List of Figures

• Preface
  • Figure P.1 The Barometer for the Influence of Teaching Test-Taking 6
  • Figure P.2 The Barometer for the Influence of Classroom Discussion 7
  • Figure P.3 Promises to Students 12
• Chapter 1. Make Learning Visible in Mathematics
  • Figure 1.1 The Barometer for the Influence of Volunteer Tutors 22
  • Figure 1.2 Comparing Direct and Dialogic Instruction 25
  • Figure 1.3 The SOLO Model Applied to Mathematics 28
  • Figure 1.4 The Relationship Between Surface, Deep, and Transfer Learning in Mathematics 34
• Chapter 2. Making Learning Visible Starts With Teacher Clarity
  • Figure 2.1 Improving Learning Intentions 47
  • Figure 2.2 Examples of Tier 2 and Tier 3 Words in Mathematics 50
  • Figure 2.3 Listening With Intention Poster 55
  • Figure 2.4 Sample “I Can . . .” Statements 60
  • Figure 2.5 Self-Reflection Rubric for Mathematics Group Collaborative Assessments 63
  • Figure 2.6 Rubric for Rich Mathematical Task 65
• Chapter 3. Mathematical Tasks and Talk That Guide Learning
  • Figure 3.1 Difficulty and Complexity 77
  • Figure 3.2 Characteristics of Mathematical Tasks at Four Levels of Cognitive Demand 81
  • Figure 3.3 Examples of Tasks at Each of the Four Levels of Cognitive Demand 84
  • Figure 3.4 Funneling and Focusing Questions in Mathematics 92
  • Figure 3.5 Types of Prompts for Mathematics 95
  • Figure 3.6 Types of Cues for Mathematics 96
• Chapter 4. Surface Mathematics Learning Made Visible
  • Figure 4.1 In the Doghouse 101
  • Figure 4.2 Exit Ticket From In the Doghouse Activity 102
  • Figure 4.3 Surface Learning of Multiplication in the SOLO Framework 106
  • Figure 4.4 Shapes With Four Sides 110
  • Figure 4.5 Comparing Attributes of Four-Sided Shapes 111
  • Figure 4.6 Sample Prompts to Use When Self-Questioning 114
  • Figure 4.7 Sentence Frames That Can Build Metacognitive Thinking 121
  • Figure 4.8 Decision Making for Language Support 124
  • Figure 4.9 Horacio’s Word Card 126
  • Figure 4.10 Manipulatives on a Place Value Mat 127
• Chapter 5. Deep Mathematics Learning Made Visible
  • Figure 5.1 A Table for Student Recording on the Box Problem 135
  • Figure 5.2 Representing 4 × 30 138
  • Figure 5.3 Mobile Data Plans 139
  • Figure 5.4 Graphic Representation of Cell Phone Plans 140
  • Figure 5.5 Exercises Versus Rich Tasks 143
  • Figure 5.6 Accountable Talk Moves 145
  • Figure 5.7 Sample Language Frames for Mathematics 147
  • Figure 5.8 Conversational Moves of a Skilled Mathematics Teacher 152
  • Figure 5.9 The Alternate Ranking Method for Grouping 156
  • Figure 5.10 Contribution Checklist 160
  • Figure 5.11 Conversation Roundtable 164
  • Figure 5.12 Important Connections Among Mathematical Representations 169
• Chapter 6. Making Mathematics Learning Visible Through Transfer Learning
  • Figure 6.1 Hugging and Bridging Methods for Low-Road and High-Road Transfer 180
  • Figure 6.2 Pre-Lesson Questions for Self-Verbalization and Self-Questioning 186
  • Figure 6.3 Prompts for Facilitating Students’ Self-Reflection and Metacognitive Awareness 188
• Chapter 7. Assessment, Feedback, and Meeting the Needs of All Learners
  • Figure 7.1 Example Exit Ticket 199
  • Figure 7.2 Additional Strategies to Check for Understanding 202
  • Figure 7.3 Feedback Strategies 204
  • Figure 7.4 Addition and Subtraction Situations 221
  • Figure 7.5 Multiplication and Division Situations 222
  • Figure 7.6 The Relationship Between Visible Teaching and Visible Learning 232
  • Figure 7.7 Mind Frames for Teachers 233