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Everything You Need for Mathematics Coaching
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Table of Contents

Preface Acknowledgements About the Authors Part 1 Creating a Roadmap: Big Ideas of Coaching, Teaching, and Learning Chapter 1. Coaching for Mathematical Proficiency Leading for Mathematical Proficiency (LMP) Framework Coaching Cycle Getting Started Chapter 2. Implementing Effective Teaching Coach's Digest Overview of Implementing Effective Teaching Coaching Considerations for Professional Learning Coaching Lessons from The Field Coaching Questions for Discussion Where to Learn More Coach's Tookit 2.1 Shifts in Classroom Practice Self-Assessment 2.2 Essential Planning Questions for Effective Teaching 2.3 Practices, Shifts, and Zones (Oh My) 2.4 Mathematical Practices by Design 2.5 Lesson Plan Template 2.6 Mathematical Practice Look Fors 2.7 Shifts in Classroom Practice 2.8 Effective Teaching Look Fors 2.9 Noticing Mathematical Practices 2.10 Mapping Teaching Moves to Shifts in Classroom Practice 2.11 Effective Teaching of Mathematics Part II Exploring Zones on the Journey: Professional Learning Focus Areas Chapter 3. Content Kowledge and Worthwhile Tasks Coach's Digest Overview of Content Knowledge and Worthwhile Tasks Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading For Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 3.1 Connecting Shifts to Content and Worthwhile Tasks Self-Assessment 3.2 Connecting Shifts to Content and Tasks 3.3 Focus on Fluency 3.4 P.I.C.S. Page 3.5 Analyzing Level of Cognitive Demand 3.6 Worthwhile Task Analysis 3.7 Developing Mathematical Proficiency 3.8 Implementing Cognitively Demanding Tasks 3.9 Impact on Students' Emerging Fluency 3.10 Reflecting on Task Implementation Chapter 4. Engaging Students Coach's Digest Overview of Engaging Students Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading for Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 4.1 Connecting Shifts to Engaging Students Self-Assessment 4.2 Total Participation Technique (TPT) Planning 4.3 Planning or Cooperative Groups 4.4 Engagement Techniques 4.5 Cooperative Groups Data Gathering 4.6 Engagement Techniques Discussion Prompts 4.7 Reflecting on Cooperative Groups 4.8 Analyzing Learning in Cooperative Groups Chapter 5. Questioning and Discourse Coach's Digest Overview of Questioning and Discourse Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading for Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 5.1 Connecting Shifts to Questioning and Discourse Self-Assessment 5.2 High-Level Thinking Questions 5.3 Questioning Across Lesson Phases 5.4 Questioning Across Lesson Phases (focus on Productive Struggle) 5.5 Bloom's Taxonomy (Revised) and Mathematical Knowledge 5.6 Questioning Patterns 5.7 Wait Time 5.8 Productive Discussion and Talk Moves 5.9 Question and Discourse Discussion Prompts 5.10 Reflecting on Bloom's Taxonomy (Revised) and Mathematical Knowledge Chapter 6. Formative Assessment Coach's Digest Overview of Formative Assessment Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading for Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 6.1 Connecting Shifts to Formative Assessment Self-Assessment 6.2 Planning for Five "Key Strategies" for Formative Assessment 6.3 Developing Questions to Target Misconceptions 6.4 Using Rubrics for Formative Assessment 6.5 Observing and Providing Feedback 6.6 Observing Students' Thinking 6.7 Observing Students' Representations 6.8 Brief Formative Assessment Interview 6.9 Five "Key Strategies" for Formative Assessment Data Collection 6.10 Using Rubrics for Formative Assessment 6.11 Analyzing Formative Assessment Key Strategies Chapter 7. Analyzing Student Work Coach's Digest Overview of Analyzing Student Work Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading for Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 7.1 Connecting Shifts to Analyzing Student Work Self-Assessment 7.2 One Day/Many Artifacts Planning 7.3 Planning Task Implementation 7.4 Understanding Student Thinking 7.5 Analyzing One Student's Work 7.6 Analysis of Students' Misconceptions 7.7 Collaborative Analysis Protocol Chapter 8. Differentiating Instruction for All Learners Coach's Digest Overview of Differentiating Instruction Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading for Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 8.1. Connecting Shifts to Differentiated Instruction Self-Assessment 8.2 Student Diversity 8.3 Meeting Individual Needs 8.4 Different Ways to Differentiate a Lesson 8.5 Opening Closed Tasks 8.6 Focus on Five 8.7 Differentiating Instruction 8.8 Learning from Focus on Five 8.9 Impact of Open /Tiered/Parallel Tasks Chapter 9. Supporting Emergent Multilingual Students Coach's Digest Overview of Supporting Emergent Multilingual Students Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading for Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 9.1 Connecting Shifts to Supporting Emerging Multilingual Students Self-Assessment 9.2 Culturally Responsive Mathematics Instruction (CRMI) 9.3 Planning Strategies to Support Emergent Multilingual Students 9.4 Diagnostic Interview 9.5 Focus on Culturally Responsive Mathematics Instruction (CRMI) 9.6 Teaching to Support Emergent Multilingual Students 9.7 Reflecting on Support Emergent Multilingual Students 9.8 Reflecting on Using a Diagnostic Interview Chapter 10. Supporting Students with Special Needs Coach's Digest Overview of Supporting Students with Special Needs Coaching Considerations for Professional Learning Coaching Lessons from the Field Connecting to the Leading for Mathematical Proficiency (LMP) Framework Coaching Questions for Discussion Where to Learn More Coach's Toolkit 10.1 Connecting Shifts to Supporting Students with Special Needs Self-Assessment 10.2 Challenges and Support Structures 10.3 Structuring a Lesson to Support Students with Special Needs 10.4 Effective Teaching for Students with Special Needs 10.5 Implementing Support Structures for Students with Special Needs 10.6 Reflecting on Effective Teaching for Students with Special Needs 10.7 Reflecting on Structuring a Lesson for Built-In Success Part III Navigating a Successful Journey: Strategies and Tools for You, the Coach Chapter 11. Interacting With Colleagues Coach's Digest Overview of Interacting with Colleagues Building Trust Establishing Rapport Listening Paraphrasing Posing Questions Where to Learn More Chapter 12. Presenting Professional Development Coach's Digest Overview of Presenting Professional Development Tips for Presenting Professional Development Coaching Lessons from the Field Where to Learn More Coach's Toolkit 12.1 Professional Development Overview Planning 12.2 Professional Development Planning Checklist 12.3 Professional Development Planning Template 12.4 Differentiating Professional Development 12.5 Evaluating Professional Development 12.6 Sample Professional Development Activity: Grouping Strategy (P.I.C.S. Page) 12.7 Sample Professional Development Activity: Grouping Strategy (Shape Partners) 12.8 Sample Professional Development Activity: Mathematical Practices Mini-Vignettes 12.9 Sample Professional Development Activity: Mathematical Practices Playing Cards 12.10 Sample Professional Development Activity: Questioning and the Mathematical Practices 12.11 Sample Professional Development Activity: Effective Teaching Practices Chapter 13. Facilitating Professional Learning Communities Coach's Digest Overview of Facilitating Professional Learning Communities Tips for Facilitating Professional Learning Communities Coaching Lessons from the Field Where to Learn More Coach's Toolkit 13.1 Meeting Standards Self-Assessment and Reflection 13.2 Facilitator Proficiency Scale 13.3 Sample Facilitation Activity: Appreciative Inquiry Protocol 13.4 Sample Facilitation Activity: Paraphrasing 13.5 Sample Facilitation Activity: Inclusion Strategies 13.6 Sample Facilitation Activity: Task Talk Protocol Appendix: Bookmarks Glossary References

About the Author

Maggie B. McGatha works full time with coaches, teacher leaders, and administrators as a Training Associate for Cognitive Coaching? and Adaptive Schools. At the University of Louisville, she teaches courses on coaching and supporting collaborative groups along with advanced mathematics methods courses. Maggie is a former middle school mathematics teacher, the author of numerous articles, a co-author of Mathematics Coaching: Resources and Tools for Coaches and Leaders, K-12 (Pearson, 2014) and On the Money: Math Activities to Build Financial Literacy, Grades 6-8 (NCTM, 2015). She is active in state and national mathematics organizations including currently serving as the Vice President for the Membership Division (2017-2020) of the Association of Mathematics Teacher Educators (AMTE) and member of the Advisory Board for the Mathematics Institute of Wisconsin. She received her doctorate from Vanderbilt University (Tennessee). Maggie enjoys traveling and spending time with her family, especially her grandkids! Beth McCord Kobett, EdD, is an associate professor in the School of Education at Stevenson University, where she works with preservice teachers and leads professional learning efforts in mathematics education both regionally and nationally. She is also the lead consultant for the Elementary Mathematics and Specialist and Teacher Leadership Project. She is a former classroom teacher, elementary mathematics specialist, adjunct professor, and university supervisor. She is the current president of the Association of Maryland Mathematics Teacher Educators (AMMTE) and former chair of the Professional Development Services Committee of the National Council of Teachers of Mathematics (NCTM). Dr. Kobett is a recipient of the Mathematics Educator of the Year Award from the Maryland Council of Teachers of Mathematics (MCTM). She has also received Stevenson University's Excellence in Teaching Award as both an adjunct and full-time member of the Stevenson faculty.

Reviews

"Whether you are a new or an experienced math coach, this book really is everything you need for coaching math instruction. There are many moving parts that coaches must work with on a yearly basis and at times, it can be really hard to make sense of it all. Alongside their toolkit, the authors lay out a purposeful plan that would help make the most difficult of instructional goals attainable."

-- Graham Fletcher, Math Specialist

"Everything You Need for Mathematics Coaching: Tools, Plans, and a Process That Works for Any Instructional Leader, Grades K-12 is couched within a solid framework for supporting coaches to engage teachers in shifting their teaching practices. This framework, Leading for Mathematical Proficiency, supports specific tangible resources coaches can use to support teachers across different contexts in which shifting in practices is understood to be a continuum. Coaches will find resources embedded in each chapter supportive of reflecting upon practices and shifts in practices."

-- Robert Q. Berry, III, President NCTM
"Whether you are an experienced mathematics coach or new to the role, this book will become your most valuable resource. By offering a doable coaching cycle as well as the specific tools you need for your daily work, the authors equip you to effectively collaborate and support teachers in shifting their instructional practices in research-informed ways to advance student learning of mathematics." -- Matt Larson, Past President NCTM
"Coaches will find this resource invaluable in two ways. First, as a source for their own professional growth; and second, as their `go-to book' for information and tools that they will come back to again and again as they help teachers achieve their professional goals." -- Donna Karsten, Co-chair of the Coaching Committee for NCSM: Leardship in Mathematics
"This is a great resource and reference for all coaches and instructional leaders who are often challenged with little time to prepare for the critical work of supporting teachers with developing mathematically proficient students. This book provides a collection of resources to assist coaches in their everyday work. Each chapter includes a topical digest connected to a high-leverage teaching practice, ideas for aiding the development of the practice, and lessons from the field-all contributing to deepening a coach's planning and preparation." -- Nicole Miller Rigelman, EdD, Professor of Mathematics Education, Elementary Mathematics * Co-coordinator, Portland State University *
"The daily work of the math coach lies in working with teachers. Yet the goal for all math coaches is student learning. This book is designed around the Leading for Mathematical Proficiency framework, which begins and ends with the students. This thoughtful, supportive, and easy to navigate book will be your go-to resource!" -- Paige Richards, Lead Mathematics Specialist
"This book is a comprehensive, cohesive, and contemporary resource for mathematics instructional coaches and teacher educators. Professional learning providers are presented an arsenal of tools to help them to prepare teachers to meet the needs of each and every student in classrooms in which students' mathematical reasoning and sense making skills are fostered and valued." -- Dr. Marilyn E. Strutchens, Emily R. and Gerald S. Leischuck Endowed Professor and Mildred Chesire Fraley Distinguided Professor, Auburn University Past President
"Mathematics coaches/specialists face a seemingly dizzying array of coaching-related responsibilities and challenges. This appropriately titled resource will be on the desk and in the book bag of coaches/specialists as they consider coaching lessons from the field, coaching questions, resources for additional learning, and adapt and use the many tools provided." -- Francis (Skip) Fennell, Professor of Education and Graduate and Professional Studies Emeritus, Project Director Elementary Mathematics Specialists and teacher Leaders Project-McDaniel College

"This book is a must-have for any professional who provides support to mathematics teachers. In particular, the Coach's Toolkit-a set of frameworks, templates and protocols-provides an invaluable resource for supporting lesson planning, observation, data collection, reflection and much more!"

-- Peg Smith, Author of The Five Practices for Orchestrating Mathematical Discussion

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