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Foreword by: Damian Cooper
Publication Date: May 3, 2019
Pages: 192
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:
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
Professors: Request an Exam Copy
Print copies available for US orders only. For orders outside the US, see our international distributors.