Mathematics Coaching Resources and Tools for Coaches and Leaders, K-12

by Bay-Williams, Jennifer M.; McGatha, Maggie; McCord Kobett, With Beth M.; Wray, With Jonathan A.

• ISBN13: 9780133007008
• ISBN10: 0133007006
• Edition: 1st
• Format: Paperback
• Copyright: 2013-01-29
• Publisher: Pearson

Summary

Mathematics Coaching Handbook gives mathematics coaches and teacher leaders solid background information and hands-on tools for supporting their efforts to help K-12 teachers effectively teach mathematics in today’s diverse classrooms. With its focus on coaching and an actual coaching cycle—planning, data gathering, and reflection—coupled with over 100 ready to use tools for a variety of settings, it’s the perfect resource for busy and sometimes isolated teacher leaders. By connecting the Leading for Mathematical Proficiency (LMP) Framework to mathematics teaching practices and the CCSS Mathematical Practices, the authors specifically illustrate how to improve math teaching to promote student understanding and mathematics proficiency.

Author Biography

Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville, Kentucky. She is an author of Elementary and Middle School: Teaching Developmentally-8e (with Karen Karp and the late John van de Walle), the just-released Professional Development Edition of this book, and the Field Experience Guide that accompanies this book. Among the other books that Jennifer has also co-authored are: Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2, Math and Literature: Grades 6-8, Math and Nonfiction: Grades 6-8, and Navigating through Connections in Grades 6-8. Bay-Williams has been published frequently in many articles on teaching and learning in NCTM journals and regularly provides professional development on effective teaching practices. She taught elementary, middle, and high school in Missouri and in Peru, and continues to work with students and teachers in classrooms at all levels. Jennifer is on the Board of Directors for TODOS: Equity for All, Editor for the 2012 NCTM Yearbook on Professional Collaborations, and is a Past-President of the Association of Mathematics Teacher Educators (AMTE).

 

Maggie B. McGatha is an associate professor of mathematics education at the University of Louisville. She is an Agency Trainer for Cognitive Coaching and regularly provides professional development on coaching and mentoring. A former middle school teacher, Maggie has also taught elementary and middle school mathematics methods courses at the university level. She currently teaches courses on coaching and mentoring and serves on the Board of Directors for the Association of Mathematics Teacher Educators (AMTE).

Table of Contents

Preface: Using the Mathematics Coaching Handbook

SECTION I: LAYING THE FOUNDATION – COACHING

 

Chapter 1. Coaching Framework and Process

Leading For Mathematical Proficiency

Standards for Mathematical Practice

Shifts in Classroom Practice

Leading for Mathematics Proficiency Framework

Coaching Cycle

Building Trust

Establishing Rapport

Listening

Paraphrasing

Posing Questions

Online Coaching Resources

 

Chapter 2. Implementing the Standards and Shifts

CHAPTER OVERVIEW

Framing the Topic

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

2.1Planning Tool: Standards for Mathematical Practice

2.2 Planning Tool:  Shifts in Classroom Practice

2.3 Planning Tool: NCTM Process Standards

2.4 Planning Tool:  Exemplary Instruction

2.5Planning Tool: Seven Essential Planning Questions

2.6Planning Tool: Lesson Plan Template

2.7 Data Gathering Tool: Standards for Mathematical Practice “Look-Fors”

2.8 Data Gathering Tool: Shifts in Classroom Practice

2.9 Data Gathering Tool: Effective Teaching

2.10 Reflection Tool: Standards for Mathematical Practice

2.11 Reflection Tool: Shifts in Classroom Practice

2.12 Reflection Tool: Teaching and Learning

 

 

SECTION III:  BUILDING CAPACITY – TEACHING SKILLS

 

Chapter 3. Content Knowledge and Worthwhile Tasks

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

3.1 Planning Tool: Content and Worthwhile Tasks Discussion Prompts

3.2 Planning Tool: P.I.C.S. Page

3.3 Planning Tool: Multiple Algebraic Representations Card (The MARC)

3.4 Planning Tool: Analyzing Level of Cognitive Demand

3.5 Planning Tool: Selecting a Worthwhile Task

3.6 Planning Tool: Worthwhile Task Analysis

3.7 Data Gathering Tool: Strands of Mathematical Proficiency

3.8 Data Gathering Tool: P.I.C.S. (for Data Gathering)

3.9 Data Gathering Tool: Levels of Cognitive Demand

3.10 Data Gathering Tool: Questioning

3.11 Reflection Tool: Lesson Analysis

3.12 Reflection Tool: Evidence of Mathematical Proficiency

3.13 Reflection Tool: Implementing a Worthwhile Task

3.14 Reflection Tool: Student Understanding

 

Chapter 4. Instructional Strategies

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

4.1 Planning Tool: Instructional Strategies Discussion Prompts

4.2 Planning Tool: Planning for Instructional Strategies

4.3 Planning Tool: Cooperative Groups

4.4 Planning Tool: Building Perseverance

4.5 Data Gathering Tool: Instructional Strategies

4.6 Data Gathering Tool: Building Perseverance

4.7 Data Gathering Tool: Cooperative Groups

4.8 Data Gathering Tool: Supporting the Mathematical Practices

4.9 Reflection Tool: Instructional Strategies Discussion Prompts

4.10 Reflection Tool: Instructional Strategies Reflection

4.11 Reflection Tool: Building Perseverance

4.12 Reflection Tool: Structuring Cooperative Groups

4.13 Reflection Tool: Analyzing learning in Cooperative Groups

 

Chapter 5. Questioning and Discourse

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

5.1 Planning Tool: Discussion Prompts for Questions and Discourse

5.2 Planning Tool: Higher-Level Thinking Questions

5.3 Planning Tool: Five Principles for Effective Questioning

5.4 Data Gathering Tool: Bloom’s Taxonomy and Mathematics Knowledge, Version A

5.5 Data Gathering Tool: Bloom’s Taxonomy and Mathematics Knowledge, Version B

5.6 Data Gathering Tool: Questioning Patterns

5.7 Data Gathering Tool: Wait Time

5.8 Data Gathering Tool: Talk Moves

5.9 Reflection Tool: Discussion Prompts for Questions and Discourse

5.10 Reflection Tool: Bloom’s Taxonomy and Mathematics Knowledge, Version A

5.11 Reflection Tool: Bloom’s Taxonomy and Mathematics Knowledge, Version B

 

Chapter 6. Formative Assessment

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

6.1 Planning Tool: Formative Assessment Discussion Prompts

6.2 Planning Tool: Questioning Planning Tool

6.3 Planning Tool: Collecting Anecdotal Evidence

6.4 Planning Tool: Five “Key Strategies” for Formative Assessment

6.5 Planning Tool: Using Rubrics for Formative Assessment

6.6 Data Gathering Tool: Collecting Anecdotal Evidence

6.7 Data Gathering Tool: Observing Students’ Thinking

6.8 Data Gathering Tool: Five “Key Strategies” for Formative Assessment

6.9 Reflection Tool: Formative Assessment Discussion Prompts

6.10 Reflection Tool: Collecting Anecdotal Evidence

6.11 Reflection Tool: Observing Students’ Thinking

6.12 Reflection Tool: Five “Key Strategies” for Formative Assessment

6.13 Reflection Tool: Using Rubrics for Formative Assessment

 

Chapter 7. Analyzing Student Work

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

7.1 Planning Tool: Analyzing Student Thinking Discussion Prompts

7.2 Planning Tool: One Day/Many Artifacts

7.3 Planning Tool: One Student (or Team)

7.4 Data Gathering Tool: Implementation of a Task

7.5 Data Gathering Tool: One Student

7.6 Data Gathering Tool: Livescribe Interview

7.7 Reflection Tool: Analyzing One Student’s Work

7.8 Reflection Tool: Livescribe Analysis

7.9 Reflection Tool: Student Error Analysis

7.10 Reflection Tool: Reflecting on Anecdotal Notes

 

Chapter 8. Differentiating Instruction for All Learners

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

8.1. Planning Tool: Discussion Prompts – Differentiated Instruction

8.2. Planning Tool: Student Diversity

8.3. Planning Tool: Meeting Individual Needs

8.4. Planning Tool: Different Ways to Differentiate a Lesson

8.5. Data Gathering Tool: Productive Classroom Culture

8.6. Data Gathering Tool: One Student’s Experience

8.7.  Data Gathering Tool: Focus on Five

8.8. Data Gathering Tool: Differentiating Instruction

8.9.  Reflection Tool: Establishing a Productive Mathematics Community

8.10. Reflection Tool: One Child’s Experience

8.11. Reflection Tool: Focus on Five

8.12. Reflection Tool: Meeting the Needs of All Learners

 

Chapter 9. Supporting English Language Learners

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

9.1 Planning Tool: Discussion Prompts – English Language Learners

9.2 Planning Tool: Reflective Questions – Culturally Responsive Instruction

9.3 Planning Tool: Select Appropriate Accommodations

9.4 Planning Tool: Accommodations for English Language Learners

9.5  Planning Tool: Diagnostic Interview for ELLs

9.6 Data Gathering Tool: Culturally Responsive Instruction

9.7 Data Gathering Tool: Accommodations for English Language Learners

9.8 Data Gathering Tool: Student Participation in Discourse

9.9 Reflection Tool: Culturally Responsive Instruction

9.10 Reflection Tool: Accommodations for ELLs

9.11 Reflection Tool: Diagnostic Interview for ELLs

 

Chapter 10. Supporting Students with Special Needs

CHAPTER OVERVIEW

Framing the Topic

Examining the Standards for Mathematical Practice

Mapping to Shifts in Classroom Practice

Coaching Considerations

Coaching Questions

Links to Related Resources

COACHING CYCLE TOOLS

10.1. Planning Tool: Discussion Prompts – Students with Special Needs

10.2. Planning Tool: Organizational, Behavioral, & Cognitive Considerations

10.3. Planning Tool: Removing Barriers, Infusing Structures

10.4. Planning Tool: Designing Diagnostic Interviews

10.5. Planning Tool: Data Gathering Tool: Explicit Instruction: Focus on Making Connections

10.6. Data Gathering Tool: Addressing Organizational, Behavioral, and Cognitive Skills

10.7. Reflection Tool: Focus on Explicit Instruction

10.8. Reflection Tool: Meeting the Needs of MyStudents with Special Needs

 

 

SECTION III: SUPPORT FOR THE COACH

 

Chapter 11. Designing Professional Development

CHAPTER OVERVIEW

Framing the Topic

Tips for Planning Professional Development

Links to Related Resources

Coaching Tools

11.1 Professional Development Planning Considerations

11.2 Professional Development Single Event Planning Guide

11.3 Event Design

11.4 Knowledge, Attitudes, Skills, Aspirations, & Beliefs (KASAB)

11.5 Evaluating Professional Development

 

Chapter 12. Working with Professional Learning Communities

CHAPTER OVERVIEW

Framing the Topic

Tips for Working with Professional Learning Communities

Links to Related Resources

Coaching Tools

12.1 Evaluating the Norms of Collaboration

12.2 Adult Learning Theory

12.3 Monitoring the Work of the PLC

12.4 Student Work Analysis Protocol, Example 1

12.5 Student Work Analysis Protocol, Example 2

12.6 Classroom-Focused Improvement Process (CFIP) At-a-Glance

12.7 CFIP Reflection Questions

 

Chapter 13. Working with a Range of Teachers

CHAPTER OVERVIEW

Framing the Topic

Tips for Planning Professional Development

Links to Related Resources

Coaching Tools

13.1 Getting to Know You

13.2 Supporting the Beginning Teacher

13.3 Concerns-Based Adoption Model