**Foreword by:** Damian Cooper

**Publication Date:** May 3, 2019

**Pages:** 192

PAPERBACK

ISBN: 9780807761427

$31.95

HARDCOVER

ISBN: 9780807761779

$96.00

EBOOK

ISBN: 9780807777794

$31.95$25.56

In this insightful math resource for grades 3–8, popular professional developer Marian Small helps teachers understand and facilitate meaningful assessments to advance student understandings. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess; construct meaningful assessments—both formative and summative—to measure student understanding; and provide students with feedback that is clear, timely, and specific. Examples for each grade level are provided, along with details on how to pose questions, analyze errors, and help students understand and learn from their mistakes. The book provides specific guidance for when and how to offer feedback on both correct and incorrect answers in order to advance students’ mathematical thinking. Like other Marian Small bestsellers, *Math That Matters* combines her special brand of lucid explanation of difficult concepts with fresh and engaging activities.

**Book Features:**

- Comprehensively addresses different mathematical domains for each grade (3–8).
- Organized around common core curriculum groupings but still applicable to other sets of mathematical standards.
- Includes student examples with suggestions for targeted, constructive feedback.
- Uses a strength-based approach to teacher education and professional learning.

**Marian Small **is the former dean of education at the University of New Brunswick and a longtime professor of mathematics education. She is widely known for her bestselling books and her in-district work with educators in the United States and Canada. Visit her website onetwoinfinity.ca for in-person and online professional development.

“ *Math that Matters *is an accessible, practical, and insightful book written for current (and future) math teachers about classroom assessment and feedback…The contribution of this book lies in the elegant way Small has distilled and packaged familiar ideas, and in the rich detail of the examples and illustrations that make the application of these ideas attractive and feasible. The book is a promising resource for teacher educators who want to introduce preservice and inservice teachers to current best practices for assessment and feedback in the mathematics classroom.”

**—Teachers College Record**

"Our understanding of the power of assessment to improve learning has deepened significantly in the past two decades. . . . Marian Small draws upon the critical research behind this understanding to explain what effective practice looks like. It is essential reading for all elementary educators and has the potential to profoundly affect the quality of mathematics assessment in our schools.”

―From the Foreword by **Damian Cooper**, president, Plan Teach Assess

“Teachers are often clamoring for concise classroom assessments that can capture students’ conceptual understanding. Clamor no more! *Math That Matters* is a timely response to that need. Marian Small removes the mystery of how to engage students in learning while collecting assessment data that drive next instructional plans. Using specific examples of discourse-rich pedagogies such as diagnostic tasks, probing questions, thoughtful approaches to delivering feedback, and differentiated performance assessments, she provides models for developing a comprehensive assessment plan.”

**—Karen Karp,** Johns Hopkins University

"The beauty of this book is that it is simple enough for brand new teachers and complex enough for experienced teachers. New teachers will learn a lot from the examples. Veteran teachers will see themselves in the examples, and the book will help them to shift their practice. The author offers an amazing gift by linking assessment ideas directly to common state standards." **―Felicia Darling, Santa Rosa Junior College**

**Contents**

**Foreword, ***by Damian Cooper*** ix**

**Preface xiii**

**Acknowledgments xvii**

**1 Linking Assessment and Feedback to Learning Goals 1**

How Assessment and Feedback Reflect Our Values 1

What Does This Look Like (More Specifically)? 2

Summary 9

**2 Assessment for Learning, as Learning, and of Learning 10**

Assessment for Learning 10

Assessment as Learning 15

Assessment of Learning 21

Summary 26

**3 Feedback 28**

Types of Feedback 29

Reactions to All Work 34

Immediacy of Feedback 35

Anticipating Errors 35

Summary 38

**4 Operations and Algebraic Thinking, Grade 3: Assessment and Feedback 40**

The Math That Matters 40

Assessment for Learning and Feedback 45

Assessment as Learning 53

Assessment of Learning 53

Summary 58

**5 Number and Operations in Base Ten, Grade 4: Assessment and Feedback 59**

The Math That Matters 59

Assessment for Learning and Feedback 64

Assessment as Learning 73

Assessment of Learning 74

Summary 78

**6 Geometry, Grade 5: Assessment and Feedback 79**

The Math That Matters 79

Assessment for Learning and Feedback 82

Assessment as Learning 91

Assessment of Learning 92

Summary 96

**7 Ratios and Proportional Relationships, Grade 6: Assessment and Feedback 97**

The Math That Matters 97

Assessment for Learning and Feedback 103

Assessment as Learning 112

Assessment of Learning 112

Summary 116

**8 Statistics and Probability, Grade 7: Assessment and Feedback 117**

The Math That Matters 117

Assessment for Learning and Feedback 126

Assessment as Learning 133

Assessment of Learning 134

Summary 138

**9 Expressions and Equations, Grade 8: Assessment and Feedback 139**

The Math That Matters 139

Assessment for Learning and Feedback 147

Assessment as Learning 156

Assessment of Learning 157

Summary 160

**;10 Conclusion 162**

Some Key Messages 162

Instruction Versus Assessment 163

An Assessment Plan 163

**References 165**

**Index 167**

**About the Author 171**

Contents (tentative)

Foreword

**Preface**

What Do We Mean by Assessment in This Resource?

What Constitutes Feedback?

What is Special About This Book?

Organization of the Book

Differentiated Assessment

Acknowledgments

**Chapter 1. What Is Foundational in Assessment and Feedback in Mathematics?**

Historical Issues in Mathematics Assessment

How Beliefs Impact Assessment

More Specific Examples

What We Might Value in Grade 3 Measurement

What We Might Value in Grade 5 Fractions

What We Might Value in Grade 7 Ratios and Proportion

Summary of Chapter 1

**Chapter 2. Assessment for Learning, as Learning, and of Learning**

Assessment for Learning

Diagnostic Assessment

Other Forms of Formative Assessment

What About the Practice Standards?

Assessment as Learning

Focusing on Detail or Not

Focusing on Answer Versus Focusing on Process

Success Criteria

Rubrics

Using Samples

Self-Assessment Templates

Learning to Self-Assess

Assessment of Learning

What Information is Collected?

Should There be Choice?

How Data are Collected

When Data are Collected

How Data are Reported

Whether Data are Permanent

Summary of Chapter 2

**Chapter 3. Feedback**

Types of Feedback

Opportunities for Self-Correction

Communication on Choice of Strategy

Communication on Perspective Taking

Communication Related to Problem Interpretation

Encouragement of Creativity

Encouragement of Extending

Reaction to All Work

Immediacy of Feedback

Anticipating Errors

Overgeneralizations

Inappropriate Assumptions

Common Misconceptions

Summary of Chapter 3

**Chapter 4. Assessment and Feedback in Grade 3 Operations and Algebraic Thinking**

The Math That Matters

Meanings of the Operations

Properties and Principles

Assessment for Learning and Feedback

Diagnostic Task

Diagnostic Questions

Tasks Designed for Formative Assessment

Assessment as Learning

Assessment of Learning

Skill Questions

Concept Questions

Performance Task and Rubric

Observation Checklist

Putting it Together

Summary of Chapter 4

**Chapter 5. Assessment and Feedback in Grade 4 Numbers and Operations**

The Math That Matters

Place Value

Adding and Subtracting Multi-Digit Numbers

Multiplying and Dividing Multi-Digit Numbers

Assessment for Learning and Feedback

Diagnostic Task

Diagnostic Questions

Tasks Designed for Formative Assessment

Assessment as Learning

Assessment of Learning

Skill Questions

Concept Questions

Performance Task and Rubric

Observation Checklist

Putting it Together

Summary of Chapter 5

**Chapter 6. Assessment and Feedback in Grade 5 Geometry**

The Math That Matters

Using a Coordinate Grid

Relating and Classifying 2-D Figures by Considering Properties

Assessment for Learning and Feedback

Diagnostic Task

Diagnostic Questions

Tasks Designed for Formative Assessment

Assessment as Learning

Assessment of Learning

Skill Questions

Concept Questions

Performance Task and Rubric

Observation Checklist

Putting It Together

Summary of Chapter 6

**Chapter 7. Assessment and Feedback in Grade 6 Ratio and Proportional Relationships**

The Math That Matters

Multiplicative Comparisons

Ratio and Rate Language

Equivalent Ratios and Rates

Representing Ratios and Rates

Percents

Comparing Rates or Ratios

Solving Problems

Assessment for Learning and Feedback

Diagnostic Task

Diagnostic Questions

Tasks Designed for Formative Assessment

Assessment as Learning

Assessment of Learning

Skill Questions

Concept Questions

Performance Task and Rubric

Observation Checklist

Putting It Together

Summary of Chapter 7

**Chapter 8. Assessment and Feedback in Grade 7 Statistics and Probability**

The Math That Matters

Statistics

Probability

Assessment for Learning and Feedback

Diagnostic Task

Diagnostic Questions

Tasks Designed for Formative Assessment

Assessment as Learning

Assessment of Learning

Skill Questions

Concept Questions

Performance Task and Rubric

Observation Checklist

Putting It Together

Summary of Chapter 8

**Chapter 9. Assessment and Feedback in Grade 8 Expressions and Equations**

The Math That Matters

Exponents

Square Roots and Cube Roots

Linear Relationships

Linear Equations

Systems of Linear Equations

Assessment for Learning and Feedback

Diagnostic Task

Diagnostic Questions

Tasks Designed for Formative Assessment

Assessment as Learning

Assessment of Learning

Skill Questions

Concept Questions

Performance Task and Rubric

Observation Checklist

Putting It Together

Summary of Chapter 9

**Chapter 10. Conclusion**

Some Key Messages

Instruction Versus Assessment

An Assessment Plan

References

Index

About the Author

- All sales throughout the U.S.A. available via our distributor.
- Co-published with, and available in Canada from, Nelson Publishing Inc.
- All other sales throughout the world available via Eurospan.

Professors: Request an Exam Copy

Print copies available for US orders only. For orders outside the US, see our international distributors.