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| Annotated Contents | |
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| Foreword | |
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| Preface and Acknowledgments | |
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| Welcome | |
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| Course Introduction | |
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| Introductory Lesson | |
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| Mathematics Education: Where Do I Stand? | |
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| Getting to Know Colleagues: Uniquely Us | |
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| A Learning Community | |
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| Mathematics Strand: Reasoning with Patterns and Algebra | |
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| Introduction | |
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| Figurate Numbers | |
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| Preparing to Interview Students about Reasoning with Patterns | |
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| Problem Solving: Careful Counting | |
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| Reasoning and Proof: Patterns and Multiplication | |
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| Generalizing from Patterns: The Concept of Variable | |
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| Using Experiments: Exploring Graphs and Lines | |
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| Learning with Materials: Integers and Equations | |
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| Using Contexts: Functions | |
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| Using Interviews to Understand Students' Reasoning with Patterns | |
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| Synthesizing Unit One | |
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| The Learning of Mathematics | |
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| Mathematics Strand: Rational Numbers and their Uses | |
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| Introduction | |
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| Unit Two Investigation: Four Fours | |
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| Preparing to Interview Students about Proportional Reasoning | |
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| Using Multiple Representations: Rational Numbers | |
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| Using Learning Theory: Fractions, Decimals, and Percents | |
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| Developing Meanings of Operations: Addition and Subtraction | |
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| Developing Meanings of Operations: Multiplication and Division | |
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| Analyzing Student Thinking: Proportional Reasoning | |
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| Using Interviews to Understand Students' Proportional Reasoning | |
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| Synthesizing Unit Two | |
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| Planning and Instruction | |
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| Mathematics Strand: Geometry, Measurement, and Transformations | |
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| Introduction | |
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| Unit Three Investigation: Historical Formulas | |
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| Preparing to Interview Students about Perimeter and Area | |
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| Identifying Worthwhile Mathematical Tasks: Measurement Formulas | |
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| Lesson Planning: Proportions among Measures in Similar Figures | |
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| Guided Discovery: Quadrilaterals | |
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| Open-Ended Exploration: Tessellations | |
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| Integrating Direct Instruction with Guided Discovery: Transformations | |
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| Effective Classroom Discourse: The Pythagorean Theorem | |
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| Using Interviews to Plan Instruction on Perimeter and Area | |
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| Synthesizing Unit Three | |
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| Assessment | |
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| Mathematics Strand: Data Analysis and Probability | |
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| Introduction | |
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| Unit Four Investigation: Pascal's Triangle | |
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| Preparing to Interview Students about Their Views on Assessment | |
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| Multiple Uses of Assessment: Categorical and Discrete Data | |
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| Assessment That Highlights Students' Thinking: Continuous Data | |
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| Managing and Grading Every Day: Introduction to Probability | |
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| Rubrics and Their Uses: Systematic Counts for Probabilities | |
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| Issues in Developing and Using Tests | |
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| Using Interviews to Develop a Classroom Assessment Plan | |
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| Synthesizing Unit Four | |
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| Collaborating with Educational Partners | |
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| Introduction | |
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| Preparing to Interview Educational Partners | |
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| Curriculum Integration | |
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| Facilitating Educational Growth | |
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| Evaluating Curriculum Materials | |
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| Using Interviews to Prepare for Educational Collaboration | |
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| Synthesizing Unit Five | |
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| Appendices | |
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| References and Permissions | |
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| Index | |