The Five Practices in Practice [Elementary]

Margaret (Peg) Smith
Victoria Bill - University of Pittsburgh (United States)
Miriam Gamoran Sherin

Foreword by Dan Meyer, NCTM Co-publication, "Includes 65+ Minutes of Online Video" Burst

Other Titles in:
Mathematics & Numeracy | Primary Maths | Teaching in Primary Schools

October 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 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

Stevenson University School of Education

“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

Howard County Public School Systems, Howard County, MD

“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

Baton Rouge, LA

"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

Atlanta, GA

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

October 21, 2020

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The book aligned with the course expectations and will facilitate productive conversations.

Dr Alesia Mickle Moldavan

Curriculum and Teaching, Fordham University-Lincoln Ctr

August 27, 2020

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