Embracing Mathematics, On Becoming a Teacher and Changing with Mathematics

Peter Appelbaum e David Scott Allen

Routledge | 2008 | 369 páginas | PDF | 7 MB

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This alternative textbook for courses on teaching mathematics asks teachers and prospective teachers to reflect on their relationships with mathematics and how these relationships influence their teaching and the experiences of their students. Applicable to all levels of schooling, the book covers basic topics such as planning and assessment, classroom management, and organization of classroom experiences; it also introduces some novel approaches to teaching mathematics, such as psychoanalytic perspectives and post-modern conceptions of curriculum. Traditional methods-of-teaching issues are recast in a new discourse, provoking new ideas for making mathematics education meaningful to teachers as well as their students. Co-authored by a professor and coordinator of mathematics education programs, with illustrative contributions from practicing elementary, middle, and high school mathematics teachers, this book is a unique collaboration across all pre-college grades, making it ideal for teacher discussion groups at any level.

Embracing Mathematics:

• integrates pedagogy and content exploration in ways that are unique in mathematics education
• features textboxes with reflection questions and suggested explorations that can be easily utilized as homework for a course or as discussion opportunities for teacher reading groups
• offers examples of teachers’ action research projects that grew out of their interactions with the main chapters in the book
• is not narrowly limited to mathematics education but incorporates curriculum studies – an invaluable asset that allows instructors to find more ways to engage students in self-reflexive acts of teaching

Embracing Mathematics is intended as a method text for undergraduate and master’s-level mathematics education courses and more specialized graduate courses on mathematics education, and as a resource for teacher discussion groups.

Contents
PREFACE: How Can I (Better) Embrace Mathematics? — David Scott Allen xvii
ACKNOWLEDGMENTS: Peter Appelbaum xxi
ACKNOWLEDGMENTS: David Scott Allen xxiii
PROLOGUE — Peter Appelbaum 1
Response to Prologue: Be a Student of Mathematics Learners 14
CHAPTER 1: Planning and Assessment 19
Response to Chapter 1: Engage Yourself in Meaningful Observation 35
Action Research 1 — Isaiah Manzella, Numbers on Trial 40
MathWorlds 1: Reverse Answer to Questions 49
CHAPTER 2: A Psychoanalytic Perspective 51
Response to Chapter 2: Ask Yourself to Change 83
Action Research 2 — Karen Cipriano, Flexible Interview Project 86
MathWorlds 2: Multiple Answers 89
CHAPTER 3: You Are a Mathematician 91
Response to Chapter 3: Explore the Vastness of Mathematics 122
Action Research 3 — Karen Cipriano, Mathematics Journals 127
MathWorlds 3: Reading and Writing Mathematics 129
CHAPTER 4: Critical Thinkers Thinking Critically 130
Response to Chapter 4: It is Critical to Think 146
Action Research 4 — Ada Rocchi, Lesson: World Population and Wealth 148
MathWorlds 4: Pitching Questions at Various Levels 158
CHAPTER 5: Consuming Culture: Commodities and Cultural Resources 159
Response to Chapter 5: Emphasize the Meaning-making of Mathematics 177
Action Research 5 — Colleen Murphy, A School-wide Survey 180
MathWorlds 5: Turning “Puzzles” into “Problems” or “Exercises” 184
CHAPTER 6: Metaphors for the Classroom Space 187
Response to Chapter 6: Take Ownership of your Classroom Space 212
Action Research 6 — Kristen Iaccio, Linking Mathematics to Social Issues 216
MathWorlds 6: Same Math, Different Metaphors 223
CHAPTER 7: Places where People Learn Mathematics 225
Response to Chapter 7: The Classroom is Always Changing 245
Action Research 7 — Petal Sumner, Empowering Students Who Don’t Learn 248
CHAPTER 8: When Students Don’t Learn 253
Response to Chapter 8: We Are All Students 282
EPILOGUE: Becoming a Teacher and Changing with Mathematics 286
AFTERWORD: What will You Write in Your Chapter? 296
APPENDICES
1. Infrastructure for a Unit 298
2. Criteria for Working as a Mathematician 300
3. Mathematician’s Notebook—Checkpoint 304
4. “Polya Was a Mathematician” Songsheet 305
5. Taking Action 306
6. MathWorlds Hints and Comments — Bernadette Bacino 310