| Foreword |
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ix | |
| Acknowledgments |
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xi | |
| NCTM Standards and Expectations |
|
xiii | |
| Introduction: The Problem-Solving Standard |
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1 | (6) |
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Building Math Understanding Through Problem Solving |
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7 | (9) |
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Teaching Math Through Problems |
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8 | (1) |
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A Look at Problem-Centered Instruction |
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8 | (1) |
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Selecting Meaningful Tasks |
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9 | (1) |
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The Role of Communication |
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10 | (2) |
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A Look at a Problem-Based Lesson |
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12 | (2) |
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Problems as a Teaching Tool |
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14 | (1) |
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15 | (1) |
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Guiding Students Through the Problem-Solving Process: Focusing on Strategies |
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16 | (14) |
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The Problem-Solving Process |
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16 | (1) |
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Breaking Down the Process |
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17 | (1) |
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Recording Steps in Solving Problems |
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18 | (3) |
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Helping Students Get ``Unstuck'' |
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21 | (1) |
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Involving Students in Instruction |
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22 | (2) |
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A Word About Word Problems |
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24 | (1) |
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The Importance of Problem-Solving Strategies |
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24 | (1) |
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Keys to Developing Strategies |
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25 | (3) |
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Exploring the Strategies in Detail |
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28 | (1) |
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28 | (2) |
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Strategy: Choose an Operation |
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30 | (12) |
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Key Words Versus Key Concepts |
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31 | (1) |
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Practice with Recognizing Key Concepts |
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31 | (3) |
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Practice with Choosing the Correct Operation |
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34 | (2) |
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Focusing on Increasingly Complex Problems |
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36 | (4) |
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Communicating About the Strategy |
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40 | (1) |
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Selecting Practice Problems |
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41 | (1) |
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41 | (1) |
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42 | (7) |
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Completing and Describing Number Patterns |
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43 | (1) |
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44 | (1) |
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Working with Geometric Patterns |
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45 | (1) |
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Patterns as a Problem-Solving Strategy |
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45 | (3) |
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Communicating About the Strategy |
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48 | (1) |
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48 | (1) |
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49 | (11) |
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Using Tables to Solve Problems |
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50 | (1) |
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Recognizing Patterns and Functions |
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51 | (1) |
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Selecting the Correct Answer |
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52 | (1) |
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Solving More Sophisticated Table Problems |
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53 | (2) |
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Using Tables to Connect to Other Math Skills |
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55 | (1) |
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Deciding When to Use a Table |
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56 | (1) |
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Communicating About the Strategy |
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56 | (2) |
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58 | (1) |
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59 | (1) |
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Strategy: Make an Organized List |
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60 | (12) |
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60 | (1) |
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Laying the Foundation for More Sophisticated Skills |
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61 | (4) |
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Combinations Versus Permutations |
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65 | (2) |
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Formulas and Organized Lists |
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67 | (2) |
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Communicating About the Strategy |
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69 | (1) |
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69 | (3) |
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Strategy: Draw a Picture or Diagram |
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72 | (9) |
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Simplifying Through Diagrams |
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73 | (3) |
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Focusing on More Complex Problems |
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76 | (1) |
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Differentiating Instruction Through Problem Solving |
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77 | (2) |
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Communicating About the Strategy |
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79 | (1) |
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80 | (1) |
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Strategy: Guess, Check, and Revise |
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81 | (9) |
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81 | (1) |
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82 | (2) |
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Using Guess, Check, and Revise with Equations |
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84 | (1) |
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Understanding the Role of Positive Attitudes |
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85 | (1) |
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Using Combined Strategies |
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85 | (2) |
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Building the Foundation for More Advanced Skills |
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87 | (1) |
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Communicating About the Strategy |
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88 | (1) |
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88 | (2) |
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Strategy: Use Logical Reasoning |
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90 | (9) |
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91 | (1) |
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92 | (2) |
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Using a List to Organize Clues |
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94 | (2) |
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Using a Venn Diagram to Organize Ideas |
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96 | (2) |
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Communicating About the Strategy |
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98 | (1) |
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98 | (1) |
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99 | (9) |
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Recognizing Familiar Problems |
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100 | (4) |
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Increasing the Complexity of Problems |
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104 | (1) |
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Working Backward with Equations |
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105 | (2) |
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Communicating About the Strategy |
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107 | (1) |
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107 | (1) |
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Assessing Problem Solving |
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108 | (8) |
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The Role of Ongoing Assessment |
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108 | (2) |
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The Value of Observations |
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110 | (1) |
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110 | (1) |
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The Value of Rubrics in Assessment |
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111 | (1) |
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A Holistic Rubric for Problem Solving |
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111 | (2) |
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The Role of Rubrics in Improvement |
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113 | (1) |
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Self-Reflections on Problem Solving |
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114 | (1) |
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114 | (1) |
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115 | (1) |
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Problem Solving Across the Content Standards |
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116 | (26) |
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Problem Solving About Number and Operations |
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117 | (4) |
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Problem Solving About Algebra |
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121 | (6) |
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Problem Solving About Measurement |
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127 | (4) |
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Problem Solving About Geometry |
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131 | (4) |
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Problem Solving About Data and Probability |
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135 | (6) |
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Linking Problem Solving and Math Content |
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141 | (1) |
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141 | (1) |
| Conclusion: Accepting the Challenge |
|
142 | (6) |
| Resources to Support Teachers |
|
148 | (3) |
| References |
|
151 | (1) |
| About the CD-ROM |
|
152 | |
