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# Uncovering Student Thinking in Mathematics, Grades 6-12: 30 Formative Assessment Probes for the Secondary Classroom / Edition 1

Uncovering Student Thinking in Mathematics, Grades 6-12: 30 Formative Assessment Probes for the Secondary Classroom / Edition 1 available in Hardcover, Paperback, NOOK Book

## Overview

Discussing standards, research, and more, these 30 probes help secondary teachers assess students' grasp of core mathematics concepts and modify their instruction to improve student achievement.

## Product Details

ISBN-13: | 9781412963770 |
---|---|

Publisher: | SAGE Publications |

Publication date: | 06/27/2008 |

Edition description: | Grades 6-12 |

Pages: | 248 |

Sales rank: | 354,328 |

Product dimensions: | 8.40(w) x 10.90(h) x 0.60(d) |

## Read an Excerpt

Discussing standards, research, and more, these 30 probes help secondary teachers assess students' grasp of core mathematics concepts and modify their instruction to improve student achievement.

## First Chapter

Discussing standards, research, and more, these 30 probes help secondary teachers assess students' grasp of core mathematics concepts and modify their instruction to improve student achievement.

## Table of Contents

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

## Reading Group Guide

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

## Interviews

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

## Recipe

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