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Table of Contents

About the Authors

Introduction

The Importance of Making Sense of Mathematics for Teaching

About This Book

PART 1: Connecting to the T in TQE: Tasks and Task Implementation

CHAPTER 1

Potential of the Task

Introductory Activities

Activity 1.1: Solving a Task

Activity 1.2: Considering Different Types of Tasks

The IQA Potential of the Task Rubric

Application Activities

Activity 1.3: Rating Mathematical Tasks Using the Potential of the Task Rubric

Activity 1.4: Using the IQA Potential of the Task Rubric to Rate and Adapt Tasks

Considerations When Rating Tasks

Defining the Task

Considering Implications of Higher-Level Thinking

Aligning With Learning Goals

Summary

CHAPTER 2

Implementation of the Task

Introductory Activities

Activity 2.1: Comparing Two Mathematics Lessons

The IQA Implementation of the Task Rubric

Application Activities

Activity 2.2: Using the Implementation of the Task Rubric

Activity 2.3: Identifying Evidence of Students’ Thinking and Reasoning in Students’ Work

Activity 2.4: Revisiting the Chapter 1 Transition Activity—Moving From Tasks to Implementation

Considerations for Implementation Based on Classroom Observations or Videos

Activity 2.5: Rating Implementation of the Task—Father and Son Race Lesson Version 1

Activity 2.6: Rating Implementation of the Task—Father and Son Race Lesson Version 2

Summary

PART 2: Connecting to the Q in TQE: Questions and Their Role as Discourse Actions

CHAPTER 3

Teacher’s Questions

Introductory Activities

Activity 3.1: Identifying Different Types of Questions

Activity 3.2: Sorting Questions

Activity 3.3: Creating Questions

Activity 3.4: Revisiting the Chapter 2 Transition Activity—How Teacher’s Questions Impact Implementation

The IQA Teacher’s Questions Rubric

Application Activities

Activity 3.5: Rating the Teacher’s Questions in the 26 Divided by 4 Lesson

Summary

CHAPTER 4

Teacher’s Linking and Teacher’s Press

Introductory Activities

Activity 4.1: Following Up on Students’ Contributions—Teacher’s Linking

Activity 4.2: Following Up on Students’ Contributions—Teacher’s Press

Activity 4.3: Revisiting the Chapter 3 Transition Activity—Teacher’s Questions and Follow-Up

The IQA Teacher’s Linking and Teacher’s Press Rubrics

Application Activities

Activity 4.4: Rating Teacher’s Linking and Teacher’s Press

Activity 4.5: Determining When It Is Appropriate to Ask a Follow-Up Question

Summary

PART 3: Connecting to the E in TQE: Evidence of Students’ Mathematical Work and Thinking

CHAPTER 5

Students’ Linking and Students’ Providing

Introductory Activities

Activity 5.1: Examining Students’ Contributions—Students’ Linking

Activity 5.2: Examining Students’ Contributions—Students’ Providing

Activity 5.3: Revisiting the Chapter 4 Transition Activity—Teacher’s Linking, Teacher’s Press, and Students’ Contributions

The IQA Students’ Linking and Students’ Providing Rubrics

Application Activities

Activity 5.4: Rating Students’ Linking and Students’ Providing

Summary

CHAPTER 6

The IQA Toolkit as a Tool to Assess and Improve Instructional Practice

Introductory Activities

Activity 6.1: Rating a Small-Group Lesson

Activity 6.2: Rating a Whole-Class Lesson

The IQA Rubrics as Tools to Reflect on and Improve Instruction

Application Activities

Activity 6.3: Considering the Teacher’s Reflection and Next Steps

Activity 6.4: Revisiting the Chapter 5 Transition Activity—Using All IQA Rubrics

Summary

EPILOGUE

Next Steps

APPENDIX A

The IQA Toolkit

IQA Potential of the Task Rubric

IQA Implementation of the Task Rubric

IQA Teacher’s Questions Rubric

IQA Teacher’s Linking Rubric

IQA Teacher’s Press Rubric

IQA Students’ Linking Rubric

IQA Students’ Providing Rubric

IQA Implementation Observation Tool

Framework for Different Types of Questions

APPENDIX B

Suggested Answers for Activity 1.4

APPENDIX C

Suggested Answers for Activity 3.2

APPENDIX D

Additional Support for Rating Tasks

Level 1

Level 2

Level 3

Level 4

APPENDIX E

List of Figures and Videos

References and Resources

Index