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