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



November 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, gradespecific examples and opportunities to reflect on classroom practice, making this resource a valuable tool for elementary educators.”

Latrenda Knighten
Baton Rouge, LA
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ISBN: 9781544321134
£25.99