Acknowledgments |
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xv | |
About the Author |
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xvii | |
Introduction |
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1 | (9) |
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Becoming a Mathematics Student |
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1 | (1) |
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Becoming a Mathematics Teacher |
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1 | (1) |
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Becoming a PBL Mathematics Educator |
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2 | (2) |
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4 | (1) |
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How to Engage in This Book |
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4 | (2) |
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6 | (2) |
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8 | (2) |
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10 | (21) |
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11 | (1) |
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Emphasis 1 The Need to Embrace the Role of Mathematician |
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12 | (9) |
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Embracing the Identity of Mathematician Through Mathematical Habits of Mind |
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13 | (6) |
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Activities to Get to Know Your Mathematicians |
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19 | (2) |
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Emphasis 2 The Need for Mathematics to Mean Something |
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21 | (2) |
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The Ideal Mathematics Classroom |
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23 | (1) |
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What Exactly Is Project-Based Learning? |
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24 | (2) |
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Addressing Hesitancies About PBL Mathematics |
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26 | (3) |
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29 | (1) |
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29 | (2) |
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Chapter 2 PBL Mathematics as Equitable, Engaging, and Effective |
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31 | (15) |
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Three Reasons for PBL Mathematics |
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35 | (9) |
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PBL Mathematics as an Equitable Teaching Practice |
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36 | (3) |
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PBL Mathematics as an Engaging Teaching Practice |
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39 | (3) |
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PBL Mathematics as an Effective Teaching Practice |
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42 | (2) |
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44 | (2) |
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Chapter 3 From Problem to Project |
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46 | (23) |
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46 | (3) |
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When Problem-Solving Tasks Aren't Enough |
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49 | (1) |
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Alignment to Equity-Based Teaching Practices |
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50 | (4) |
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The Twofold Pressure of Ti IT16 |
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54 | (2) |
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Weaving Tasks and Projects Together |
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56 | (2) |
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Turning Textbook Problems Into Problem-Solving Tasks, Performance Tasks, and Projects |
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58 | (7) |
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58 | (1) |
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59 | (3) |
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PBL Mathematics Experiences |
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62 | (3) |
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65 | (4) |
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Chapter 4 Rigorous Content |
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69 | (16) |
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71 | (3) |
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Rigorous Content Illustrated in PBL |
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74 | (2) |
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74 | (1) |
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75 | (1) |
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75 | (1) |
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Making Moves to Increase Rigor in the PBL Mathematics Classroom |
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76 | (8) |
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Encourage Risk-Taking Through Creative Solutions |
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77 | (2) |
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Design Open-Ended Problem-Solving Tasks and Performance Tasks |
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79 | (2) |
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Connect Mathematical Habits of Mind With Authentic Situations |
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81 | (3) |
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84 | (1) |
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Chapter 5 Productive Inquiry |
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85 | (27) |
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86 | (2) |
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Productive Inquiry Illustrated: Directed Inquiry Versus Productive Inquiry |
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88 | (1) |
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Directed Inquiry in a Mathematics Classroom |
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88 | (1) |
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Making Moves to Increase Productive Inquiry in Your Classroom |
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89 | (5) |
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90 | (1) |
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Students as Critical Questioners |
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91 | (3) |
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Productive Inquiry in the PBL Mathematics Classroom |
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94 | (3) |
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97 | (2) |
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99 | (1) |
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Identity and Agency Defined |
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100 | (1) |
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Identity and Agency Illustrated |
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101 | (5) |
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101 | (2) |
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103 | (3) |
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Making Moves to Increase Identity and Agency |
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106 | (5) |
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111 | (1) |
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Chapter 7 Authentic Connections |
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112 | (14) |
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Authentic Connections Defined |
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113 | (4) |
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Realistic Versus Authentic |
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115 | (2) |
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Authentic Connections Illustrated |
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117 | (3) |
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From Authentic Task to Authentic Project |
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120 | (2) |
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122 | (2) |
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124 | (2) |
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Chapter 8 Meaningful Assessment |
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126 | (15) |
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Assessment in the Mathematics Classroom |
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127 | (1) |
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Meaningful Assessment Defined |
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128 | (2) |
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Meaningful Assessment Illustrated |
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130 | (6) |
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Productive Inquiry as Formative Assessment |
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131 | (1) |
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Student-Led Feedback as Assessment |
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132 | (2) |
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Summative Assessment Through a Culminating Experience Illustrated |
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134 | (2) |
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Essential Attributes Highlighted by Public Product |
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136 | (3) |
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139 | (2) |
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Chapter 9 Growth Through Reflection |
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141 | (15) |
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Growth Through Reflection Defined |
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142 | (1) |
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Growth Through Reflection Illustrated |
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143 | (2) |
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Reflection Leading to Critique and Revision |
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145 | (1) |
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146 | (5) |
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151 | (2) |
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153 | (3) |
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Chapter 10 Classroom Culture |
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156 | (17) |
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Establish a Classroom Culture |
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157 | (1) |
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Develop Community Agreements |
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158 | (3) |
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Honor Student Identity and Relationship to Mathematics |
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161 | (2) |
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Embrace Curiosity and Wonderment |
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163 | (2) |
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Act Like a Four-Year-Old--Question Everything! |
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163 | (1) |
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Follow the Curiosity Path |
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164 | (1) |
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165 | (3) |
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165 | (1) |
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166 | (2) |
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Value Process Over Product |
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168 | (3) |
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168 | (1) |
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169 | (1) |
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169 | (2) |
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171 | (2) |
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Chapter 11 Role of the PBL Mathematics Teacher |
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173 | (10) |
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174 | (2) |
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176 | (1) |
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176 | (1) |
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177 | (1) |
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178 | (4) |
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182 | (1) |
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Chapter 12 Find Inspiration |
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183 | (15) |
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Our Students as Inspiration |
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184 | (2) |
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186 | (5) |
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Our Everyday World as Inspiration |
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188 | (1) |
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Project Types as Inspiration |
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189 | (2) |
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Our Standards as Inspiration |
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191 | (5) |
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Readily Available Projects |
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194 | (2) |
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196 | (2) |
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198 | (15) |
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199 | (1) |
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200 | (2) |
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202 | (5) |
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Crafting a Driving Question |
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204 | (3) |
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207 | (1) |
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207 | (4) |
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"Need to Knows" Sustain Inquiry |
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210 | (1) |
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211 | (2) |
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Chapter 14 Craft Milestones |
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213 | (18) |
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214 | (1) |
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215 | (2) |
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217 | (2) |
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219 | (6) |
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225 | (5) |
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230 | (1) |
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231 | (14) |
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232 | (1) |
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232 | (7) |
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233 | (2) |
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235 | (2) |
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237 | (1) |
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Accountability Through Products |
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238 | (1) |
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239 | (5) |
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240 | (1) |
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240 | (1) |
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240 | (1) |
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241 | (1) |
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242 | (2) |
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244 | (1) |
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245 | (32) |
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Assessment in PBL Mathematics |
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246 | (5) |
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247 | (2) |
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Assessments Tied to "Need to Know" Questions |
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249 | (2) |
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Formative Assessments as Evidence of Learning |
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251 | (3) |
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Summative Assessment: Public Products as Evidence of Learning |
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254 | (4) |
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Culminating Experience Ideas |
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258 | (1) |
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259 | (2) |
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261 | (2) |
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263 | (1) |
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What Are Students Reflecting On? |
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263 | (4) |
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How Are Students Reflecting? |
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267 | (3) |
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Growth Through Critique and Revision |
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270 | (1) |
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270 | (4) |
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274 | (2) |
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276 | (1) |
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Chapter 18 Design the Experience |
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277 | (13) |
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278 | (1) |
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278 | (3) |
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281 | (1) |
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281 | (1) |
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Engaging Hook + Project Overview + "Need to Knows" |
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282 | (1) |
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Plan the Project Conclusion |
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283 | (2) |
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Map the Milestones From Launch to Conclusion |
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285 | (4) |
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Plan for Daily Lessons From Launch to Conclusion |
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289 | (1) |
Concluding Thoughts |
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290 | (2) |
Conclusion |
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292 | (1) |
References |
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293 | (5) |
Index |
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298 | |