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

About the Author

Margaret (Peg) Smith is a Professor Emerita at University of Pittsburgh. Over the past three decades she has been developing research-based materials for use in the professional development of mathematics teachers. She has coauthored several books including Five Practices for Orchestrating Productive Discussions (with Mary Kay Stein), the middle and high school versions of the Taking Action series (with Melissa Boston, Fredrick Dillon, Stephen Miller, and Lynn Raith), and The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussion in Your Classroom series (with Victoria Bill, Miriam Gameron Sherin, and Michael Steele). In 2006 she received the Chancellor’s Distinguished Teaching Award given annually to honor outstanding faculty at the University of Pittsburgh. In 2009 she received the award for Excellence in Teaching in Mathematics Teacher Education from AMTE. In April 2019 she received the Lifetime Achievement Award from NCTM.

Victoria Bill is a former elementary and middle school mathematics teacher. She is currently a Fellow and lead of the mathematics team with the Institute for Learning at the Learning Research and Development Center, University of Pittsburgh.  She has been designing and facilitating professional development with administrators, coaches and teachers in urban districts for more than 20 years. She also develops curriculum, intervention materials and performance-based assessments. Bill was the Co-Pi on a collaborative research project between researchers from the LRDC, the IFL, and the Tennessee Department of Education in which an instructional Mathematics Coaching Model was developed. Bill regularly speaks at the National Council of Teachers of Mathematics, National Supervisors of Mathematics, and National Council of Teachers of Mathematics Research Conferences. She is co-author of the NCTM best seller Taking Action: Implementing Effective Mathematics Teaching Practices Grades k-5.  

Reviews

"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*

"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*

"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*

"Peg Smith has done it again. Building on her previous work with Mary Kay Stein (2018), Smith and coauthors Miriam Sherin and Victoria Bill have taken the next step in supporting teachers to engage students in rich mathematics discussions. Filled with examples and insights, both in print and on video, this book allows teachers to ‘see it in action,’ make sense, and reflect on the challenges, and it provides support and guidance to implement the five practices in their own instruction. Perfect for teachers, teacher leaders, coaches, or others who support teachers in their instructional practices, this book literally connects theory to practice and provides honest and thoughtful reflections and guidance to work towards our ultimate goals—students’ mathematics learning and agency."
*Cynthia H. Callard*

"Every elementary school math teacher needs to understand the practices in this book and know how to use them effectively in the classroom. Use of these practices will empower elementary school students to understand mathematics and feel like they can do math!"
*Lois A. Williams*

"This book is a comprehensive, ready-to-use, professional development plan inside a book’s covers! Its components include student work, classroom video, features addressing challenges teachers face, as well as providing reflective opportunities to pause and consider. This amazing, must-have resource will truly engage elementary school mathematics teachers in ‘doing’ The 5 Practices."
*Francis (Skip) Fennell*

"This book takes 5 Practices for Orchestrating Productive Mathematics Discussions to the next level as readers experience what these practices look like in real mathematics classrooms in Grades K–5. Readers will engage in analysis of videos and student work as they deepen their understanding of the five practices. The authors specifically address the challenges one might face in implementing the five practices in classrooms by providing recommendations and concrete examples to avoid these challenges."
*Cathy Martin*

"As an elementary math teacher, nothing has helped me become more intentional and purposeful than the 5 Practices. In a continued effort to move student thinking forward, I really appreciated how the authors walked us through specific K−5 examples because this will definitely help me improve my craft."
*Ruth M. Heaton*

"At Illustrative Mathematics we were looking for a framework that would enable us to embed in our curriculum ambitious but achievable goals for teacher practice. The five practices was the perfect fit: a memorable, learnable set of principles that could be used by novice and veteran teachers alike to get their students thinking and sharing their reasoning."
*Bill McCallum*

"Mathematical discourse is the heart of effective instruction, but is challenging to implement well. Finally, this book provides a step-by-step guide for bringing the five practices for orchestrating discourse—anticipating, monitoring, selecting, sequencing, and connecting—fully into classroom practice at the elementary level. Through video examples, tasks, and student work, the authors provide practical advice for engaging young students in powerful class discussions centered on their strategies and mathematical thinking. This book is an invaluable professional resource."
*DeAnn Huinker*

"This book is a must for all elementary teachers who want to teach mathematics deeply and equitably, or as Smith, Bill, and Sherin write—ambitiously. From the first page, you are invited to take a deep dive into each of the 5 Practices by unpacking the practice, considering the potential instructional challenges associated with the practice, and, through the use of videos, teacher responses, and student work, analyze the challenging and rewarding work of facilitating productive student discourse. Read this book, try what’s suggested in your classroom, and watch ALL of your students truly shine as they demonstrate meaningful mathematical thinking and reasoning."
*Beth Kobett*

"The Five Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom is THE tool for helping ambitious elementary mathematics teaching a reality. It gives a rich, elementary lens to the original groundbreaking work through classroom examples, tasks, and accompanying videos. Simply put, it is a must-have for any mathematics teacher, coach, or administrator."
*John SanGiovanni*

"I’ve been a fan of 5 Practices for Orchestrating Productive Mathematics Discussions for a long time! In this practical, teacher-friendly follow up to the popular resource, the authors provide educators with a roadmap to support facilitating productive mathematics discussions in their classrooms. In this new addition to the series, educators are treated to a comprehensive blueprint for implementing the five practices that includes scaffolds, realistic suggestions grounded by research, feedback and authentic data from practicing teachers, vignettes, grade-specific examples and opportunities to reflect on classroom practice, making this resource a valuable tool for elementary educators."
*Latrenda Knighten*

"As an elementary math teacher, nothing has helped me become more intentional and
purposeful than the 5 Practices. In a continued effort to move student thinking forward, I
really appreciated how the authors walked us through specific K−5 examples because this will
definitely help me improve my craft."
*Graham Fletcher*