**Foreword by Johnny W. Lott**

**Preface**

**Acknowledgments**

**About the Authors**

**1. Mathematics Assessment Probes**

Introduction

What Types of Understandings and Misunderstandings Does a Mathematics Assessment Probe Uncover?

How Were the Mathematics Assessment Probes Developed?

What Is the Structure of a Mathematics Assessment Probe?

What Additional Information Is Provided With Each Mathematics Assessment Probe?

What Mathematics Assessment Probes Are Included in the Book?

**2. Instructional Implications**

Differentiating Instruction

Assessing Points of Entry

Analyzing Trends in Student Thinking

Giving Student Interviews

Promoting Student-to-Student Dialogue

Developing Vocabulary

Allowing for Individual Think Time

Improving Students' Process Skills

Assessing Effectiveness of Instructional Activities

Moving Beyond the Individual Classroom

Summary

**3. Number and Operations Assessment Probes**

Probe 1: What Is the Value of the Digit?

Teachers' Notes: What Is the Value of the Digit?

Probe 1a: What Is the Value of the Digit? Variation

Probe 2: What Is the Meaning of 2/3?

Teachers' Notes: What Is the Meaning of 2/3?

Probe 2a: What Is the Meaning of 2/3? Variation

Probe 3: Is It Equivalent?

Teachers' Notes: Is It Equivalent?

Probe 3a: Is It Equivalent? Variation

Probe 4: What's Your Estimate?

Teachers' Notes: What's Your Estimate?

Probe 5: Is It an Estimate?

Teachers' Notes: Is It an Estimate?

Probe 6: Is It Simplified?

Teachers' Notes: Is It Simplified?

Probe 6a: Is It Simplified? Algebraic Variation

Probe 7: Where Is a Million?

Teachers' Notes: Where Is a Million?

Probe 8: How Low Can You Go?

Teachers’ Notes: How Low Can You Go?

Probe 8a: How Low Can You Go? Variation

Probe 9: What’s Your Addition Strategy?

Teachers’ Notes: What’s Your Addition Strategy?

Probe 9a: What’s Your Addition Strategy? Decimals Variation

Probe 9b: What’s Your Addition Strategy? Fractions Variation

Probe 10: What’s Your Subtraction Strategy?

Teachers’ Notes: What’s Your Subtraction Strategy?

Probe 10a: What’s Your Subtraction Strategy? Decimals Variation

Probe 10b: What’s Your Subtraction Strategy? Fractions Variation

Probe 11: What’s Your Multiplication Strategy?

Teachers’ Notes: What’s Your Multiplication Strategy?

Probe 11a: What’s Your Multiplication Strategy? Decimals Variation

Probe 12: What’s Your Division Strategy?

Teachers’ Notes: What’s Your Division Strategy?

Probe 12a: What’s Your Division Strategy? Decimals Variation

**4. Geometry, Measurement, and Data Assessment Probes**

Probe 1: What’s the Measure?

Teachers’ Notes: What’s the Measure?

Probe 1a: What’s the Measure? Variation

Probe 2: Are Area and Perimeter Related?

Teachers’ Notes: Are Area and Perimeter Related?

Probe 3: What’s the Area?

Teachers’ Notes: What’s the Area?

Probe 4: What’s the Capacity?

Teachers’ Notes: What’s the Capacity?

Probe 5: Is It Transformed?

Teachers’ Notes: Is It Transformed?

Probe 6: Are They Similar?

Teachers’ Notes: Are They Similar?

Probe 7: What Do You Mean?

Teachers’ Notes: What Do You Mean?

Probe 7a: What Do You Mean? Variation

Probe 8: Name of the Graph?

Teachers’ Notes: Name of the Graph?

Probe 9: Graph Construction?

Teachers’ Notes: Graph Construction?

**5. Algebra and Data Assessment Probes**

Probe 1: Equal or Not Equal?

Teachers’ Notes: Equal or Not Equal?

Probe 2: Is It the Same as a+b?

Teachers’ Notes: Is It the Same as a+b?

Probe 3: M & N’s?

Teachers’ Notes: M & N’s?

Probe 4: What’s the Substitute?

Teachers’ Notes: What’s the Substitute?

Probe 5: Is It True?

Teachers’ Notes: Is It True?

Probe 6: Solving Equations?

Teachers’ Notes: Solving Equations?

Probe 7: Correct Representation of the Inequality?

Teachers’ Notes: Correct Representation of the Inequality?

Probe 8: Is It a Variable?

Teachers’ Notes: Is It a Variable?

Probe 9: Binomial Expansion?

Teachers’ Notes: Binomial Expansion?

Probe 10: Is It Quadratic?

Teachers’ Notes: Is It Quadratic?

**Resource A: Note Template for QUEST Cycle**

**References**

**Index**