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What is included with this book?
About the Author | p. iii |
Video Clips | p. x |
Preface | p. xi |
Why Whole Class Discussions? | p. 1 |
Common Core and NCTM Standards | p. 2 |
Whole Class Discussion and Student Achievement | p. 3 |
Communication and Mathematical Learning | p. 4 |
"Math Talk" with Partners, Small Groups, and Whole Class | p. 5 |
Case Study: Problem Solving with Partners | p. 5 |
Video Clip 1.1: Student Interview: Student Perspectives on "Math Talkö and Math Learning | p. 7 |
Video Clip 1.2: Fifth & Sixth Grade Teacher Perspectives on Class Discussions | p. 8 |
Characteristics of Effective Whole Class Discussions | p. 9 |
Planning a Whole Class Discussion | p. 10 |
Planning Prior to Discussion | p. 11 |
Video Clip 1.3: Fifth & Sixth Grade Teacher Interview on Lesson Planning | p. 11 |
Planning the Discussion During the Lesson | p. 12 |
The Whole Class Discussion: Facilitating Mathematical Connections | p. 12 |
Video Clip 1.4: Fifth & Sixth Grade Problem-Solving Lesson | p. 12 |
Additional Considerations for Facilitating Effective Discussions | p. 17 |
Chapter Summary | p. 17 |
Study Guide | p. 18 |
Video Case Study | p. 19 |
Problem-Solving Using Schematic Drawings | p. 19 |
Strategies for Your Classroom | p. 20 |
How and When to Use Whole Class Discussion to Support Learning | p. 20 |
Reflecting on Video Clips | p. 21 |
Reflecting on Practice | p. 22 |
Using Whole Class Discussions | p. 22 |
Designing the Physical Classroom Space for Discussions | p. 23 |
Design Elements for Classroom Space | p. 23 |
Designing a Functional Space for Discussions | p. 25 |
Designing Space for Small Group Discussion | p. 26 |
Designing a Functional Space for Whole Class Discussions | p. 26 |
Creating a Focal Point | p. 27 |
Visualization and Representations | p. 28 |
Access to Materials for Students' Work | p. 29 |
Access to Technology | p. 29 |
Displaying and Saving Students' Work | p. 30 |
Further Suggestions for Classroom Layouts | p. 31 |
Chapter Summary | p. 32 |
Study Guide | p. 33 |
Strategies for your Classroom | p. 34 |
Considerations for Creating Physical Space | p. 34 |
Reflecting on Practice | p. 35 |
Designing Classroom Space | p. 35 |
Physical Layouts for Classroom Discussions Checklist | p. 36 |
Developing Classroom Routines for Whole Class Discussions | p. 37 |
Building a Supportive Classroom Community | p. 38 |
Establish Mutual Respect | p. 39 |
Video Clip 3.1: Student Interview: Cultivating a Classroom Community | p. 39 |
Value Students' Experiences and Home Language | p. 39 |
Use Small Groups/Partners | p. 40 |
Video Clip 3.2: Fifth & Sixth Grade Teacher Interview: Using Flexible Grouping | p. 40 |
Physical Classroom Routines to Prepare for Whole Class Discussions | p. 41 |
Strategies and Social Routines for Whole Class Discussions | p. 42 |
Routines for Communication | p. 43 |
Communicating and Listening During Whole Class Discussions | p. 44 |
Active Listening During Whole Class Discussions | p. 45 |
Using Representations to Record Thinking | p. 46 |
Create, Share, and Explain Representations | p. 46 |
Using Representations to Connect to Another Student's Method | p. 47 |
Video Clip 3.3: Second Grade Measurement Lesson and Teacher Interview | p. 47 |
Case Study 1: Examining an Unsuccessful Discussion | p. 49 |
Case Study 2: Examining a Successful Discussion | p. 52 |
Chapter Summary | p. 53 |
Study Guide | p. 55 |
Video Case Study | p. 57 |
Second Grade Measurement Lesson and Teacher Interview | p. 57 |
Video Clip 3.4: Second Grade Teacher Interview: Teaching Measurement | p. 57 |
Strategies for Your Classroom | p. 60 |
Ideas for Developing Classroom Routines | p. 60 |
Reflecting on Video Clips | p. 61 |
Reflecting on Practice | p. 62 |
Building a Supportive Classroom Community | p. 62 |
Thinking about Physical and Social Routines for Discussion | p. 63 |
Routines for Listening | p. 65 |
Student Self-Evaluation Checklist for Participation in Whole Class Discussion | p. 67 |
Whole Class Student Participation Checklist | p. 67 |
What Do We Talk About? Planning the Discussion | p. 68 |
Planning the Lesson to Optimize Learning | p. 69 |
Mathematical Goals, Concepts, and Skills | p. 70 |
What Does It Mean to Understand a Concept or "Big Idea"? | p. 71 |
Using a Concept Map to Show Connections | p. 72 |
Curriculum Tasks and Sequencing | p. 75 |
Sequencing Lessons | p. 75 |
Anticipating Student Reasoning: The 5E Lesson Plan | p. 76 |
Chapter Summary | p. 78 |
Study Guide | p. 79 |
Level 1: Identify Long-Term Goals, Short-Term Goals, and Interconnections | p. 79 |
Level 2: Plan the Individual Lesson | p. 81 |
Level 3: Examine Student Work to Build Whole Class Discussion | p. 81 |
Classroom Case Study | p. 83 |
Analyzing Student Work to Plan Discussion | p. 83 |
Student Work Sample A: Richard's Solution | p. 84 |
Student Work Sample B: Katie's Solution | p. 85 |
Student Work Sample C: Juan's Solution | p. 86 |
Student Work Sample D: Samantha's Solution | p. 87 |
Student Work Sample E: Conner's Solution | p. 88 |
An Overall Analysis of Students' Solutions | p. 89 |
Strategies for Your Classroom | p. 91 |
Three Levels of Planning | p. 91 |
Reflecting on Practice | p. 92 |
Level 1 Planning | p. 92 |
Rubric For Unit Planning: Level 1 | p. 93 |
Rubric For The 5E Lesson Plan: Level 2 | p. 94 |
Rubric For Planning the Discussion: Level 3 | p. 95 |
Teacher Questioning and Mathematical Connections | p. 96 |
Posing a Question to Start the Whole Class Discussion | p. 97 |
Using Questions to Identify Discussion Topics | p. 97 |
The Three Levels of Sense-Making in Discussion | p. 98 |
Phase 1: Making Thinking Explicit | p. 99 |
Case Study 1: Clarifying an Explanation | p. 99 |
Phase 2: Analyzing Each Other's Solutions to Make Connections | p. 101 |
Phase 3: Developing New Mathematical Insights by Making Generalizations | p. 103 |
Case Study 2: Writing a Number Sentence to Represent a Fair Sharing Problem | p. 103 |
Chapter Summary | p. 108 |
Study Guide | p. 109 |
Video Case Study | p. 110 |
Third Grade Lesson: Using Arrays to Find Area and Perimeter | p. 110 |
Sixth Grade Problem-Solving Lesson | p. 112 |
Strategies for Your Classroom | p. 116 |
The Three Levels of Sense-Making in Discussion | p. 116 |
Sequence of a Whole Class Discussion | p. 117 |
Reflecting on Video Clips | p. 118 |
Reflecting on Practice | p. 119 |
Making Mathematical Connections | p. 119 |
Strategies for Evaluating and Improving Your Discussion | p. 120 |
Improving Whole Class Discussions | p. 121 |
Making Classroom Teaching Visible to Improve Discussion | p. 121 |
Signs of Effective Whole Class Discussions | p. 123 |
Chapter Summary | p. 123 |
Study Guide Part 1 | p. 124 |
Video Case Study | p. 126 |
Second Grade Lesson on Two-Digit Addition with Regrouping | p. 126 |
Strategies for Your Classroom | p. 130 |
Refining Your Whole Class Discussion: Long-Term Strategies | p. 130 |
Refining Your Whole Class Discussion: Making Teaching Visible | p. 130 |
Reflecting on Video Clips | p. 131 |
Reflecting on Practice | p. 132 |
Next Steps after Holding a Whole Class Discussion | p. 132 |
Improving Your Discussion | p. 133 |
Whole Class Discussion Checklist: Informal Assessment of Student Understanding | p. 134 |
Student Rubric for Self-Evaluation of Whole Class Discussion | p. 135 |
Whole Class Discussion Participation Checklist | p. 136 |
Classroom Observation Rubric | p. 137 |
Math Discussion Rubric | p. 138 |
Self-Reflection Rubric for Evaluating Whole Class Discussions | p. 140 |
Reference | p. 141 |
Index | p. 144 |
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