Mapping Equity and Quality in Mathematics Education (eBook)

Preface 5
Contents 9
Contributors 13
Part I 34
The Theoretical Landscape 34
Chapter 1 35
Disrupting ‘Development’ as the Quality/Equity Discourse: Cyborgs and Subalterns in School Technoscience 35
Women, Mathematics, Technology and other Dangerous Things 36
Development as Quality: Intensity for Change 39
Development as Equity: The Urgency for All to Change 43
Conclusionary Remarks 46
References 49
Chapter 2 52
Beyond Gap Gazing: How Can Thinking About Education Comprehensively Help Us (Re)envision Mathematics Education? 52
Destabilizing the Achievement Gap Discourse 53
Thinking About Education Comprehensively 57
Exploring Mathematics Education Comprehensively 58
Rethinking (the Roles of) Mathematics 59
Conclusion 62
References 63
Chapter 3 66
Beyond Disavowing the Politics of Equity and Quality in Mathematics Education 66
Introduction 66
The Framing of the Research Field 67
The Framing of “Equity” 69
The Framing of “Quality” 71
The Disavowing of Politics in Mathematics Education 74
Threshold 76
References 77
Chapter 4 80
Does Every Child Count? Quality, Equity and Mathematics with/in Neoliberalism 80
Our Framework 81
Policy Documents 82
Student-Teacher Interviews 87
Conclusions 91
References 92
Chapter 5 94
Quality and Equity in Mathematics Education as Ethical Issues 94
Tensions Within the Discourses of Quality and Equity 95
Relationship Between Equity and Quality 98
Ethical Responsibility 100
Constructing Quality and Equity as Ethical Concerns 101
Conclusions 104
References 104
Chapter 6 107
Ghettoes in the Classroom and the Construction of Possibilities 107
Introduction 107
Episodes from the School 108
Equity and Quality 113
Emerging Categories 115
Ghettoes in the Classroom 116
Construction of Possibilities 117
Final Considerations 119
References 120
Chapter 7 121
Identity as the Cornerstone of Quality and Equitable Mathematical Experiences 121
Introduction 121
Identity at the Core of Quality Mathematical Experiences 123
Identity at the Core of Equitable Mathematical Experiences 125
Equity and Quality Under Erasure 127
The Lacanian Response 128
Conclusion 131
References 132
Chapter 8 135
A Framework for Evaluating Quality and Equity in Post-Compulsory Mathematics Education 135
Introduction 135
Quality in Post-Compulsory Education 136
Towards a Quality Framework 142
Conclusion 149
References 150
Chapter 9 152
The Theoretical Landscape 152
Editor’s Reaction to Part I 152
References 155
Part II 157
Mapping Social Constructions andComplexities 157
Chapter 10 158
Equity in Quality Mathematics Education: A Global Perspective1 158
Potential Inequity Factors in Mathematics Education at the Global Level 160
Country Indicators and Mathematics Achievement 162
Relationship Between Equity and Quality at the Country Level 164
How Does the Country’s Economic and Educational Status Moderate the Relationship Between Equity and Quality of Mathematics Educa 166
Optimal and Separate Modes of Development in Mathematics Education 167
Contrasting the Developmental Profiles of Optimal and Separate Modes of Development 168
Concluding Remarks 169
References 170
Chapter 11 172
Effects of Student-Level and School-Level Characteristics on the Quality and Equity of Mathematics Achievement in the United Sta 172
Introduction and Literature Review 172
Data and Results 174
Conclusions and Discussion 184
Appendix 186
References 187
Chapter 12 189
Equity and Quality Issues in Mathematics Education in Malawi Schools 189
Introduction 189
Background 190
Equity Groups 191
Indicators of “Quality” 195
Prospects of Change 197
Critical Reflection of Prospects 198
Conclusion 201
References 201
Chapter 13 203
Looking for Equity in Policy Recommendations for Instructional Quality 203
Introduction 203
Equity as an Analytical Lens 204
Overview of Reports and Methods 207
Analysis: Looking for Equity 208
Discussion 212
Conclusion 214
References 214
Chapter 14 217
Whose ‘Quality’ and ‘Equity’? The Case of Reforming 14–16 Mathematics Education in England 217
Introduction 217
The Context 219
Recent Developments 222
Mapping the Field 225
Final Comments 227
References 229
Chapter 15 231
Equity and Quality of Mathematics Education: Research and Media Portrayals 231
Introduction 231
Scholarly Research on Equity and Quality in Mathematics Learning 233
Concluding Comments 244
References 246
Chapter 16 249
Equity Concerns About Mathematical Modelling 249
Introduction 249
Modelling as Recontextualisation 251
Different Versions of Modelling in the Classroom: Who Has Access to the Principles? 252
Equity Concerns About Modelling in the Classroom 255
Modelling as a Basis for Curriculum Construction: Concerns and Potential 259
References 261
Chapter 17 263
Equity and the Quality of the Language Used in Mathematics Education 263
Introduction 263
An Episode from the Lesson Sequence “Least Common Multiple” 265
Prospects 275
Appendix References 276
Chapter 18 278
Foundational Mathematics: A Neglected Opportunity 278
Early Childhood Education: Why Does It Neglect Mathematics? 280
Mathematics Education: Why Does It Neglect Early Childhood? 282
Why Should We Call Early Mathematics Foundational? 283
Improving Teachers’ Understandings of Foundational Mathematics 286
Conclusion 289
References 290
Chapter 19 294
How Many Sides Does a Box Have? The Struggle to Respect Young People’s Thinking 294
Introduction: How a Riddle Helped Me Become More Respectful of Students 294
What Does Respect Mean? 295
The Relationship of Respect to Equity and Quality in Mathematics Education 296
The Struggle in Society 298
The “Math Wars” in California 300
Why Does the Struggle Exist? Why Has There Been Progress? 301
Toward a Strategy for Respecting Young People’s Thinking 302
Conclusion 306
References 307
Chapter 20 309
‘Sometimes I Think Wow I’m Doing Further Mathematics…’: Balancing Tensions Between Aspiring and Belonging 309
Why Does Further Mathematics Matter? 309
Historical Constructions of Further Mathematics 311
Changing Further Mathematics 314
Practices of the Self 317
Conclusion 320
References 321
Chapter 21 323
Mapping Social Constructions and Complexities 323
Editor’s Reaction to Part II 323
Part III 329
Landmarks of Concern 329
Chapter 22 330
Students with ‘Special Rights’ for Mathematics Education 330
Introduction 330
Special Rights in Mathematics Education 331
Quality Mathematics Education for Students with Special Rights 334
Equitable Access to Quality Curriculum 340
Advocating for Research and Development for Students with Special Rights 342
Conclusion 343
References 343
Chapter 23 347
Females in Mathematics: Still on the Road to Parity 347
Perceptions of Gender Equality in Mathematics 348
Mathematics Achievement 348
Course Completion and Career Paths 350
Mathematics-Related Dispositions 351
Role of Teachers, Parents, and Society 352
Quality Mathematics Education for Females 354
Closing Comments 355
References 357
Chapter 24 362
Quality and Equity in Mathematics Education: A Swedish Perspective 362
Introduction 362
The Swedish Situation Today 363
A Short History of Swedish Education 365
Back to the Current Situation 367
Taking Stock and Looking Ahead 368
Summing It Up 369
References 369
Chapter 25 372
Equity Issues Concerning Gifted Children in Mathematics: A perspective from Mexico 372
Introduction 372
Some Concerns About the Education of Mathematically Gifted Students 375
Societal Concerns 376
Our Approach 379
Internet Cafés 380
Concluding Comments 382
References 383
Chapter 26 386
Enhancing Quality and Equity in Mathematics Education for Australian Indigenous Students1 386
Introduction 386
Building Mathematics Curriculum Through Partnership 387
Mathematics Education and Indigenous Students—Program Criteria and Reflections from an Aboriginal Educator 388
Mathematics Programs for Indigenous Students 394
Conclusion 396
References 397
Chapter 27 400
Qualities of Respectful Positioning and Their Connections to Quality Mathematics 400
Quality Mathematics Education in Context 401
Positioning Students as Participants in Community Interaction 403
Examining Student Work 406
Reflection 409
References 411
Chapter 28 413
The Effects of Poverty and Language on Mathematics Achievement for English Language Learners 413
System Factors That Impede ELLs Mathematics Achievement 414
Closing the Gap Between Theory and Practice 419
Conclusions 422
References 423
Chapter 29 427
Toward a Framework of Principles for Ensuring Effective Mathematics Instruction for Bilingual Learners Through Curricula 427
Background 429
Examination of FO/D 431
A Framework for Equity and Quality in Mathematics 432
Implications and Conclusions 439
References 440
Chapter 30 443
Reconceptualizing Quality and Equity in the Cultivation of Minority Scholars in Mathematics Education 443
The Intersection of Equity and Quality 443
HBCUs as Spaces for Equity as Social Justice 447
The Doctor of Education (EdD) in Mathematics Education at MSU 448
Enhancing Achievement Outcomes 449
Increasing Sensitivity to the Exclusionary Nature of Mathematics Education 450
Developing Commitment to Social Justice 451
Conclusion 452
References 453
Chapter 31 456
What Does Quality Mean in the Context of White Institutional Space? 456
Framing Quality 456
Quality in Service to Nationalism—Nationalism in Service to Racism 458
Does All Really Mean All? 460
White Institutional Space and Mathematics Education Reform 462
Quality, Good Intentions, and the Needs of Black Children 464
Conclusion 466
References 467
Chapter 32 470
Landmarks of Concern 470
Editor’s Reaction to Part III 470
Exploring the Chapters 471
Part IV 474
No Highway and No Destination? 474
Chapter 33 475
The CERME Spirit: Issues of Quality and Inclusion in an Innovative Conference Style 475
Introduction 475
Locating Concepts and Concerns Within a Wider Frame 477
Views of Participants Regarding the CERME Activity 481
Discussion of Emergent Issues and a Tentative Framework for Further Consideration 489
References 494
Chapter 34 496
Productive Pedagogies in the Mathematics Classroom: Case Studies of Quality and Equity 496
Introduction 496
Magnolia State School 498
Azalea P-10 502
Conclusion 506
References 508
Chapter 35 509
Mathematical Literacy in South Africa: Increasing Access and Quality in Learners’ Mathematical Participation Both in and Beyond 509
Introduction 509
Mathematical Literacy in South Africa 510
Defining Identity 513
Reflecting on the Story 518
What Curricula Features Support “Living Different (Mathematical) Stories?” 519
Discussion and Conclusions 522
References 523
Chapter 36 525
Together-and-APart for Quality and Equity in Mathematics Education 525
The Conflict Between Quality and Equity 525
The TAP Rationale 528
TAP’s Main Guidelines 529
Achieving TAP’s Goals 531
References 533
Chapter 37 536
Research from Practice: Using Technology to Provide Advanced Mathematics and Equity to High School Students in the United States 536
The Advanced Placement (AP) Program and Equity Issues 537
The AP Problem at Jefferson High School 538
A Solution to Jefferson High School’s AP Problem 539
Forming a Connection with Washington High School 539
Creating Quality and Equity in the Classroom: One Class in Two Locations 540
Results of the Collaboration 541
Analysis of the Collaboration: Benefits and Affordances 542
Analysis of the Collaboration: Problems and Concerns 544
Conclusion 545
References 547
Chapter 38 548
Parents and Teachers Collaborate to Achieve Equity and Quality in Mathematics: A Case Study 548
Background 548
High-Quality Mathematics Instruction for English Learners 550
Results from the “Classroom Project” 552
References 556
Chapter 39 558
Critical Mathematics in a Secondary Setting: Promise and Problems 558
Introduction 558
Study Context 559
Inequalities and Area 561
Discussion 566
References 569
Chapter 40 570
Mathematics Education: What is the Point? 570
Alternatives to Traditional and Reform Emphases in Mathematics Education 571
Mathematics Teacher Education and the MEPI Project 572
Math for Social Analysis 574
MEPI Research Results 576
Discussion 579
References 581
Chapter 41 584
Equity and Quality in a Mathematics Program for Under-Represented Students at an Elite Public University 584
Background 585
The University of Michigan, the Introductory Calculus Program, and DHSP 586
Documenting Impact on Students 589
Instruction Matters 591
Keeping the Program Running 595
References 598
Chapter 42 600
Children’s Numerical Thinking in the Early School Grades and How to Foster and Understand Its Development 600
The Social Setting of Primary School in Mexico 601
Primary School and Low Academic Performance 601
The Psychologists’ Role in Low Mathematics Achievement 603
The Program to Address Low Academic Performance 604
Arithmetic in the Early Grades of Primary School 605
Final Remarks 613
References 613
Chapter 43 615
No Highway and No Destination? 615
Editor’s Reaction to Part IV 615
Many Ways to Promote Equity and Quality 615
No Highways 617
No Destination 618
References 618
Author Index 619
Subject Index 626