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The Five Practices in Practice
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The Five Practices in Practice
Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom

Foreword by Dan Meyer, NCTM Co-publication



September 2019 | 240 pages | Corwin

"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.


 
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

“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

“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
University of Rochester, Rochester, NY

“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
Mary Baldwin University, Scottsville, VA

“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
McDaniel College

“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
Denver Public Schools, Denver, CO

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
West Linn, OR

“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
University of Arizona

“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
University of Wisconsin-Milwaukee
Key features

This book is a comprehensive, ready-to-use, professional development plan inside a book’s covers!

—Francis (Skip) Fennell, Author, Past President, NCTM

 

Includes:

  • Description of three real teachers through planning and conducting a lesson—see all 5 practices play out
  • Solutions to the most common math discussion-related challenges
  • 65+ minutes of video, plus video-analysis activities
  • Teaching takeaways, pause and consider moments, vignettes, student work, tasks, tools, and templates.
  • A companion website with downloadable tools and templates

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ISBN: 9781544321134
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