Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville (Kentucky). She has co-authored numerous books for teachers and teacher leaders. Among them are Elementary and Middle School Mathematics: Teaching Developmentally (including the new Professional Development Edition) and the related Field Experience Guide, the three-volume Van de Walle Professional Mathematics Series (Teaching Student-Centered Mathematics: Grades PreK-2, Grades 3-5 and Grade 6-8), Developing Essential Understandings of Addition and Subtraction for Teaching Mathematics in Prekindergarten -Grade 2, and Math and Literature: Grades 6-8. She edited the NCTM 2012 Yearbook, Professional Collaborations in Mathematics Teaching and Learning. Jennifer has served as president of the Association of Mathematics Teacher Educators (AMTE), member of the board of directors of TODOS: Mathematics for All, member of the board of directors of the National Council of teachers of Mathematics (NCTM) and chair of the NCTM Emerging Issues Committee. She taught K-12 mathematics in Missouri and Peru. She received her doctoral and master's degrees from the University of Missouri-Columbia (Missouri) and her bachelor's degree from DePauw University (Indiana).

Maggie B. McGatha is a professor of mathematics education at the University of Louisville (Kentucky). She is a former middle school mathematics teacher. She is co-author of On the Money: Math Activities to Build Financial Literacy, Grades 6-8 (NCTM, 2015). Maggie has served as president of the Kentucky Council of Teachers of Mathematics (KCTM), member of the board of directors and vice president of the Association of Mathematics Teacher Educators (AMTE), member of the Elementary Mathematics Specialist advisory board for The Brookhill Institute of Mathematics, and member of the Educational Materials Committee for the National Council of Teacher of Mathematics (NCTM). Maggie works with coaches, teacher leaders, and administrators as a training associate for Cognitive CoachingSM and an agency trainer for Adaptive Schools. She received her doctorate from Vanderbilt University (Tennessee), her master's degree from Austin Peay State University (Tennessee), and her bachelor's degree from Morehead State University (Kentucky).

Beth McCord Kobett is an assistant professor of mathematics education at Stevenson University (Maryland). She is co-author of The Formative Five: Everyday Assessment Techniques for Every Math Classroom (Corwin, 2017). She is a former elementary teacher and mathematics resource teacher/specialist in Howard County public schools. She is the lead consultant on the Elementary Mathematics Specialists & Teacher Leaders (EMS&TL) Project. At the undergraduate level, Beth teaches early childhood, elementary, and middle school mathematics methods courses, as well as equity-in-education courses. At the graduate level, she teaches courses on diagnostics and interventions in education. Beth conducts professional development throughout her region, including workshops, coaching, and demonstration lessons with elementary and middle school staff. She has a particular interest in developing problem-solving dispositions in students through problem-based teaching. Beth received her doctoral and master's degrees from John Hopkins University (Maryland) and bachelor's degree from the University of Missouri-Columbia (Missouri).

Jonathan A. Wray is the secondary mathematics instructional facilitator for the Howard County Public School System and has served as a member of the board of directors of the National Council of Teachers of Mathematics (NCTM). He is co-author of The Formative Five: Everyday Assessment Techniques for Every Math Classroom (Corwin, 2017). He is the president elect of the Association of Maryland Mathematics Teacher Educators (AMMTE) and served as president of the Maryland Council of Teachers of Mathematics (MCTM). A contributor to Elementary and Middle School Mathematics: Teaching Developmentally, Jon manages the Elementary Mathematics Specialists & Teacher Leaders (EMS&TL) Project. His interests include the leadership roles of mathematics coaches/specialists, teacher collaboration, effective and engaging teaching and learning strategies, strategic uses of technology, and issues related to access and equity in mathematics education. Jon received his master's in technology, and issues related to access and equity in mathematics degree from Towson University (Maryland).

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
Coachs Digest
Overview of Implementing Effective Teaching
Coaching Considerations for Professional Learning
Coaching Lessons from The Field
Coaching Questions for Discussion
Where to Learn More
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs 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
Coachs Digest
Overview of Interacting with Colleagues
Building Trust
Establishing Rapport
Listening
Paraphrasing
Posing Questions
Where to Learn More
Chapter 12. Presenting Professional Development
Coachs Digest
Overview of Presenting Professional Development
Tips for Presenting Professional Development
Coaching Lessons from the Field
Where to Learn More
Coachs 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
Coachs Digest
Overview of Facilitating Professional Learning Communities
Tips for Facilitating Professional Learning Communities
Coaching Lessons from the Field
Where to Learn More
Coachs 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