Theory of Objectification

Luis Radford is a full professor at Laurentian University in Canada. His research focuses on the teaching and learning of mathematics from a cultural-historical perspective, and education as a transformative societal process. He conducts classroom research with primary and high school teachers.

• PrefaceFigures and TablesIntroduction: The Ascent from the Abstract to the Concrete1 Theories in Mathematics Education1 Outline2 A Classroom Episode3 Research Questions4 Method5 Theoretical Principles6 Piaget’s Genetic Epistemology7 From Method to Methodology8 Mathematics Education Theories: Two Short Examples9 The Theory of Objectification2 An Overview of the Theory of Objectification1 Outline2 Introduction3 Theoretical Underpinnings of the Theory of Objectification4 Summing up and Looking Ahead3 Knowledge and Knowing1 Outline2 Knowledge3 Knowing4 The Piggy Bank Example5 The Dialectic between Knowledge and Knowing6 Mathematics as an Entity at the Same Time Ideal, Sensible, and Material7 Synthesis4 Learning1 Outline2 Learning as Participation in Social Practice3 Internalisation4 Processes of Objectification5 Some Meanings of Objectification6 Processes of Objectification7 Learning as Objectification8 Consciousness9 Teaching-Learning Activity10 Processes of Subjectification11 Synthesis5 Processes of Objectification1 Outline2 The Investigation of Processes of Objectification3 Teaching-Learning Activity4 An Example of Investigation of Processes of Objectification5 Semiotic Means of Objectification6 Semiotic Nodes7 Semiotic Contraction8 Concept9 Synthesis6 Embodiment1 Outline2 Introduction3 The Intertwining of the Senses and Culture4 Perception5 A Classroom Example6 The Poetry of Objectification7 Counting the Unseen8 Synthesis7 Task Design: Or Configuring Teaching-Learning Activities1 Outline2 General Considerations3 The Motion of Tina, John, and the Dog4 Synthesis8 The Cultural Nature of Mathematical Thinking1 Outline2 Introduction3 Boas’s Relativist Conception of Culture4 The Anthropological Venerable Conflict5 A Dialectical Materialist View of Culture6 Greek Mathematical Thinking Revisited7 Synthesis9 Processes of Subjectification1 Outline2 The Question of the Subject3 Semiotic Systems of Cultural Signification4 Being, Becoming, and Subjectivity5 Solving Equations in a Grade 3 Classroom6 Synthesis10 Ethics1 Outline2 The Ineludible Presence of Ethics in the Mathematics Classroom3 Kant4 Hobbes5 Lévinas’s Ethics6 The Indispensable Task of (Mathematics) Education7 Towards a Communitarian Ethics8 SynthesisReferencesIndex