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| Foreword | |
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| Preface | |
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| Acknowledgments | |
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| Turning to the Evidence | |
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| What Are Artifacts, and Why Analyze Them? | |
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| Learning to See through Multiple Lenses | |
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| Our Vision of Mathematics Learning and Teaching | |
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| A Framework for Using Artifacts Skillfully | |
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| Attention to Thinking | |
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| Describing and Interpreting Classroom Artifacts | |
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| Why Focus on Evidence? | |
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| Creating a Description of Student Work | |
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| Exercise 1: Danny | |
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| Process for Analyzing Danny's Work | |
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| Commentary on Danny's Work | |
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| Exercise 2: Melissa | |
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| Process for Viewing and Analyzing the Melissa Video | |
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| Commentary on Melissa's Interview | |
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| Reflecting on Exercise 2 | |
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| Using Artifacts in Your Own Classroom | |
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| Warm-Ups | |
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| Homework, Quizzes, and Tests | |
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| Exercise 3: Sorting Homework | |
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| Process for Sorting the Homework Samples | |
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| Commentary on Exercise 3 | |
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| Making Videos of Your Own | |
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| Wrapping Up | |
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| Additional Exercises: Video Clips of Two Math Interviews | |
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| Exercise 4: Kasage | |
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| Process for Viewing and Analyzing the Kasage Video | |
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| Exercise 5: Myrna | |
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| Process for Viewing and Analyzing the Myrna Video | |
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| Seeing the Potential in Students' Thinking | |
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| Why Focus on Errors? | |
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| Using Errors to See Potential Instead of Just Deficits in Students' Thinking | |
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| Exercise 1: Lemonade Lesson Part 1-Alberto and Kisha | |
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| Process for Viewing and Analyzing Lemonade Lesson Part 1 | |
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| Commentary on Lemonade Lesson Part 1 | |
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| Reflecting on Exercise 1 | |
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| Exercise 2: Lemonade Lesson Part 2-Rosa and Maria | |
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| Process for Viewing and Analyzing Lemonade Lesson Part 2 | |
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| Commentary on Lemonade Lesson Part 2 | |
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| Reflecting on Exercise 2 | |
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| General Commentary About Errors | |
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| Working with Errors in Your Own Practice | |
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| Homework | |
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| Warm-Ups | |
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| Class Discussions | |
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| Periodic Diagnostic Interviews | |
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| Wrapping Up | |
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| Attention to Content | |
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| Keeping an Eye on Rigorous Mathematics: Big Ideas and Habits of Mind | |
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| Naming and Framing Mathematical Rigor | |
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| Mathematical Frameworks: Big Ideas and Habits of Mind | |
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| Big Ideas | |
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| Habits of Mind | |
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| Choosing and Using a Mathematical Framework for Analyzing Artifacts | |
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| Exercise 1: Identifying Big Ideas in Your Math Textbook | |
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| Process for Analyzing Your Textbook | |
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| Commentary on Exercise 1 | |
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| Exercise 2: A Tale of Two Lessons-Using Mathematical Frameworks to Think About Rigor and Cognitive Demand | |
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| Process for Analyzing the Lessons | |
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| Commentary on Exercise 2 | |
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| General Commentary on Using Mathematical Frameworks to Consider Mathematical Rigor | |
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| Using Mathematical Frameworks in Your Lessons | |
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| Lesson Planning | |
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| Teaching the Lesson | |
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| Wrapping Up | |
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| Choosing, Using, and Connecting Mathematical Representations | |
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| General Commentary About Representations | |
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| Exercises | |
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| Exercise 1: Larry's Seventh-Grade Classroom Scenario | |
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| Process for Analyzing Larry's Classroom Scenario | |
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| Commentary on Larry's Classroom Scenario | |
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| Reflecting on Exercise 1: Implications for Practice | |
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| Your Own Practice and Work with Representations | |
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| Using Artifacts to Examine Representations in Your Classroom | |
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| Homework | |
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| Warm-Ups | |
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| Class Discussion | |
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| Diagnostic Interviews | |
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| Wrapping Up | |
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| Additional Exercises | |
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| Exercise 2: Video Games Fraction Lesson | |
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| Process for Analyzing the Video Game Fractions Lesson Video | |
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| Exercise 3: Garden Border Task: Student Methods | |
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| Process for Analyzing the Garden Border Work Samples | |
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| Putting It All Together in the Classroom | |
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| Putting It All Together | |
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| Exercises: Integrated Analysis of Whole Lessons | |
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| Exercise 1: Building Triangles Lesson | |
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| Process for Viewing and Analyzing the Building Triangles Lesson | |
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| Commentary on the Building Traiangles Lesson | |
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| Some Additional Points of Reflection | |
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| Exercise 2: Multiplication Lesson | |
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| Process for Viewing and Analyzing the Multiplication Lesson | |
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| Commentary on the Multiplication Lesson | |
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| Some Additional Points of Reflection | |
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| Linking to Your Own Practice | |
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| Final Thoughts | |
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| Appendix | |
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| Blank Worksheet (Chapter 2) | |
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| Student Work Samples | |
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| Blank Worksheets (Chapters 3-6) | |
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| Lesson Graphs (Chapter 6) | |
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| Blank Lesson Graph (Chapter 6) | |
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| References | |
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| Book Study Guide | |
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| Deciding on a Facilitator | |
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| Structuring Your Book Study Sessions | |
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| Using the Reading Reaction Sheet | |
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| Chapter Guiding Questions | |
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| Combination of Structure 1 and 2 | |
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| Guiding Questions for Each Chapter | |
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| Turning to the Evidence | |
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| Describing and Interpreting Classroom Artifacts | |
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| Seeing the Potential in Student Thinking | |
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| Keeping an Eye on Rigorous Mathematics | |
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| Choosing, Using, and Connecting Representations | |
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| Putting It All Together | |
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| Reading Reaction Sheet | |
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| Index | |