Alternative Theoretical Frameworks for Mathematics Education Research (eBook)

Elizabeth de Freitas is an associate editor at the journal Educational Studies in Mathematics, and has published over 40 articles and chapters, both in mathematics education and education more generally, including articles in Qualitative Inquiry, Educational Theory and Philosophy, Studies in Philosophy of Education, and Teaching Education. Her research spans cultural studies, philosophy of education, research methods, and empirical studies in mathematics education. She is co-editor of the book: Opening the research text: Critical in(ter)ventions into mathematics education (2008, Springer), and co-author of the book Mathematics and the body: Material entanglements in the classroom (2014, Cambridge University Press). Margaret Walshaw is sole author of two books: Working with Foucault in Education, published by Sense Publishers in 2007, and Getting to Grips with Doctoral Research, published by Palgrave Macmillan in 2012. She is co-author of the book Are our Standards Slipping? Debates over Literacy and Numeracy Standards in New Zealand since 1945, published by NZCER in 2010, and co-author of Effective Pedagogy in Mathematics/Pāngarau: Best Evidence Synthesis Iteration [BES], published by Learning Media in 2007. In addition, she is sole editor of the book Mathematics Education Within the Postmodern, published by Information Age in 2004, and sole editor of the book Unpacking Pedagogy: New Perspectives for Mathematics Classrooms, published by Information Age in 2010. Margaret is currently associate editor of the Journal of Mathematics Teacher Education [JMTE]. She has published in the Review of Educational Research; Curriculum Inquiry; Pedagogies: An International Journal; the Journal for Research in Mathematics Education; Educational Studies in Mathematics; Cambridge Journal of Education; and in the British Journal of Sociology of Education.

Preface 5
Contents 6
Chapter 1: Introduction 9
Idea Clusters 9
Mapping Theory 12
Context 14
Book Outline 17
References 17
Chapter 2: Lev Vygotsky 19
The Key Theme in Vygotsky’s Work 25
Concepts Fundamental to Vygotsky’s Work 25
Mediation 27
The Interrelationship Between Thought and Language 28
The Psychology of Play 28
Zone of Proximal Development 29
Scaffolding 30
Applications 31
Different Kinds of Activity 36
Explanation of Notation Used for the Following Sections 36
Situational Activities 36
Pedagogical activities 38
Mathematizing Activities 40
Summary 43
References 43
Chapter 3: Michel Foucault 46
Foucault’s Early Work 48
Foucault’s Archaeological Phase 49
Foucault’s Genealogical Phase 50
Foucault’s Turn to Ethics 51
Key Concepts in Foucault’s Toolkit 53
Discourse 53
The Subject 55
Power 56
Power-Knowledge 57
Power-Knowledge-Truth 57
Regime of Truth 58
Governmentality 58
Technologies of the Self 58
Applications 59
Summary 68
References 69
Chapter 4: Jacques Lacan 72
Subjectivity 75
Concepts Grounding the Theory of the Subject 77
Applications 82
Contextualizing an Analysis of Gendered Subjectivity 86
Stories from Home and Early School 87
The Order of the Classroom 89
Mathematical Identity in Conflict 92
Summary 94
References 95
Chapter 5: Gilles Deleuze 99
Introduction 100
State Versus Nomadic Mathematics 101
Difference, Identity and Number 102
Chance and the Differential 103
A Zigzag Learning Trajectory 106
Smooth and Striated Space 109
Applications 112
The Philosophy of Mathematics 113
What Is Number? 114
Expanding the Concept of Number 117
Summary 123
References 124
Chapter 6: Bruno Latour 127
Introduction 128
What is the Social? 129
Follow the Actors 130
Follow the Controversy 132
The Role of Speculation and Art 134
Assemblages and Relational Ontology 136
Imitation and the Quantitative 137
Applications 139
Big Networks and Graph Analysis 139
Tracking Associations and Imitations 140
The Nonhuman Actant: Instructional Technology 143
Summary 152
References 153
Chapter 7: Karen Barad 155
Introduction 156
Rethinking Matter 157
The Material-Discursive and Relationality 159
What Does Diffraction Look Like? 161
More Than Human Performativity 164
The Polyamorous Field of Concepts 167
Applications 171
Design and Teaching Experiments 171
A Diffractive Apparatus 173
The Virtuality of Time and Gesture 175
Summary 178
References 178
Chapter 8: Concluding Narratives 180
Phase 1: Preliminary Email Discussions 182
Phase 2: Skype Meetings and Further Emails 184
Phase 3: Face-to-Face Discussions 186
Phase 4: Continuing Email Discussions and Skype Meetings 187
Phase 5: Reviewing and Finalizing the Theorists 193
References 195
Index 196