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Preface
6
Contents
8
Part I Equity in Quality in Mathematics Education: Contexts and Perspectives
14
My Journey Toward Equity in Quality
15
The Nineteen Fifties: The School Years
15
The Nineteen Sixties: The University Years
17
The Start of a Career in Mathematics Education
19
The Nineteen Eighties: The Beginning of the Social Turn
24
The Nineteen Nineties: Problem Solving in School and Outside
26
The Present: Reflecting on the Past and Looking Ahead
28
Historical Evolution of Equity and Quality in Education and in Math Education
30
The Evolution of Educational Equity and Quality
30
The Fifties and Sixties
30
The Seventies
31
The Eighties
31
The Nineties
31
The First Decade of the Twenty-First Century
32
The Evolution of Equity and Quality in Mathematics Education Literature
33
The Fifties and Sixties
33
The Seventies
36
The Eighties
36
The Nineties
37
The Evolution of Equity and Quality in Mathematics Education in ICMI and PME Activities
38
ICMI Studies
39
The ICME Congresses
39
The PME Annual Conferences
39
Conclusion
43
Equity in Quality: Towards a Theoretical Framework
45
Quotations
46
Quotation 1: Inside and Outside School
46
Quotation 2: In the Same Classroom
46
Quotation 3: Inside and Outside a Country
47
Quotation 4: Across Countries
48
Equity and Quality in the School as a Production System
48
The School as a Production System
48
Equity in the Production System
49
Quality in the Production System
50
Revisiting the Quotations from the Perspective of the Production System
51
Comments on Equity and Quality in the School as a Production System
52
Activity Theory and Mathematics Education
53
Activity Theory
53
Activity System
54
Mathematics Education as an Activity System
55
Mathematics Education as a Nested Hierarchical Complex Activity System
56
Equity and Quality in the Activity System
56
Equity in the Activity System
57
Quality in the Activity System
57
The Activity System and the Social-Cultural-Political Nature of Math Education
58
Revisiting the Quotations from the Perspective of Activity System
59
The School Context
61
Math Education System at the School Level: Factors and Their Attributes
61
Mathematics Learning
62
Student
62
Classroom Community
63
Mediating Artifacts
63
Division of Labor
63
Rules
64
Interactions and Inequities: Two Examples
64
Inequities Related to Student, Mediating Artifacts, and Division of Labor Interactions
65
Student Personal Traits and Mathematics Mediating Artifacts in the Classroom
65
Student Socioeconomic Background and Mathematics Mediating Artifacts in the Classroom
66
Student Cultural Background and Mathematics Mediating Artifacts in the Classroom
67
Distribution of Labor and Classroom Community
70
Inequities Related to Student, Classroom, and Mathematics Achievement Interactions
70
Gender and Mathematics Achievement
71
Student Socioeconomic Background and Mathematics Achievement
72
Student Cultural Background and Mathematics Achievement
73
Student Perceptions of Self in Relation to the Class Community and Mathematics Achievement
74
Classroom Practices and Mathematics Achievement
75
Inequities Related to School Policies and Sociocultural Context
76
Concluding Remarks
77
The National Context
78
Math Education System at the National Level: Factors and Their Attributes
78
School
79
Educational System Community
80
Division of Labor
80
Interactions and Inequities: An Example
80
Inequities Related to School, Education School System, and Mediating Artifacts Interactions
81
General Pattern of Interactions
81
The Two-Tier Education System in Developing Countries
83
The Two-Tier Education System in Developed Countries
85
Inequities Related to the Interaction of School and Mathematics Learning Outcomes
88
School Socioeconomic Cultural Background and Mathematics Achievement
88
Other School Factors and Mathematics Achievement
88
Inequities Related to the Interaction of State Policies and the Education System
89
Decentralization of the Education System and Mathematics Achievement
89
Differentiation of the Education System and Mathematics Achievement
90
School Privatization and Mathematics Achievement
91
Concluding Remarks
91
The Global Context
93
Math Education System at the Global Level: Factors and Their Attributes
93
Math Education
93
Country
94
The Math Mediating Artifacts
95
The International Math Education Community
95
Division of Labor
95
Rules
95
Interactions and Inequities: An Example
96
Inequities Related to Country, Community, and Division of Labor Interactions
96
Inequities Related to the Interaction of Country and Mathematics Learning
97
Inequities Related to the Interaction of International Policies and Participation
99
International Policies
99
Exchange and Transfer
100
Concluding Remarks
101
Part II Equity in Quality in Mathematics Education: Across Countries Comparisons Based on TIMSS 2003 Results
103
Methodology
104
A Theoretical-Methodological Issue
104
Research Method in Activity Theory
104
Research Method in Contextualism
105
TIMSS 2003 Background Questionnaires
106
Summary Indices and Derived Variables from Questionnaire Data
106
Student-Level Indices
107
Teacher-Level Indices
108
School-Level Indices
108
Single-Item Variables
109
Student-Level Variables
109
Teacher-Level Variables
109
Dependent Variables
110
The Sample of Countries
110
Statistical Analysis
111
Equity Measure
112
Inequity Index
112
Inequity Factor
112
Student-Related Inequity Factors
113
Student Indices
114
Index of Student Educational Aspiration Relativeto Parents' Education
114
Index of Student Self-confidence in Learning Mathematics
115
Index of Parents Highest Education Level
119
Index of Computer Use
119
Index of Student Perception of Being Safe in School
121
Summary of Student Indices as Inequity Factors
124
Student Practices
125
How Often Students Explain Their Answersin Mathematics Lessons
125
How Often Students Work Problems on Their Own in Mathematics Lessons
126
How Often Students Have a Quiz or Test in Mathematics Lessons
129
How Often Students Use Calculators in Mathematics Lessons
129
How Often Students Work Together in Small groups in Mathematics Lessons
132
Summary of Student Practices as Inequity Factors
132
Teacher-Related Inequity Factors
135
Teachers' Indices
136
Index of Mathematics Teachers' Perception of School Climate
136
Index of Teachers' Reports on Teaching Mathematic Classes with Few or no Limitations on Instruction due to Student Factors
138
Index of Teachers' Emphasis on Mathematics Homework
140
Class Size for Mathematics Instruction
143
Teacher Practices
143
Concluding Remarks
144
School-Related Inequity Factors
145
Index of Principal Perception of School Climate
146
Index of Good School and Class Attendance
148
Concluding Remarks
148
Global Inequity Factors
151
Country Indicators
151
Educational Indicators
151
Economic Educators
152
Country Indicators and Mathematics achievement
153
The Relationship Between Equity and Quality at the Country Level
154
Country Inequity Index
154
Country Quality Index
155
Quality-Inequity Matrix
155
Optimal and Separate Modes of Development in Mathematics Education
156
Contrasting the Developmental Profiles of Optimal and Separate Modes of Development
157
Concluding remarks
159
Epilogue
160
Some Generalizations
160
A Cross-Layer Perspective of the Math Education Activity System
161
Interpretation of TIMSS 2003 Data Analysis Through the Activity System Lens
163
System-Wise Transformation to Achieve Equity In Quality
163
Transformation in the Activity System
165
System-Wise Transformation: The Case of Lebanon
166
The Context
166
The Inequity
166
The Conflict
167
A Suggested Strategy
167
References
170
Index
179
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