Math That Matters

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 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.

"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

"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 (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