MODERN MATHEMATICS
PART I: UNDERSTANDING HIGH-QUALITY MATH DISCOURSE FOR ALL STUDENTS CHAPTER 1: HIGH-QUALITY DISCOURSE IN MATH CLASSROOMS 2 Comparing Discourse Scenarios 2 Defining Math Discourse 6 Different Types of Math Discourse 8 High-Quality Math Discourse 12 Discuss With Colleagues 13 Connect to Your Practice 13 CHAPTER 2: ENGAGING EMERGENT MULTILINGUAL LEARNERS IN DISCOURSE 14 Knowing More About Emergent Multilingual Learners 14 Guiding Principles for Effective Math Instruction of Emergent Multilingual Learners 16 Avoiding the Deficit Language Trap 18 Using Appropriate Supports in Your Classroom 19 Promoting the Learning of Your Emergent Math Communicators 21 Discuss With Colleagues 22 Connect to Your Practice 22 CHAPTER 3: MATH KNOWLEDGE FOR FACILITATING DISCOURSE 23 Mathematics Knowledge for Teaching 23 Connecting Mathematics Knowledge for Teaching and Discourse 24 Using Mathematics Knowledge for Teaching to Select Tasks Worth Talking About 25 Attending to Your Own Mathematics Knowledge for Teaching 27 Discuss With Colleagues 29 Connect to Your Practice 30 Key Takeaways About High-Quality Math Discourse 31 PART II: ACTIVATING MATH DISCOURSE IN THE CLASSROOM CHAPTER 4: TEACHING STUDENTS TO TALK ABOUT MATH 34 Setting Norms 34 Using Instructional Moves 36 Implementing Practices for Orchestrating Discussions 39 Taking Stock 41 Considering Literacy Techniques 42 Discuss With Colleagues 43 Connect to Your Practice 43 CHAPTER 5: STRUCTURING MATH LESSONS FOR HIGH-QUALITY DISCOURSE 44 The Discuss Phase 46 The Explore Phase 47 The Launch Phase 48 The Plan Phase 50 The Reflect Phase 51 Discuss With Colleagues 52 Connect to Your Practice 52 Key Takeaways About Activating High-Quality Math Discourse 53 PART III: TALK TECHNIQUES FOR THE LAUNCH PHASE CHAPTER 6: STORY PROBLEM RETELLING 56 What Is Story Problem Retelling? 56 Why Might You Use Story Problem Retelling? 56 Getting Started With Story Problem Retelling 58 Supports That Help With Story Problem Retelling 60 Improving and Adapting Story Problem Retelling 61 Examine Practice 63 Discuss With Colleagues 66 Connect to Your Practice 67 CHAPTER 7: TASK THINK-ALOUD 68 What Is a Task Think-Aloud? 68 Why Might You Use a Task Think-Aloud? 69 Getting Started With Task Think-Alouds 72 Supports That Help With the Task Think-Aloud 72 Improving and Adapting Task Think-Alouds 74 Examine Practice 74 Discuss With Colleagues 79 Connect to Your Practice 80 CHAPTER 8: MATH BET LINES 81 What Are Math Bet Lines? 81 Why Might You Use Math Bet Lines? 82 Getting Started With Math Bet Lines 84 Supports That Help With Math Bet Lines 86 Improving and Adapting Math Bet Lines 88 Examine Practice 89 Discuss With Colleagues 93 Connect to Your Practice 93 Key Takeaways About the Launch Phase 94 PART IV: TALK TECHNIQUES FOR THE EXPLORE PHASE CHAPTER 9: THINK-PAIR-REHEARSE-SHARE 96 What Is Think-Pair-Rehearse-Share? 96 Why Might You Use Think-Pair-Rehearse-Share? 97 Getting Started With Think-Pair-Rehearse-Share 97 Supports That Help With Think-Pair-Rehearse-Share 98 Improving and Adapting Think-Pair-Rehearse-Share 100 Examine Practice 100 Discuss With Colleagues 105 Connect to Your Practice 106 CHAPTER 10: MATH FOUR SQUARE 107 What Is Math Four Square? 107 Why Might You Use Math Four Square? 108 Getting Started With Math Four Square 110 Supports That Help With Math Four Square 111 Improving and Adapting Math Four Square 112 Examine Practice 113 Discuss With Colleagues 118 Connect to Your Practice 118 CHAPTER 11: TALK TRIANGLE 119 What Is Talk Triangle? 119 Why Might You Use Talk Triangle? 120 Getting Started With Talk Triangle 121 Supports That Help With Talk Triangle 123 Improving and Adapting Talk Triangle 124 Examine Practice 126 Discuss With Colleagues 130 Connect to Your Practice 130 CHAPTER 12: SOLUTION DRAFT AND FINAL COPY 131 What Is Solution Draft and Final Copy? 131 Why Might You Use Solution Draft and Final Copy? 132 Getting Started With Solution Draft and Final Copy 133 Supports That Help With Solution Draft and Final Copy 134 Improving and Adapting Solution Draft and Final Copy 136 Examine Practice 137 Discuss With Colleagues 142 Connect to Your Practice 142 Key Takeaways About the Explore Phase 143 PART V: TALK TECHNIQUES FOR THE DISCUSS PHASE CHAPTER 13: MATH TALK CHAIN 146 What Is Math Talk Chain? 146 Why Might You Use Math Talk Chain? 147 Getting Started With Math Talk Chain 147 Supports That Help With Math Talk Chain 150 Improving and Adapting Math Talk Chain 152 Examine Practice 153 Discuss With Colleagues 159 Connect to Your Practice 160 CHAPTER 14: ALL TALK MATH 161 What Is All Talk Math? 161 Why Might You Use All Talk Math? 162 Getting Started With All Talk Math 162 Supports That Help With All Talk Math 163 Improving and Adapting All Talk Math 165 Examine Practice 165 Discuss With Colleagues 171 Connect to Your Practice 172 CHAPTER 15: PROBING AND PRESSING MATH QUESTIONS 173 What Are Probing and Pressing Math Questions? 173 Why Might You Use Probing and Pressing Math Questions? 174 Getting Started With Probing and Pressing Math Questions 174 Supports That Help With Probing and Pressing Math Questions 176 Improving and Adapting Probing and Pressing Math Questions 178 Examine Practice 179 Discuss With Colleagues 184 Connect to Your Practice 184 CHAPTER 16: MATH LEARNING SUMMARY 185 What Is Math Learning Summary? 185 Why Might You Use Math Learning Summary? 186 Getting Started With Math Learning Summary 187 Supports That Help With Math Learning Summary 188 Improving and Adapting Math Learning Summary 190 Examine Practice 192 Discuss With Colleagues 196 Connect to Your Practice 197 Key Takeaways About the Discuss Phase 198 PART VI: PUTTING IT ALL TOGETHER CHAPTER 17: PLANNING AND REFLECTING TO PROMOTE HIGH-QUALITY DISCOURSE 200 The Key Is in the Planning 200 Reflecting to Grow and Improve Your Discourse Practice 203 Discuss With Colleagues 204 Connect to Your Practice 204 Key Takeaways About Putting It All Together 205 Continuing the Journey Toward High-Quality Discourse 206 References 207