |
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| Expanded Lesson | |
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| Helping Children Master the Basic Facts | |
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| From Concepts and Strategies to Fact Mastery | |
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| Strategies for Addition Facts | |
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| Strategies for Subtraction Facts | |
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| Strategies for Multiplication Facts | |
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| Division Facts and "Near Facts" | |
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| Effective Drill | |
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| Expanded Lesson | |
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| Base-Ten Concepts and Place Value | |
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| Children's Pre-Base-Ten Concepts | |
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| Goals of Place Value Development | |
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| Models for Place Value | |
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| Developing Place-Value Concepts and Procedures | |
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| Number Sense Development | |
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| Activities for Flexible Thinking | |
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| Helping Children Work with Money | |
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| Expanded Lesson | |
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| Strategies for Whole-Number Computation | |
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| Toward Computational Fluency | |
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| Development of Invented Strategies: A General Approach | |
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| Invented Strategies for Addition and Subtraction | |
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| Traditional Algorithms for Addition and Subtraction | |
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| Invented Strategies for Multiplication | |
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| The Traditional Algorithm for Multiplication | |
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| Invented Strategies for Division | |
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| The Traditional Algorithm for Division | |
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| Expanded Lesson | |
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| Geometric Thinking and Geometric Concepts | |
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| Geometry Goals for Your Students | |
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| Geometric Thought: Reasoning about Shapes and Relationships | |
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| Shapes and Properties Activities | |
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| Transformation Activities | |
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| Location Activities | |
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| Visualization Activities | |
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| Expanded Lesson | |
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| Developing Measurement Concepts | |
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| The Meaning and Process of Measuring | |
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| Developing Measurement Concepts and Skills | |
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| Measuring Length | |
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| Measuring Area | |
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| Measuring Volume and Capacity | |
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| Measuring Weight and Mass | |
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| Measuring Time | |
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| Introducing Standard Units | |
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| Expanded Lesson | |
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| Early Fraction Concepts | |
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| Sharing and the Concept of Fractional Parts | |
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| Models for Fractions | |
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| From Fractional Parts to Fraction Symbols | |
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| Fraction Number Sense | |
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| Equivalent-Fraction Concepts | |
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| Expanded Lesson | |
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| Algebraic Reasoning | |
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| Repeating Patterns | |
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| Growing Patterns | |
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| Patterns with Numbers | |
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| Representing Ideas | |
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| Variables and Equations | |
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| Relations and Functions | |
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| Expanded Lesson | |
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| Helping Children Use Data | |
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| Gathering Data to Answer Questions | |
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| Classification and Data Analysis | |
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| Graphical Representations | |
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| Describing a Set of Data | |
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| Expanded Lesson | |
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| Early Experiences with Probability Concepts | |
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| Probability on a Continuum | |
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| Sample Spaces and Probability | |
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| Short-Run versus Long-Run Results | |
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| Expanded Lesson | |
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| Principles and Standards for School Mathematics | |
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| A Guide to the Blackline Masters | |
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| References | |
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| Index | |