The Five Practices in Practice [Elementary]

Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom
Margaret (Peg) Smith - University of Pittsburgh, USA
Victoria L. Bill - University of Pittsburgh (United States)
Miriam Gamoran Sherin - Northwestern University, USA
The Five Practices in Practice [Elementary]
August 2019 | 240 pages | Corwin
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ISBN: 9781544321165
Available from January 0001
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ISBN: 9781544321134
Available from January 0001

Description

"Neither a love of students nor a love of mathematics can sustain the work of math education on its own. We work with math students, a composite of their mathematical ideas and their identities as people. The five practices for orchestrating productive mathematical discussions, and these ideas for putting those practices into practice, offer the actions that can develop and sustain the belief that both math and students matter.” 
From the Foreword by Dan Meyer, Chief Academic Officer, Desmos 

Take a deeper dive into understanding the five practices—anticipating, monitoring, selecting, sequencing, and connecting—for facilitating productive mathematical conversations in your elementary classrooms and learn to apply them with confidence. This follow-up to the modern classic, Five Practices for Orchestrating Productive Mathematics Discussions, shows the five practices in action in Grades K-5 classrooms and empowers teachers to be prepared for and overcome the challenges common to orchestrating math discussions.

The chapters unpack the five practices and guide teachers to a deeper understanding of how to use each practice effectively in an inquiry-oriented classroom. This book will help you launch meaningful mathematical discussion through 

• Key questions to set learning goals, identify high-level tasks, anticipate student responses, and develop targeted assessing and advancing questions that jumpstart productive discussion—before class begins  • Video excerpts from real elementary classrooms that vividly illustrate the five practices in action and include built-in opportunities for you to consider effective ways to monitor students’ ideas, and successful approaches for selecting, sequencing, and connecting students’ ideas during instruction 
“Pause and Consider” prompts that help you reflect on an issue—and, in some cases, draw on your own classroom                   experience—prior to reading more about it
• “Linking To Your Own Instruction” sections help you implement the five practices with confidence in your own instruction
The book and companion website provide an array of resources including planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks. Enhance your fluency in the five practices to bring powerful discussions of mathematical concepts to life in your classroom.

Contents

List of Video Clips

List of Video Clips

Foreword by Dan Meyer

Foreword by Dan Meyer

Preface

Preface

Chapter 1: Introduction

  • The Five Practices in Practice: An Overview
  • Purpose and Content
  • Classroom Video Context
  • Meet the Teachers
  • Using This Book
  • Norms for Video Viewing
  • Getting Started!

Chapter 2: Setting Goals and Selecting Tasks

  • Part One: Unpacking the Practice: Setting Goals and Selecting Tasks
  • Specifying the Learning Goal
  • Identifying a High-Level Task That Aligns With the Goal
  • Tara Tyus’ Attention to Key Questions: Setting Goals and Selecting Tasks
  • Part Two: Challenges Teachers Face: Setting Goals and Selecting Tasks
  • Identifying Learning Goals
  • Identifying a Doing-Mathematics Task
  • Adapting an Existing Task
  • Finding a Task in Another Resource
  • Creating a Task
  • Ensuring Alignment Between Task and Goals
  • Launching a Task to Ensure Student Access
  • Launching a Task—Analysis
  • Conclusion

Chapter 3: Anticipating Student Responses

  • Part One: Unpacking the Practice: Anticipating Student Responses
  • Getting Inside the Problem
  • Getting Inside a Problem—Analysis
  • Planning to Respond to Student Thinking
  • Planning to Notice Student Thinking
  • Tara Tyus’ Attention to Key Questions: Anticipating
  • Part Two: Challenges Teachers Face: Anticipating Student Responses
  • Moving Beyond the Way YOU Solved the Problem
  • Being Prepared to Help Students Who Cannot Get Started
  • Creating Questions That Move Students Toward the Mathematical Goal
  • Conclusion

Chapter 4: Monitoring Student Work

  • Part One: Unpacking the Practice: Monitoring Student Work
  • Tracking Student Thinking
  • Assessing Student Thinking
  • Exploring Student Problem-Solving Approaches—Analysis
  • Assessing Student Thinking—Analysis
  • Advancing Student Thinking
  • Advancing Student Thinking, Part One—Analysis
  • Advancing Student Thinking, Part Two—Analysis
  • Tara Tyus’ Attention to Key Questions: Monitoring
  • Part Two: Challenges Teachers Face: Monitoring Student Work
  • Trying to Understand What Students Are Thinking
  • Determining What Students Are Thinking, Part One—Analysis
  • Determining What Students Are Thinking, Part Two—Analysis
  • Keeping Track of Group Progress
  • Following Up With Students—Analysis
  • Involving All Members of a Group
  • Holding All Students Accountable—Analysis
  • Conclusion

Chapter 5: Selecting and Sequencing Student Solutions

  • Part One: Unpacking the Practice: Selecting and Sequencing Student Solutions
  • Identifying Student Work to Highlight
  • Selecting Student Solutions—Analysis
  • Purposefully Selecting Individual Presenters
  • Establishing a Coherent Storyline
  • Ms. Tyus’ Attention to Key Questions: Selecting and Sequencing
  • Part Two: Challenges Teacher Face: Selecting and Sequencing Student Solutions
  • Selecting Only Solutions Relevant to Learning Goals
  • Selecting Solutions That Highlight Key Ideas—Analysis
  • Expanding Beyond the Usual Presenters
  • Deciding What Work to Share When the Majority of Students Were Not Able to Solve the Task and Your Initial Goal No Longer Seems Obtainable
  • Moving Forward When a Key Strategy Is Not Produced by Students
  • Determining How to Sequence Errors, Misconceptions, and/or Incomplete Solutions
  • Conclusion

Chapter 6: Connecting Student Solutions

  • Part One: Unpacking the Practice: Connecting Student Solutions
  • Connecting Student Work to the Goals of the Lesson
  • Connecting Student Work to the Goals of Lesson Part One—Analysis
  • Connecting Student Work to the Goals of Lesson Part Two—Analysis
  • Connecting Student Work to the Goals of Lesson Part Three—Analysis
  • Connecting Different Solutions to Each Other
  • Connecting Different Solutions to Each Other—Analysis
  • Ms. Tyus’ Attention to Key Questions: Connecting
  • Part Two: Challenges Teachers Face: Connecting Student Responses
  • Keeping the Entire Class Engaged and Accountable During Individual Presentations
  • Holding Students Accountable—Analysis
  • Ensuring That Key Mathematical Ideas are Made Public and Remain the Focus
  • Making Key Ideas Public—Analysis
  • Making Sure That You Do Not Take Over the Discussion and Do The Explaining
  • Running Out of Time
  • Running Out of Time—Analysis
  • Conclusion

Chapter 7: Looking Back and Looking Ahead

  • Why Use the Five Practices Model
  • Getting Started with the Five Practices
  • Plan Lessons Collaboratively
  • Observe and Debrief Lessons
  • Reflect on Your Lesson
  • Video Clubs
  • Organize a Book Study
  • Explore Additional Resources
  • Frequency and Timing of Use of the Five Practices Model
  • Conclusion

Resources

  • Appendix A—Web-based Resources for Tasks and Lesson Plans
  • Appendix B—Monitoring Chart
  • Appendix C—Ms. Tyus’ Monitoring Chart
  • Appendix D—Resources for Holding Students Accountable
  • Appendix E—Lesson-Planning Template

Description

"Neither a love of students nor a love of mathematics can sustain the work of math education on its own. We work with math students, a composite of their mathematical ideas and their identities as people. The five practices for orchestrating productive mathematical discussions, and these ideas for putting those practices into practice, offer the actions that can develop and sustain the belief that both math and students matter.” 
From the Foreword by Dan Meyer, Chief Academic Officer, Desmos 

Take a deeper dive into understanding the five practices—anticipating, monitoring, selecting, sequencing, and connecting—for facilitating productive mathematical conversations in your elementary classrooms and learn to apply them with confidence. This follow-up to the modern classic, Five Practices for Orchestrating Productive Mathematics Discussions, shows the five practices in action in Grades K-5 classrooms and empowers teachers to be prepared for and overcome the challenges common to orchestrating math discussions.

The chapters unpack the five practices and guide teachers to a deeper understanding of how to use each practice effectively in an inquiry-oriented classroom. This book will help you launch meaningful mathematical discussion through 

• Key questions to set learning goals, identify high-level tasks, anticipate student responses, and develop targeted assessing and advancing questions that jumpstart productive discussion—before class begins  • Video excerpts from real elementary classrooms that vividly illustrate the five practices in action and include built-in opportunities for you to consider effective ways to monitor students’ ideas, and successful approaches for selecting, sequencing, and connecting students’ ideas during instruction 
“Pause and Consider” prompts that help you reflect on an issue—and, in some cases, draw on your own classroom                   experience—prior to reading more about it
• “Linking To Your Own Instruction” sections help you implement the five practices with confidence in your own instruction
The book and companion website provide an array of resources including planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks. Enhance your fluency in the five practices to bring powerful discussions of mathematical concepts to life in your classroom.

Contents

List of Video Clips

List of Video Clips

Foreword by Dan Meyer

Foreword by Dan Meyer

Preface

Preface

Chapter 1: Introduction

  • The Five Practices in Practice: An Overview
  • Purpose and Content
  • Classroom Video Context
  • Meet the Teachers
  • Using This Book
  • Norms for Video Viewing
  • Getting Started!

Chapter 2: Setting Goals and Selecting Tasks

  • Part One: Unpacking the Practice: Setting Goals and Selecting Tasks
  • Specifying the Learning Goal
  • Identifying a High-Level Task That Aligns With the Goal
  • Tara Tyus’ Attention to Key Questions: Setting Goals and Selecting Tasks
  • Part Two: Challenges Teachers Face: Setting Goals and Selecting Tasks
  • Identifying Learning Goals
  • Identifying a Doing-Mathematics Task
  • Adapting an Existing Task
  • Finding a Task in Another Resource
  • Creating a Task
  • Ensuring Alignment Between Task and Goals
  • Launching a Task to Ensure Student Access
  • Launching a Task—Analysis
  • Conclusion

Chapter 3: Anticipating Student Responses

  • Part One: Unpacking the Practice: Anticipating Student Responses
  • Getting Inside the Problem
  • Getting Inside a Problem—Analysis
  • Planning to Respond to Student Thinking
  • Planning to Notice Student Thinking
  • Tara Tyus’ Attention to Key Questions: Anticipating
  • Part Two: Challenges Teachers Face: Anticipating Student Responses
  • Moving Beyond the Way YOU Solved the Problem
  • Being Prepared to Help Students Who Cannot Get Started
  • Creating Questions That Move Students Toward the Mathematical Goal
  • Conclusion

Chapter 4: Monitoring Student Work

  • Part One: Unpacking the Practice: Monitoring Student Work
  • Tracking Student Thinking
  • Assessing Student Thinking
  • Exploring Student Problem-Solving Approaches—Analysis
  • Assessing Student Thinking—Analysis
  • Advancing Student Thinking
  • Advancing Student Thinking, Part One—Analysis
  • Advancing Student Thinking, Part Two—Analysis
  • Tara Tyus’ Attention to Key Questions: Monitoring
  • Part Two: Challenges Teachers Face: Monitoring Student Work
  • Trying to Understand What Students Are Thinking
  • Determining What Students Are Thinking, Part One—Analysis
  • Determining What Students Are Thinking, Part Two—Analysis
  • Keeping Track of Group Progress
  • Following Up With Students—Analysis
  • Involving All Members of a Group
  • Holding All Students Accountable—Analysis
  • Conclusion

Chapter 5: Selecting and Sequencing Student Solutions

  • Part One: Unpacking the Practice: Selecting and Sequencing Student Solutions
  • Identifying Student Work to Highlight
  • Selecting Student Solutions—Analysis
  • Purposefully Selecting Individual Presenters
  • Establishing a Coherent Storyline
  • Ms. Tyus’ Attention to Key Questions: Selecting and Sequencing
  • Part Two: Challenges Teacher Face: Selecting and Sequencing Student Solutions
  • Selecting Only Solutions Relevant to Learning Goals
  • Selecting Solutions That Highlight Key Ideas—Analysis
  • Expanding Beyond the Usual Presenters
  • Deciding What Work to Share When the Majority of Students Were Not Able to Solve the Task and Your Initial Goal No Longer Seems Obtainable
  • Moving Forward When a Key Strategy Is Not Produced by Students
  • Determining How to Sequence Errors, Misconceptions, and/or Incomplete Solutions
  • Conclusion

Chapter 6: Connecting Student Solutions

  • Part One: Unpacking the Practice: Connecting Student Solutions
  • Connecting Student Work to the Goals of the Lesson
  • Connecting Student Work to the Goals of Lesson Part One—Analysis
  • Connecting Student Work to the Goals of Lesson Part Two—Analysis
  • Connecting Student Work to the Goals of Lesson Part Three—Analysis
  • Connecting Different Solutions to Each Other
  • Connecting Different Solutions to Each Other—Analysis
  • Ms. Tyus’ Attention to Key Questions: Connecting
  • Part Two: Challenges Teachers Face: Connecting Student Responses
  • Keeping the Entire Class Engaged and Accountable During Individual Presentations
  • Holding Students Accountable—Analysis
  • Ensuring That Key Mathematical Ideas are Made Public and Remain the Focus
  • Making Key Ideas Public—Analysis
  • Making Sure That You Do Not Take Over the Discussion and Do The Explaining
  • Running Out of Time
  • Running Out of Time—Analysis
  • Conclusion

Chapter 7: Looking Back and Looking Ahead

  • Why Use the Five Practices Model
  • Getting Started with the Five Practices
  • Plan Lessons Collaboratively
  • Observe and Debrief Lessons
  • Reflect on Your Lesson
  • Video Clubs
  • Organize a Book Study
  • Explore Additional Resources
  • Frequency and Timing of Use of the Five Practices Model
  • Conclusion

Resources

  • Appendix A—Web-based Resources for Tasks and Lesson Plans
  • Appendix B—Monitoring Chart
  • Appendix C—Ms. Tyus’ Monitoring Chart
  • Appendix D—Resources for Holding Students Accountable
  • Appendix E—Lesson-Planning Template
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The Five Practices in Practice [Elementary]

Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom


August 2019 | 240 pages | Corwin

Format Published Date ISBN Price
Paperback 01/01/2025 9781544321134 $39.95
Lifetime 01/01/2025 9781544321165 $36.00

"Neither a love of students nor a love of mathematics can sustain the work of math education on its own. We work with math students, a composite of their mathematical ideas and their identities as people. The five practices for orchestrating productive mathematical discussions, and these ideas for putting those practices into practice, offer the actions that can develop and sustain the belief that both math and students matter.” 
From the Foreword by Dan Meyer, Chief Academic Officer, Desmos 

Take a deeper dive into understanding the five practices—anticipating, monitoring, selecting, sequencing, and connecting—for facilitating productive mathematical conversations in your elementary classrooms and learn to apply them with confidence. This follow-up to the modern classic, Five Practices for Orchestrating Productive Mathematics Discussions, shows the five practices in action in Grades K-5 classrooms and empowers teachers to be prepared for and overcome the challenges common to orchestrating math discussions.

The chapters unpack the five practices and guide teachers to a deeper understanding of how to use each practice effectively in an inquiry-oriented classroom. This book will help you launch meaningful mathematical discussion through 

• Key questions to set learning goals, identify high-level tasks, anticipate student responses, and develop targeted assessing and advancing questions that jumpstart productive discussion—before class begins  • Video excerpts from real elementary classrooms that vividly illustrate the five practices in action and include built-in opportunities for you to consider effective ways to monitor students’ ideas, and successful approaches for selecting, sequencing, and connecting students’ ideas during instruction 
“Pause and Consider” prompts that help you reflect on an issue—and, in some cases, draw on your own classroom                   experience—prior to reading more about it
• “Linking To Your Own Instruction” sections help you implement the five practices with confidence in your own instruction
The book and companion website provide an array of resources including planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks. Enhance your fluency in the five practices to bring powerful discussions of mathematical concepts to life in your classroom.


Table Of Contents:

  • List of Video Clips
  • Foreword by Dan Meyer
  • Preface
  • Chapter 1: Introduction
  • The Five Practices in Practice: An Overview
  • Purpose and Content
  • Classroom Video Context
  • Meet the Teachers
  • Using This Book
  • Norms for Video Viewing
  • Getting Started!
  • Chapter 2: Setting Goals and Selecting Tasks
  • Part One: Unpacking the Practice: Setting Goals and Selecting Tasks
  • Specifying the Learning Goal
  • Identifying a High-Level Task That Aligns With the Goal
  • Tara Tyus’ Attention to Key Questions: Setting Goals and Selecting Tasks
  • Part Two: Challenges Teachers Face: Setting Goals and Selecting Tasks
  • Identifying Learning Goals
  • Identifying a Doing-Mathematics Task
  • Adapting an Existing Task
  • Finding a Task in Another Resource
  • Creating a Task
  • Ensuring Alignment Between Task and Goals
  • Launching a Task to Ensure Student Access
  • Launching a Task—Analysis
  • Conclusion
  • Chapter 3: Anticipating Student Responses
  • Part One: Unpacking the Practice: Anticipating Student Responses
  • Getting Inside the Problem
  • Getting Inside a Problem—Analysis
  • Planning to Respond to Student Thinking
  • Planning to Notice Student Thinking
  • Tara Tyus’ Attention to Key Questions: Anticipating
  • Part Two: Challenges Teachers Face: Anticipating Student Responses
  • Moving Beyond the Way YOU Solved the Problem
  • Being Prepared to Help Students Who Cannot Get Started
  • Creating Questions That Move Students Toward the Mathematical Goal
  • Conclusion
  • Chapter 4: Monitoring Student Work
  • Part One: Unpacking the Practice: Monitoring Student Work
  • Tracking Student Thinking
  • Assessing Student Thinking
  • Exploring Student Problem-Solving Approaches—Analysis
  • Assessing Student Thinking—Analysis
  • Advancing Student Thinking
  • Advancing Student Thinking, Part One—Analysis
  • Advancing Student Thinking, Part Two—Analysis
  • Tara Tyus’ Attention to Key Questions: Monitoring
  • Part Two: Challenges Teachers Face: Monitoring Student Work
  • Trying to Understand What Students Are Thinking
  • Determining What Students Are Thinking, Part One—Analysis
  • Determining What Students Are Thinking, Part Two—Analysis
  • Keeping Track of Group Progress
  • Following Up With Students—Analysis
  • Involving All Members of a Group
  • Holding All Students Accountable—Analysis
  • Conclusion
  • Chapter 5: Selecting and Sequencing Student Solutions
  • Part One: Unpacking the Practice: Selecting and Sequencing Student Solutions
  • Identifying Student Work to Highlight
  • Selecting Student Solutions—Analysis
  • Purposefully Selecting Individual Presenters
  • Establishing a Coherent Storyline
  • Ms. Tyus’ Attention to Key Questions: Selecting and Sequencing
  • Part Two: Challenges Teacher Face: Selecting and Sequencing Student Solutions
  • Selecting Only Solutions Relevant to Learning Goals
  • Selecting Solutions That Highlight Key Ideas—Analysis
  • Expanding Beyond the Usual Presenters
  • Deciding What Work to Share When the Majority of Students Were Not Able to Solve the Task and Your Initial Goal No Longer Seems Obtainable
  • Moving Forward When a Key Strategy Is Not Produced by Students
  • Determining How to Sequence Errors, Misconceptions, and/or Incomplete Solutions
  • Conclusion
  • Chapter 6: Connecting Student Solutions
  • Part One: Unpacking the Practice: Connecting Student Solutions
  • Connecting Student Work to the Goals of the Lesson
  • Connecting Student Work to the Goals of Lesson Part One—Analysis
  • Connecting Student Work to the Goals of Lesson Part Two—Analysis
  • Connecting Student Work to the Goals of Lesson Part Three—Analysis
  • Connecting Different Solutions to Each Other
  • Connecting Different Solutions to Each Other—Analysis
  • Ms. Tyus’ Attention to Key Questions: Connecting
  • Part Two: Challenges Teachers Face: Connecting Student Responses
  • Keeping the Entire Class Engaged and Accountable During Individual Presentations
  • Holding Students Accountable—Analysis
  • Ensuring That Key Mathematical Ideas are Made Public and Remain the Focus
  • Making Key Ideas Public—Analysis
  • Making Sure That You Do Not Take Over the Discussion and Do The Explaining
  • Running Out of Time
  • Running Out of Time—Analysis
  • Conclusion
  • Chapter 7: Looking Back and Looking Ahead
  • Why Use the Five Practices Model
  • Getting Started with the Five Practices
  • Plan Lessons Collaboratively
  • Observe and Debrief Lessons
  • Reflect on Your Lesson
  • Video Clubs
  • Organize a Book Study
  • Explore Additional Resources
  • Frequency and Timing of Use of the Five Practices Model
  • Conclusion
  • Resources
  • Appendix A—Web-based Resources for Tasks and Lesson Plans
  • Appendix B—Monitoring Chart
  • Appendix C—Ms. Tyus’ Monitoring Chart
  • Appendix D—Resources for Holding Students Accountable
  • Appendix E—Lesson-Planning Template

Recent Product Reviews:

I love the videos that go along with each chapter of this book. I find this to be an approachable version of larger math texts that (hopefully) my students will keep for their personal library.
Deborah Secord, Teacher Education Dept, Dickinson State University
The book aligned with the course expectations and will facilitate productive conversations.
Dr Alesia Mickle Moldavan, Curriculum and Teaching, Fordham University-Lincoln Ctr
“This book is so incredibly practical and grounded in the hands-on implementation of the five practices! It takes the ideas of the earlier book, which focused more on the “what” of each practice, and looks closer at the when, why, and how that is so important for teachers in their planning. In each chapter, I found myself nodding in agreement as the authors described challenges in using the five practices and thoroughly enjoyed the opportunities to reflect on the practices in relation to my own planning and teaching.”
Kristin Gray, Illustrative Mathematics
“This is a powerful and readable guide to shifting our elementary school mathematics instruction toward maximizing our students’ learning. But it’s the clarity and familiarity of the challenges we all face when trying to implement these five practices—and the practicality and detail of the guidance provided in each chapter to address these challenges—that set this book apart and make it so useful for professional growth.”
Steve Leinwand, American Institutes for Research, Washington, DC
“This book is packed with practical guidance, support, and actual footage of what it looks like to enact ambitious teaching through these practices. If there’s a teacher or leader out there wondering how to ensure their classroom embraces ambitious teaching that is empowering and equitable, this is your guide. Read it. Practice it. Make it yours. There just isn’t anything else out there pushing us to think and act as strategically in our math classrooms like this does.”
Levi J. Patrick, Oklahoma State Department of Education

Recommendations