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‘This book makes the five practices accessible for high school mathematics teachers. Teachers will see themselves and their classrooms throughout the book. High school mathematics departments and teams can use this book as a framework for engaging professional collaboration. I am particularly excited that this book situates the five practices as ambitious and equitable practices.’
Robert Q. Berry, III
NCTM President 2018-2020
Samuel Braley Gray Professor of Mathematics Education, University of Virginia
Take a deeper dive into understanding the five practices—anticipating, monitoring, selecting, sequencing, and connecting—for facilitating productive mathematical conversations in your high school classrooms and learn to apply them with confidence. This follow-up to the modern classic, 5 Practices for Orchestrating Productive Mathematics Discussions, shows the five practices in action in high school 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 high school 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, 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.
Daftar Isi
List of Video Clips
Foreword – Dan Meyer
Acknowledgments
About the Authors
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
Cori Moran’s 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
Ensuring Alignment Between Task and Goals
Launching a Task to Ensure Student Access
Conclusion
Chapter 3: Anticipating Student Responses
Part One: Unpacking the Practice: Anticipating Student Responses
Getting Inside the Problem
Planning to Respond to Student Thinking
Planning to Notice Student Thinking
Cori Moran’s 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
Advancing Student Thinking
Cori Moran’s Attention to Key Questions: Monitoring
Part Two: Challenges Teachers Face: Monitoring Student Work
Trying to Understand What Students Are Thinking
Keeping Track of Group Progress
Involving All Members of a Group
Conclusion
Chapter 5: Selecting and Sequencing Student Solutions
Part One: Unpacking the Practice: Selecting and Sequencing Student Solutions
Identifying Student Work to Highlight
Purposefully Selecting Individual Presenters
Establishing a Coherent Storyline
Cori Moran’s Attention to Key Questions: Selecting and Sequencing
Part Two: Challenges Teacher Face: Selecting and Sequencing Student Solutions
Selecting Only Solutions Relevant to Learning Goals
Expanding Beyond the Usual Presenters
Deciding What Work to Share When the Majority of Students Were Not Able to Solve the Task
Determining How to Sequence Incorrect 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 Different Solutions to Each Other
Cori Moran’s Attention to Key Questions: Connecting
Part Two: Challenges Teachers Face: Connecting Student Responses
Keeping the Entire Class Engaged and Accountable During Individual Presentations
Ensuring That Key Mathematical Ideas are Made Public and Remain the Focus
Making Sure That You Do Not Take Over the Discussion and Do The Explaining
Running Out of Time
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. Moran’s Monitoring Chart
Appendix D—Resources for Holding Students Accountable
Appendix E—Lesson-Planning Template
References
Index
Tentang Penulis
Michael D. Steele is a Professor and Chairperson of the Department of Educational Studies in Teachers College at Ball State University. He is a Past President of the Association of Mathematics Teacher Educators, current director-at-large of the National Council of Teachers of Mathematics, and editor of the journal Mathematics Teacher Educator. A former middle and high school mathematics and science teacher, Dr. Steele has worked with preservice secondary mathematics teachers, practicing teachers, administrators, and doctoral students across the country. He has published several books and research articles focused on supporting mathematics teachers in enacting research-based effective mathematics teaching practices.Dr. Steele’s work focuses on supporting secondary math teachers in developing mathematical knowledge for teaching, integrating content and pedagogy, through teacher preparation and professional development. He is the co-author of NCTM’s Taking Action: Implementing Effective Mathematics Teaching Practice in Grades 6-8. He is a co-author of several research-based professional development volumes, including The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your High School Classroom, Mathematics Discourse in Secondary Classrooms, and We Reason and Prove for All Mathematics. He directed the NSF-funded Milwaukee Mathematics Teacher Partnership, an initiative focused on microcredential-based teacher professional development and leadership. His research focuses on teacher learning through case-based professional development, and he has been an investigator on several National Science Foundation-funded projects focused on teacher learning and development. He also studies the influence of curriculum and policy in high school mathematics, with a focus on Algebra I policy and practice, and is the author of A Quiet Revolution: One District’s Story of Radical Curricular Change in Mathematics, a resource focused on reforming high school mathematics teaching and learning. He works regularly with districts across the country to design and deploy teacher professional development to strengthen effective secondary teaching practice.Dr. Steele was awarded the inaugural Best Reviewer award for Mathematics Teacher Educator and was author of the 2016 Best Article in Journal of Research in Leadership Education. He is an active member of and regular presenter for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematics, and the Association of Mathematics Teacher Educators. He reviews regularly for major mathematics education and teacher education journals.
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