The Five Practices in Practice [Elementary]
Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom
- Margaret (Peg) Smith - University of Pittsburgh, USA
- Victoria Bill - University of Pittsburgh (United States)
- Miriam Gamoran Sherin - Northwestern University, USA
Foreword by Dan Meyer, NCTM Co-publication, "Includes 65+ Minutes of Online Video" Burst
Corwin Mathematics Series
"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.
Free resources
How to: Keeping the Entire Class Engaged and Accountable During Individual Presentations
This handy chart from The Five Practices in Practice, Elementary, by Margaret “Peg” Smith, Victoria Bill, and Miriam Gamoran Sherin identifies a set of moves that teachers can make to hold students accountable for attending to mathematics discussions and presentations.
Unpacking the Practice: Anticipating Student Responses
This practice activity from The Five Practices in Practice, Elementary, by Margaret “Peg” Smith, Victoria Bill, and Miriam Gamoran Sherin involves thinking about different ways students might solve the task, planning to respond to students using assessing and advancing questions, and preparing to notice key aspects of students’ thinking in the midst of instruction.
“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.”
“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.”
“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.”
“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.”
“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!”
“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.”
“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.”
"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.”
“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.”
“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.”