Everything You Need for Mathematics Coaching

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!Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville, where she teaches preservice teachers, emerging elementary mathematics specialists, and doctoral students in mathematics education. She has authored over 40 books and 100 journal articles/book chapters, many of which focus on procedural fluency and developing mathematical proficiency. Beyond the Figuring out Fluency series, these include Math Fact Fluency, and Everything you Need for Mathematics Coaching and Elementary: Teaching Developmentally and Middle School Mathematics. Jennifer′s national leadership includes NCTM Board of Directors, the TODOS: Mathematics for All Board of Directors, and as president and secretary of the Association of Mathematics Teacher Educators (AMTE). Beth McCord Kobett serves as Professor and Dean in the School of Education at Stevenson University, where she works closely with early childhood, elementary, and middle school preservice teachers. She brings experience as a classroom teacher, mathematics specialist, and university supervisor.  Beth served on the NCTM Board and served as president of Association of Maryland Mathematics Teacher Educators. Beth has authored ten mathematics education books and supports professional learning efforts nationwide. She has been honored with awards such as the MCTM Mathematics Educator of the Year and Stevenson’s Rose Dawson Award for Excellence in Teaching. Deeply committed to her students, she strives to create a supportive, strengths-based learning environment that fosters curiosity, collaboration, and meaningful growth.

"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."

• PrefaceAcknowledgementsAbout the AuthorsPart 1 Creating a Roadmap: Big Ideas of Coaching, Teaching, and LearningChapter 1. Coaching for Mathematical ProficiencyLeading for Mathematical Proficiency (LMP) FrameworkCoaching CycleGetting StartedChapter 2. Implementing Effective TeachingCoach′s DigestOverview of Implementing Effective TeachingCoaching Considerations for Professional LearningCoaching Lessons from The FieldCoaching Questions for DiscussionWhere to Learn MoreCoach′s Tookit2.1 Shifts in Classroom Practice Self-Assessment2.2 Essential Planning Questions for Effective Teaching2.3 Practices, Shifts, and Zones (Oh My)2.4 Mathematical Practices by Design2.5 Lesson Plan Template2.6 Mathematical Practice Look Fors2.7 Shifts in Classroom Practice2.8 Effective Teaching Look Fors2.9 Noticing Mathematical Practices2.10 Mapping Teaching Moves to Shifts in Classroom Practice2.11 Effective Teaching of MathematicsPart II Exploring Zones on the Journey: Professional Learning Focus AreasChapter 3. Content Kowledge and Worthwhile TasksCoach′s DigestOverview of Content Knowledge and Worthwhile TasksCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading For Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit3.1 Connecting Shifts to Content and Worthwhile Tasks Self-Assessment3.2 Connecting Shifts to Content and Tasks3.3 Focus on Fluency3.4 P.I.C.S. Page3.5 Analyzing Level of Cognitive Demand3.6 Worthwhile Task Analysis3.7 Developing Mathematical Proficiency3.8 Implementing Cognitively Demanding Tasks3.9 Impact on Students’ Emerging Fluency3.10 Reflecting on Task ImplementationChapter 4. Engaging StudentsCoach′s DigestOverview of Engaging StudentsCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading for Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit4.1 Connecting Shifts to Engaging Students Self-Assessment4.2 Total Participation Technique (TPT) Planning4.3 Planning or Cooperative Groups4.4 Engagement Techniques4.5 Cooperative Groups Data Gathering4.6 Engagement Techniques Discussion Prompts4.7 Reflecting on Cooperative Groups4.8 Analyzing Learning in Cooperative GroupsChapter 5. Questioning and DiscourseCoach′s DigestOverview of Questioning and DiscourseCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading for Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit5.1 Connecting Shifts to Questioning and Discourse Self-Assessment5.2 High-Level Thinking Questions5.3 Questioning Across Lesson Phases5.4 Questioning Across Lesson Phases (focus on Productive Struggle)5.5 Bloom’s Taxonomy (Revised) and Mathematical Knowledge5.6 Questioning Patterns5.7 Wait Time5.8 Productive Discussion and Talk Moves5.9 Question and Discourse Discussion Prompts5.10 Reflecting on Bloom’s Taxonomy (Revised) and Mathematical KnowledgeChapter 6. Formative AssessmentCoach′s DigestOverview of Formative AssessmentCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading for Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit6.1 Connecting Shifts to Formative Assessment Self-Assessment6.2 Planning for Five “Key Strategies” for Formative Assessment6.3 Developing Questions to Target Misconceptions6.4 Using Rubrics for Formative Assessment6.5 Observing and Providing Feedback6.6 Observing Students’ Thinking6.7 Observing Students’ Representations6.8 Brief Formative Assessment Interview6.9 Five “Key Strategies” for Formative Assessment Data Collection6.10 Using Rubrics for Formative Assessment6.11 Analyzing Formative Assessment Key StrategiesChapter 7. Analyzing Student WorkCoach′s DigestOverview of Analyzing Student WorkCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading for Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit7.1 Connecting Shifts to Analyzing Student Work Self-Assessment7.2 One Day/Many Artifacts Planning7.3 Planning Task Implementation7.4 Understanding Student Thinking7.5 Analyzing One Student’s Work7.6 Analysis of Students’ Misconceptions7.7 Collaborative Analysis ProtocolChapter 8. Differentiating Instruction for All LearnersCoach′s DigestOverview of Differentiating InstructionCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading for Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit8.1. Connecting Shifts to Differentiated Instruction Self-Assessment8.2 Student Diversity8.3 Meeting Individual Needs8.4 Different Ways to Differentiate a Lesson8.5 Opening Closed Tasks8.6 Focus on Five8.7 Differentiating Instruction8.8 Learning from Focus on Five8.9 Impact of Open /Tiered/Parallel TasksChapter 9. Supporting Emergent Multilingual StudentsCoach′s DigestOverview of Supporting Emergent Multilingual StudentsCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading for Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit9.1 Connecting Shifts to Supporting Emerging Multilingual Students Self-Assessment9.2 Culturally Responsive Mathematics Instruction (CRMI)9.3 Planning Strategies to Support Emergent Multilingual Students9.4 Diagnostic Interview9.5 Focus on Culturally Responsive Mathematics Instruction (CRMI)9.6 Teaching to Support Emergent Multilingual Students9.7 Reflecting on Support Emergent Multilingual Students9.8 Reflecting on Using a Diagnostic InterviewChapter 10. Supporting Students with Special NeedsCoach′s DigestOverview of Supporting Students with Special NeedsCoaching Considerations for Professional LearningCoaching Lessons from the FieldConnecting to the Leading for Mathematical Proficiency (LMP) FrameworkCoaching Questions for DiscussionWhere to Learn MoreCoach′s Toolkit10.1 Connecting Shifts to Supporting Students with Special Needs Self-Assessment10.2 Challenges and Support Structures10.3 Structuring a Lesson to Support Students with Special Needs10.4 Effective Teaching for Students with Special Needs10.5 Implementing Support Structures for Students with Special Needs10.6 Reflecting on Effective Teaching for Students with Special Needs10.7 Reflecting on Structuring a Lesson for Built-In SuccessPart III Navigating a Successful Journey: Strategies and Tools for You, the CoachChapter 11. Interacting With ColleaguesCoach′s DigestOverview of Interacting with ColleaguesBuilding TrustEstablishing RapportListeningParaphrasingPosing QuestionsWhere to Learn MoreChapter 12. Presenting Professional DevelopmentCoach′s DigestOverview of Presenting Professional DevelopmentTips for Presenting Professional DevelopmentCoaching Lessons from the FieldWhere to Learn MoreCoach′s Toolkit12.1 Professional Development Overview Planning12.2 Professional Development Planning Checklist12.3 Professional Development Planning Template12.4 Differentiating Professional Development12.5 Evaluating Professional Development12.6 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-Vignettes12.9 Sample Professional Development Activity: Mathematical Practices Playing Cards12.10 Sample Professional Development Activity: Questioning and the Mathematical Practices12.11 Sample Professional Development Activity: Effective Teaching PracticesChapter 13. Facilitating Professional Learning CommunitiesCoach′s DigestOverview of Facilitating Professional Learning CommunitiesTips for Facilitating Professional Learning CommunitiesCoaching Lessons from the FieldWhere to Learn MoreCoach′s Toolkit13.1 Meeting Standards Self-Assessment and Reflection13.2 Facilitator Proficiency Scale13.3 Sample Facilitation Activity: Appreciative Inquiry Protocol13.4 Sample Facilitation Activity: Paraphrasing13.5 Sample Facilitation Activity: Inclusion Strategies13.6 Sample Facilitation Activity: Task Talk ProtocolAppendix: BookmarksGlossaryReferences