TABLE OF CONTENTS
PREFACE v
ACKNOWLEDGMENTS xi
DEDICATION xiv
LIST OF TABLES xv
LIST OF FIGURES xvi
LIST OF VIGNETTES xvii
FOREWORD xviii
CHAPTER 1: CULTURE, COMMUNITY, AND MATHEMATICS
ACHIEVEMENT 1
Introduction 1
Mathematics Achievement in the U.S. 5 School Demographics and Education Reform 9
Theoretical Framework 12
Prior Research on Culturally Based Education 18
Teachers’ Beliefs about Culture and Mathematics 23
Mathematics Identity and Mathematics Socialization 29
CHAPTER 2: COGNITION AND CULTURAL PEDAGOGY 33
Culture, Cultural Transmission, and Cultural Capital 33
Theories about Cognition and Culture 35
Cognitive Theory 36
The Saxe Model of Cognition 39
Children’s Cognition and Learning in Mathematics 43
Culture and Children’s Mathematical Reasoning 50
Reform-based Education to Opportunities to Learn 56
Definitions and Descriptions of Constructivism 63
Role of Culture in Constructing Knowledge 64
Beliefs about Constructivist Pedagogy 65
Summary 67
CHAPTER 3: CULTURAL PEDAGOGY 69
The Need for Cultural Pedagogy 69
Types of Cultural Pedagogy 73
Culturally Relevant Teaching 75
Cultural Brokering 78
Border Crossing 82
Culturally Responsive Teaching 85
Culturally Specific Pedagogy 87
Diversity Pedagogy 98
Summary 101
CHAPTER 4: PROBLEM SOLVING, PROBLEM POSING, MULTI-CULTURAL LITERATURE AND COMPUTER SCAFFOLDING 105
Introduction 105
How Children Learn to Solve Mathematics Problems 105
The Problem Solving Process 107
Learning to Pose Problems to Students 117
Using Multicultural Literature as a Context for Problem Solving 118
Emerging Technology and Problem Solving 122
Computer-Assisted Instruction 123
The Benjamin Banneker Project 127
The Classroom Discourse 128
The Computer Module 136
Analysis of Computer-based Mathematics Problems 138
Student Interviews 143
Analysis of Student Interviews 145
Teacher Interviews 147
Mr. Perez 147
Ms. Jordan 147
Ms. Clark 148
Analysis of Teacher Interviews 148
Discussion 149
Summary 150
CHAPTER 5: THE UNDERGROUND RAILROAD: A CONTEXT
FOR LEARNING MATHEMATICS AND SOCIAL JUSTICE 152
On the Socialization of African American Children 152
The Mis-Education of African American Students in Mathematics 153
Linking Mathematics with Culture 156
Using Stars and Constellations as a Context for Learning
Mathematics 158
The Case of Ms. Cho 158
The Case of Ms. Baker 165
Multicultural Literature, Mathematics Literacy and Social
Consciousness 170
Sweet Clara and the Freedom Quilt 172
Analysis of Quilting Lesson 175
Making Connections to Issues of Social Justice 176
Linking Social Justice to Literacy 178
Analysis of Student Journals 181
Violence and Fear 183
Freedom for Self and Family 183
Determination and Hope 184
Summary 187
CHAPTER 6: WOMEN IN AVIATION AND SPACE: THE
IMPORTANCE OF GENDER ROLE MODELS IN MATHEMATICS
EDUCATION 190
Introduction 190
Gender Equity in Mathematics and Science 191
Gender and Academic Achievement in Mathematics 195
Single-Sex Education 202
Gender-Inclusive Culturally Specific Practices 204
The Bessie Coleman Project 205
Space Links: Integrating Space Science and Mathematics 210
Teacher Efficacy 213
Science Instruction 214
Preservice Teacher Reflections 221
Analysis of Reflections 223
Discussion 225
Implications 226
CHAPTER 7: LEARNING MATHEMATICS FOR
EMPOWERMENT IN LINGUISTICALLY AND CULTURALLY
DIVERSE CLASSROOMS 227
Introduction 227
Understanding Language Acquisition 232
Developing Additive Perspectives 237
Use of Multimedia to Support Mathematics Learning 238
Parental Involvement 244
Fostering Native Language Literacy in the Mathematics Classroom 246
Reflections of a Mathematics Educator 252
Reflections on Practice 252
Reflections on Classroom Research 260
CHAPTER 8: RACE AND ACHIEVEMENT IN MATHEMATICS 268
A Historical Perspective 268
Perspectives on the Achievement Gap 278
Mathematics Socialization and Identity among African American
Students 282
Links to Everyday Mathematics 289
Conclusions and Recommendations 291
APPENDIX A: Research Methods: Benjamin Banneker Project 297
APPENDIX B: Interview Protocol 303
APPENDIX C: Culturally Specific Lesson Plans 304
APPENDIX D : Research Methods: Space Links 310
APPENDIX E: Galaxy Lab Sheet 313
APPENDIX F: Preservice Teacher Interview Protocol 314
REFERENCES 315
BIOGRAPHICAL NOTE 356