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xx | |
Foreword |
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xxi | |
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Preface |
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xxiv | |
Acknowledgments |
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xxvii | |
About the Authors |
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xxix | |
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The Five Practices in Practice: An Overview |
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3 | (2) |
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5 | (5) |
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6 | (2) |
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8 | (2) |
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10 | (4) |
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10 | (1) |
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11 | (3) |
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Chapter 2 Setting Goals and Selecting Tasks |
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Part One Unpacking the Practice: Setting Goals and Selecting Tasks |
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14 | (7) |
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Specifying the Learning Goal |
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14 | (2) |
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Identifying a High-Level Task That Aligns With the Goal |
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16 | (3) |
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Tara Tyus's Attention to Key Questions: Setting Goals and Selecting Tasks |
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19 | (2) |
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Part Two Challenges Teachers Face: Setting Goals and Selecting Tasks |
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21 | (12) |
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Identifying Learning Goals |
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21 | (2) |
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Identifying a Doing-Mathematics Task |
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23 | (1) |
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Adapting an Existing Task |
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23 | (2) |
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Finding a Task in Another Resource |
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25 | (2) |
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27 | (2) |
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Ensuring Alignment Between Task and Goals |
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29 | (1) |
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Launching a Task to Ensure Student Access |
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30 | (2) |
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Launching a Task---Analysis |
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32 | (1) |
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33 | (5) |
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Chapter 3 Anticipating Student Responses |
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Part One Unpacking the Practice: Anticipating Student Responses |
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38 | (12) |
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Getting Inside the Problem |
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39 | (1) |
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Getting Inside a Problem---Analysis |
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39 | (4) |
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Planning to Respond to Student Thinking |
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43 | (6) |
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Planning to Notice Student Thinking |
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49 | (1) |
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Tara Tyus's Attention to Key Questions: Anticipating |
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50 | (1) |
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Part Two Challenges Teachers Face: Anticipating Student Responses |
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50 | (14) |
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Moving Beyond the Way YOU Solved the Problem |
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51 | (8) |
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Being Prepared to Help Students Who Cannot Get Started |
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59 | (2) |
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Creating Questions That Move Students Toward the Mathematical Goal |
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61 | (3) |
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64 | (6) |
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Chapter 4 Monitoring Student Work |
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Part One Unpacking the Practice: Monitoring Student Work |
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70 | (14) |
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Tracking Student Thinking |
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71 | (1) |
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Assessing Student Thinking |
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72 | (2) |
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Exploring Student Problem-Solving Approaches---Analysis |
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74 | (3) |
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Assessing Student Thinking---Analysis |
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77 | (1) |
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Advancing Student Thinking |
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78 | (2) |
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Advancing Student Thinking, Part One---Analysis |
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80 | (3) |
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Advancing Student Thinking, Part Two---Analysis |
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83 | (1) |
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Tara Tyus's Attention to Key Questions: Monitoring |
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84 | (1) |
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Part Two Challenges Teachers Face: Monitoring Student Work |
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84 | (14) |
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Trying to Understand What Students Are Thinking |
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85 | (2) |
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Determining What Students Are Thinking, Part One---Analysis |
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87 | (2) |
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Determining What Students Are Thinking, Part Two---Analysis |
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89 | (2) |
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Keeping Track of Group Progress |
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91 | (2) |
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Following Up With Students---Analysis |
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93 | (2) |
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Involving All Members of a Group |
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95 | (2) |
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Holding All Students Accountable---Analysis |
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97 | (1) |
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98 | (6) |
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Chapter 5 Selecting and Sequencing Student Solutions |
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Part One Unpacking the Practice: Selecting and Sequencing Student Solutions |
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104 | (11) |
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Identifying Student Work to Highlight |
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105 | (3) |
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Selecting Student Solutions---Analysis |
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108 | (2) |
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Purposefully Selecting Individual Presenters |
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110 | (2) |
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Establishing a Coherent Storyline |
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112 | (3) |
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Tara Tyus's Attention to Key Questions: Selecting and Sequencing |
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115 | (1) |
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Part Two Challenges Teachers Face: Selecting and Sequencing Student Solutions |
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115 | (21) |
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Selecting Only Solutions Relevant to Learning Goals |
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116 | (8) |
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Selecting Solutions That Highlight Key Ideas---Analysis |
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124 | (2) |
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Expanding Beyond the Usual Presenters |
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126 | (5) |
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Deciding What Work to Share When the Majority of Students Were Not Able to Solve the Task and Your Initial Goal No Longer Seems Obtainable |
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131 | (2) |
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Moving Forward When a Key Strategy Is Not Produced by Students |
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133 | (1) |
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Determining How to Sequence Errors, Misconceptions, and/or Incomplete Solutions |
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134 | (2) |
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136 | (6) |
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Chapter 6 Connecting Student Solutions |
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Part One Unpacking the Practice: Connecting Student Solutions |
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142 | (10) |
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Connecting Student Work to the Goals of the Lesson |
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143 | (2) |
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Connecting Student Work to the Goals of the Lesson, Part One---Analysis |
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145 | (2) |
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Connecting Student Work to the Goals of the Lesson, Part Two---Analysis |
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147 | (1) |
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Connecting Student Work to the Goals of the Lesson, Part Three---Analysis |
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148 | (2) |
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Connecting Different Solutions to Each Other |
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150 | (1) |
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Connecting Different Solutions to Each Other---Analysis |
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151 | (1) |
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Tara Tyus's Attention to Key Questions: Connecting |
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152 | (1) |
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Part Two Challenges Teachers Face: Connecting Student Responses |
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152 | (18) |
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Keeping the Entire Class Engaged and Accountable During Individual Presentations |
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153 | (5) |
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Holding Students Accountable---Analysis |
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158 | (4) |
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Ensuring That Key Mathematical Ideas Are Made Public and Remain the Focus |
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162 | (2) |
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Making Key Ideas Public---Analysis |
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164 | (2) |
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Making Sure That You Do Not Take Over the Discussion and Do the Explaining |
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166 | (1) |
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167 | (3) |
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170 | (4) |
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Chapter 7 Looking Back and Looking Ahead |
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Why Use the Five Practices Model |
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174 | (3) |
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Getting Started With the Five Practices |
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177 | (5) |
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Plan Lessons Collaboratively |
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177 | (2) |
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Observe and Debrief Lessons |
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179 | (1) |
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179 | (1) |
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180 | (1) |
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181 | (1) |
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Explore Additional Resources |
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181 | (1) |
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Frequency and Timing of Use of the Five Practices Model |
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182 | (1) |
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183 | (3) |
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Appendix A Web-Based Resources for Tasks and Lesson Plans |
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186 | (1) |
Appendix B Monitoring Chart |
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187 | (1) |
Appendix C Ms. Tyus's Monitoring Chart |
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188 | (4) |
Appendix D Resources for Holding Students Accountable |
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192 | (1) |
Appendix E Lesson-Planning Template |
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193 | (2) |
References |
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195 | (6) |
Index |
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201 | |