| Preface: How Can I (Better) Embrace Mathematics? |
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xvii | |
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| Acknowledgments |
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xxi | |
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| Acknowledgments |
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xxiii | |
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| Prologue |
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1 | (1) |
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1 | (1) |
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2 | (5) |
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7 | (1) |
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7 | (1) |
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8 | (2) |
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10 | (1) |
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String Figures (``Cat's Cradle'') |
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11 | (3) |
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Response to Prologue: Be a Student of Mathematics Learners |
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14 | (5) |
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19 | (32) |
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Irony and the ``Problem of Culture'' |
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19 | (3) |
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The Five-part Inquiry Unit |
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22 | (3) |
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25 | (7) |
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Teaching Journeys, Infrastructure, and the Stories We Tell |
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32 | (3) |
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Response to
Chapter 1: Engage Yourself in Meaningful Observation |
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35 | (5) |
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Action Research 1---Isaiah Manzella, Numbers on Trial |
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40 | (9) |
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Math Worlds 1: Reverse Answer to Questions |
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49 | (2) |
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A Psychoanalytic Perspective |
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51 | (40) |
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56 | (2) |
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Psychoanalytic Selves: Learners and Teachers |
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58 | (4) |
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62 | (5) |
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67 | (3) |
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70 | (5) |
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Teachers' Object Realtions |
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75 | (3) |
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Neither Tough-Love nor Dream of Love |
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78 | (3) |
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81 | (2) |
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Response to
Chapter 2: Ask Yourself to Change |
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83 | (3) |
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Action Research 2---Karen Cipriano, Flexible Interview Project |
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86 | (3) |
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Math Worlds 2: Multiple Answers |
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89 | (2) |
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91 | (39) |
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100 | (2) |
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102 | (2) |
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Polya and Problem Solving Phases |
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104 | (2) |
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Mason: Specializing and Generalizing |
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106 | (1) |
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On Reading a Book: How Mathematicians Read |
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107 | (7) |
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The Art of Problem Posing |
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114 | (6) |
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Continuing the Conversation |
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120 | (2) |
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Response to
Chapter 3: Explore the Vastness of Mathematics |
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122 | (5) |
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Action Research 3---Karen Cipriano, Mathematics Journals |
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127 | (2) |
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Math Worlds 3: Reading and Writing Mathematics |
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129 | (1) |
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Critical Thinkers Thinking Critically |
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130 | (29) |
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Critical Points in Pedagogy |
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133 | (1) |
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Treat Mathematical Actors as Mathematical Critics |
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134 | (1) |
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Make a Choice, Pursue it, and Consider the Consequences |
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134 | (1) |
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Obsess About Functional Relationships |
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135 | (1) |
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Problematize the ``Answer'' |
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136 | (1) |
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Problematize the Pedagogy |
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137 | (1) |
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Understand Mathematics as Rhetoric |
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138 | (1) |
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Realize Apprentice Mathematicians and Citizens as Objects of Mathematics |
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138 | (1) |
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Perform Celebratory Archaeology |
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139 | (1) |
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Critical Thinkers Thinking |
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139 | (2) |
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From Critical Thinking to Critical Mathematics Education |
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141 | (5) |
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Response to
Chapter 4: It is Critical to Think |
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146 | (2) |
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Action Research 4---Ada Rocchi, Lesson: World Population and Wealth |
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148 | (10) |
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Math Worlds 4: Pitching Questions at Various Levels |
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158 | (1) |
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Consuming Culture: Commodities and Cultural Resources |
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159 | (28) |
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Buying and Selling Mathematics? |
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160 | (3) |
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Intercultural Mathematics |
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163 | (5) |
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Finding Mathematics: Commodities and Object Relations |
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168 | (2) |
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Being Limited by ``Vision'' |
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170 | (1) |
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The Author as Teacher-Educator |
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171 | (4) |
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From Complicity to Heterarchy |
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175 | (2) |
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Response to
Chapter 5: Emphasize the Meaning-making of Mathematics |
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177 | (3) |
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Action Research 5---Colleen Murphy, A School-wide Survey |
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180 | (4) |
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Math Worlds 5: Turning ``Puzzles'' into ``Problems'' or ``Exercises'' |
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184 | (3) |
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Metaphors for the Classroom Space |
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187 | (38) |
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Spaces of Learning and Teaching |
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188 | (2) |
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190 | (1) |
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191 | (2) |
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193 | (3) |
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196 | (1) |
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196 | (2) |
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198 | (1) |
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198 | (1) |
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199 | (4) |
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Relate to the Space, Stop Creating Spaces |
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203 | (5) |
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208 | (3) |
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Achieving Expectations through Metaphors |
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211 | (1) |
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Response to
Chapter 6: Take Ownership of Your Classroom Space |
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212 | (4) |
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Action Research 6---Kristen Iaccio, Linking Mathematics to Social Issues |
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216 | (7) |
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Math Worlds 6: Same Math, Different Metaphors |
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223 | (2) |
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Places where People Learn Mathematics |
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225 | (28) |
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Structuring Ways of Working |
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228 | (10) |
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Criteria for ``Performance'' |
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238 | (1) |
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Leadership, Voice, and Participation |
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239 | (4) |
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The Teacher's Way of Working |
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243 | (2) |
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Response to
Chapter 7: The Classroom is Always Changing |
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245 | (3) |
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Action Research 7---Petal Sumner, Empowering Students Who Don't Learn |
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248 | (5) |
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When Students Don't Learn |
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253 | (33) |
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255 | (2) |
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257 | (4) |
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Practicing Thinking Mathematically Outside of the Regular Work |
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261 | (3) |
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Concretizing Academic Literacy |
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264 | (2) |
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266 | (3) |
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Separate and Connected Knowing |
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269 | (4) |
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The Myth of Instructive Interaction |
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273 | (4) |
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Stories and Explanations; Causes and Treatments |
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277 | (5) |
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Response to
Chapter 8: We Are All Students |
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282 | (4) |
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EPILOGUE: Becoming a Teacher and Changing with Mathematics |
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286 | (10) |
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Habituation, Conceptual Construction, and Enculturation |
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290 | (3) |
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Youth Culture and the Smell of Content |
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293 | (3) |
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AFTERWORD: What will You Write in Your
Chapter? |
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296 | (2) |
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298 | (33) |
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1. Infrastructure for a Unit |
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298 | (2) |
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2. Criteria for Working as a Mathematician |
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300 | (4) |
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3. Mathematician's Notebook---Checkpoint |
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304 | (1) |
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4. ``Polya Was a Mathematician'' Songsheet |
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305 | (1) |
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306 | (4) |
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6. Math Worlds Hints and Comments---Bernadette Bacino |
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310 | (21) |
| Bibliography |
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331 | (7) |
| Name Index |
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338 | (3) |
| Subject Index |
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341 | |
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