Foreword |
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viii | |
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Acknowledgments |
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xi | |
Introduction What Does an Open Middle Classroom Look Like? |
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1 | (7) |
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Chapter One How Will These Problems Help Me? |
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8 | (5) |
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Chapter Two How Are Open Middle Problems Different? |
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13 | (42) |
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Problems at Each Grade Level |
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19 | (29) |
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Sixth-Grade Example: Dividing Fractions |
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21 | (3) |
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Seventh-Grade Example: Solving Two-Step Equations |
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24 | (3) |
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Eighth-Grade Example: Evaluating Exponents |
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27 | (3) |
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Algebra Example: Interpreting Key Features of Quadratics in Vertex Form |
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30 | (4) |
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Geometry Example: Finding the Midpoint of a Line Segment |
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34 | (4) |
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Algebra 2 Example: Multiplying Complex Numbers |
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38 | (3) |
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Trigonometry and Pre-Calculus Example: Evaluating Trigonometric Functions |
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41 | (3) |
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Calculus Example: Evaluating Definite Integrals |
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44 | (4) |
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What Are Open Middle Problems? |
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48 | (4) |
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Connections to Other Kinds of Problems |
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52 | (3) |
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Chapter Three What Do We Need to Do Before Using a Problem with Students? |
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55 | (21) |
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How Should We Get Started? |
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57 | (2) |
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When Would We Want to Use an Open Middle Problem? |
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59 | (1) |
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How Do We Choose a Problem? |
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60 | (3) |
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How Do We Prepare to Use the Problem? |
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63 | (7) |
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What Understandings Do We Want Students to Gain from the Problem? |
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70 | (6) |
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Chapter Four How Do We Use a Problem with Students? |
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76 | (54) |
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How Do We Get Students Started on the Problem? |
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77 | (1) |
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What Happens After We Explain the Directions to Students? |
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78 | (1) |
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What Should We Do While Students Are Working? |
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79 | (3) |
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What If Students Don't Use the Method We Had Hoped? |
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82 | (3) |
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What If Students Solve the Problem Using a Method We Don't Understand? |
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85 | (3) |
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What Should We Do If Students Give Up After Trying the Problem a Couple of Times? |
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88 | (10) |
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How Can We Tell When Productive Struggle Becomes Unproductive Struggle? |
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98 | (3) |
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What Should We Do If Students Are Unproductively Struggling? |
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101 | (1) |
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What Should We Do When Kids Get Stuck in Unexpected Ways? |
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102 | (3) |
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What Should We Do After Students Are Finished with the Problem? |
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105 | (9) |
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How Do We Facilitate the Classroom Conversation? |
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114 | (6) |
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What If Students Are Not Ready for a Conversation by the End of Class? |
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120 | (2) |
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How Do We Avoid Hurting Students' Feelings? |
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122 | (1) |
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What Should We Do If Students Struggle to Explain Their Thinking? |
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123 | (3) |
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How Much Class Time Should This All Take? |
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126 | (1) |
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What Should We Do with the Information We Learn About What Students Know? |
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127 | (3) |
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Chapter Five Where Can I Get More Open Middle Problems? |
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130 | (29) |
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130 | (2) |
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Make Your Own Open Middle Problems |
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132 | (18) |
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Step 1: Start with a Level 1 Problem |
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136 | (2) |
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Step 2: Increase the Problem from Level 1 to Level 2 |
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138 | (5) |
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Step 3: Increase the Problem from Level 2 to Level 3 |
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143 | (7) |
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Make More Advanced Problems |
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150 | (8) |
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Share Your Open Middle Problems with Other Math Educators |
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158 | (1) |
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Chapter Six What Comes Next? |
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159 | (12) |
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163 | (4) |
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167 | (4) |
References |
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171 | (2) |
Index |
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173 | |