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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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Number and Operation Sense | |
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Developing Number Relationships | |
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Numbers Beyond 1000 | |
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Activities for Flexible Thinking with Whole Numbers | |
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Developing Multiplication and Division Operation Sense | |
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Solving Contextual 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 Additional 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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Fact Remediation with Upper-Grade Students | |
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Facts: No Barrier to Good Mathematics | |
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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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Developing 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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Fraction Computation | |
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Number Sense and Fraction Algorithms | |
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Addition and Subtraction | |
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Multiplication | |
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Division | |
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Expanded Lesson | |
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Decimal and Percent Concepts and Decimal Computation | |
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Connecting Two Different Representational Systems | |
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Developing Decimal Number Sense | |
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Introducing Percents | |
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Computation with Decimals | |
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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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Measuring Angles | |
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Introducing Standard Units | |
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Estimating Measures | |
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Developing Formulas for Area and Volume | |
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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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Functions | |
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Expanded Lesson | |
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Exploring Data Analysis | |
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Gathering Data to Answer Questions | |
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Descriptive Statistics | |
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Understanding the Mean: Two Concepts | |
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Graphical Representations | |
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Expanded Lesson | |
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Exploring Concepts of Probability | |
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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 | |