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Realizing Rigor in the Mathematics Classroom

Realizing Rigor in the Mathematics Classroom

Foreword by Suzanne Mitchell

February 2014 | 192 pages | Corwin

Rigor put within reach!

Rigor: Everyone is talking about it, and now the Common Core has made it policy. But how exactly do you design a math classroom where achieving that goal is guaranteed? This first-of-its-kind guidebook will help teachers and leaders across the grades make that goal a reality. You’ll not only come to understand once and for all what rigor is, you’ll also learn how to consistently apply that ideal from math classroom to math classroom.

Using their Proficiency Matrix as a framework, Hull, Harbin Miles, and Balka offer proven strategies for successful implementation of the CCSS mathematical practices—with practical tools you can use right away. Whether working individually or as part of a team, you’ll learn how to

  • Define rigor in the context of each mathematical practice
  • Identify and overcome potential issues and obstacles, including differentiating instruction, monitoring classrooms, and using data
  • Relate specific roles and goals for students, teachers, math leaders, school leaders, and collaborative teams
  • Use assessment tools to guide work and monitor progress

With action checklists and record sheets, self-assessments, a teacher planning guide, and much more, this is the only resource you need to guide your team to rigor—and your students to achievement.

Foreword by Suzanne Mitchell
CCSS Content and Practice: Opportunity for Rigor

A Clue to Rigor

Outline of the Book

How to Use This Book

Part I. The Foundation
1. Understanding and Meeting the Challenge of Rigor
National Assessments

Teacher Evaluation

Learning Shifts

Meeting the Challenges

Looking at Assessments

Rigor as a Common Factor

2. Defining and Instituting Rigor
Searching for Evidence

Dictionary and Thesaurus

Professional Opinions

Indicators of Rigor

Drawing Conclusions

Decision Point

Contrasting Example Lessons

Problem Analysis

Transforming Classrooms to Support Rigor

Having Productive Conversations

3. Building Team Leadership to Support Rigor
Role of a Steering Committee

Role of a Leadership Team

Role of the Principal

Developing Learning Communities

A Principal's Story

Having Productive Conversations

4. Rigor and the Standards for Practice
Rigor and Practices

A Principal's Story

Having Productive Conversations

5. Rigor Related to Classroom Formative Assessment
Assessment Types

Classroom Formative Assessment

Refining Formative Assessment

Classroom Formative Assessment

Formative Assessment and Intervention

Current Learning

Effective Intervention

Instructional Research


A Principal's Story

Having Productive Conversations

6. Rigor and the Proficiency Matrix

Progress Toward Rigor

Strategy Relationship in the Matrix

Classroom Formative Assessment and the Matrix

Ms. Edward's Classroom

A Principal's Story

Having Productive Conversations

Part II. Issues and Obstacles
7. Issues to Resolve
Issue: Teaching the Identified Content

Issue: Deepening Mathematical Understandings

Issue: Reaching All Students

8. Obstacles to Success
Obstacle: Working in Isolation

Obstacle: Attempting to Evaluate People to Change

Obstacle: Failing to Monitor Student Actions

Obstacle: Over Adoption

Obstacle: Mistaken Efforts

Understanding MAAT

Having Productive Conversations

Part III. Solutions
9. Solution Step One: Monitoring Student Actions Related to the Practices
Opening Classroom Doors

Non-Evaluative Monitoring

Starting With Students

Teacher Self-Assessment of Student Actions


Having Productive Conversations

10. Solution Step Two: Using Classroom Visit Data-Assessment of Student Actions
Conducting Productive Conversations

Understanding Change Process

Levels of Adoption

Intervention as Support

Building a Critical Mass

Changing the Culture

Connecting Actions Chart

Having Productive Conversations

11. Solution Step Three: Monitoring Teacher Actions Related to the Practices
Using the Classroom Visit Tally - Teachers

Conversations About the Data

Working on Individual Needs

Mathematics Collaborative Log

Teacher Planning Guide

Having Productive Conversations

12. Solution Step Four: Gathering and Using Additional Data
Assessments Collectively

Specified Classroom Visits

Validity Visits

Reverse Visits

Teacher Requested Visits

Supporting Teachers' Change Efforts

Adoption Stages

Documenting Progress

Completing the Form

Having Productive Conversations

13. Solution Step Five: Maintaining Progress Toward Rigor

Relating Mathematical Rigor and the Practices

Inferences from the Standards for Mathematical Practices

Rigor as an Outcome


Rigor Analysis Form



Guiding the Work

Input and Outcomes

Having Productive Conversations

Part IV. Inputs and Outcomes
14. Teaching for Rigor


Teaching for Progress in Rigor

Having Productive Conversations

15. Coaching for Rigor


Coaching for Progress in Rigor

Having Productive Conversations

16. Leading for Rigor


Leading for Progress in Rigor

Having Productive Conversations

Part V. Momentum
17. Linking Responsibilities - Assessing Progress
Professional Trust

Professional Conversations

Supporting Teacher Change

Documenting Change


Having Productive Conversations


"This comprehensive, step-by-step guide for enhancing student thinking and reasoning through rigor is yet another major contribution to the field of mathematics education by this outstanding author trio! Hull, Balka, and Harbin Miles tackle the challenges related to rigor head-on, providing support for teachers and teacher leaders through well over a dozen new tools geared toward engaging teacher teams in the work of enhancing student thinking and reasoning through mathematical rigor."

Jon Wray, Mathematics Instructional Facilitator
Howard County Public Schools, NCTM Board of Directors

"The value of this book is in its capacity to explain rigor in the context of teach­ing and learning mathematics. The authors have succeeded in presenting the case for rigor by developing definitions and tools that can be used to find evidence of stu­dent learning including a deep understanding of mathematics as well as the ability to transfer learning into new and challenging situations."

From the Foreword by Suzanne Mitchell
Key features
    • In their most recent book, The Common Core Math Standards, the authors created The Proficiency Matrix. The Proficiency Matrix helps teachers identify learning progression in each of the mathematical practices. The Matrix, combined with the formative assessment strategies and techniques, help teachers assess where student are in their learning progression. With this knowledge teachers can adjust their teaching to achieve advanced proficiency of the individual practice and help students succeed. The Matrix plays a critical role in helping teachers and leaders purposefully transform classrooms and places the focus on students' proficiency, thinking, and reasoning as called for in the CCSS-M.
    • At the Common Core Institute, participants commented on how much they liked the Proficiency Matrix. This book will provide a step-by-step guide for teachers and leaders on how to use the Matrix and chart progression implementation of the CCSS-M.
    • Supporting tools are also provided and described within the chapters to assist teachers in transforming instruction:
      • Classroom Visit Tally - Student Actions
      • Classroom Visit Tally - Teacher Actions
      • Teacher self assessment for student actions
      • Teacher self assessment for teacher actions
      • Action Record Sheet
      • Teacher Implementation Progression
      • Coaching Feedback Quadrant
      • Teacher Planning Guide
      • Linking Responsibilities Chart

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