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Everything You Need for Mathematics Coaching
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Everything You Need for Mathematics Coaching
Tools, Plans, and a Process That Works for Any Instructional Leader, Grades K-12


Other Titles in:
Mathematics

April 2018 | 360 pages | Corwin

Math coaches wear many hats. You think on your feet and have to invent, react, and respond—often without time to prepare—in a myriad of professional contexts. What’s your go-to resource for support?   

Plan, focus, and lead: Your toolkit for inspiring math teachers 

Meet Everything You Need For Mathematics Coaching: Tools, Plans, and a Process That Works for Any Instructional Leader. This one-stop, comprehensive toolkit for improving mathematics instruction and learning is designed for busy math coaches and teacher leaders who often have to rely on their own competencies. Using the Leading for Mathematical Proficiency Framework, the authors position student outcomes as the focus of all professional work and connect the Eight Mathematical Practices for students with NCTM’s Eight Effective Teaching Practices to help you guide teachers toward growing mathematics proficiency in their classrooms.  

This hands-on resource details critical coaching and teaching actions, and offers nearly a hundred tools for: 

  • Shifting classroom practice in a way that leads to student math proficiency and understanding of mathematical concepts.
  • Honing in on key areas, including content knowledge and worthwhile tasks, student engagement, questioning and discourse, analysis of student work, formative assessment, support for emergent language learners and students with special needs, and more.
  • Navigating a coaching conversation.
  • Planning and facilitating professional learning communities.
  • Finding a focus for professional development or a learning cycle.
  • Making connections between professional learning activities, teaching, and student learning.
  • Using the coaching cycle—plan, gather data, reflect—to build trust and rapport with teachers.  

With examples from the field, a comprehensive list of resources for effective coaching, and a plethora of tools you can download and share with teachers, this toolkit is your must-have guide to designing a professional learning plan and leading with clarity and purpose.

 
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

“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
Atlanta, GA

"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
University of Virgina

“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
Education and former Novia Scotia Provincial Mathematics Coordinator

“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
Instructional Leader Program Coordinator, Co-teaching/Collaboration Initiatives and Supervisor
Co-coordinator, Portland State University

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