Adventures of Mind and Mathematics

Description

This monograph uses the concept and category of “event” in the study of mathematics as it emerges from an interaction between levels of cognition, from the bodily experiences to symbolism. It is subdivided into three parts.The first moves from a general characterization of the classical approach to mathematical cognition and mind toward laying the foundations for a view on the mathematical mind that differs from going approaches in placing primacy on events.The second articulates some common phenomena–mathematical thought, mathematical sign, mathematical form, mathematical reason and its development, and affect in mathematics–in new ways that are based on the previously developed ontology of events. The final part has more encompassing phenomena as its content, most prominently the thinking body of mathematics, the experience in and of mathematics, and the relationship between experience and mind. The volume is well-suited for anyone with a broad interest in educational theory and/or social development, or with a broad background in psychology. Preface Contents Part I: Foundations Chapter 1: Toward an Organismic Theory of Mind 1.1 Mathematics in Action 1.2 Self-Action and Interaction 1.3 Transaction 1.4 Ways of Thinking about and Researching the Mind References Chapter 2: Primacy of Events 2.1 An Exemplifying Analysis 2.2 Events and their Relations 2.3 Object–Things 2.4 Family of Events (Nexus) 2.5 Events Before Things References Part II: Extensions Chapter 3: Mathematical Thinking as Event 3.1 From an Ethnography of Mathematical Thinking 3.2 The Event of Thinking 3.2.1 The Advent(ure) of Thinking 3.2.2 From States to Flow 3.2.3 From Thinking-as-Event to Entitative Thought 3.2.4 From the Saying-as-Event to the Said-Thing 3.3 From Mathematical Thought to Moving Thinking 3.4 Acknowledging a World in Constant Flux References Chapter 4: On Signifier Things and Signing-as-Event 4.1 Toward a Pragmatic Position on Signs and Signing 4.2 An Episode of Graphing 4.3 Signing: An Evental Perspective 4.3.1 A Recurrent Feature 4.3.2 Bodily Movements 4.3.3 Repetition and Difference 4.4 Passage Rather than Thing References Chapter 5: When Does Mathematical Form Make Sense? 5.1 Sense-Constituting Contextures 5.2 An Investigation into Sense-Constitutive Contextures 5.3 The Making of Sense 5.4 Communication as Instruction 5.5 What Scientists Do when Data Do Not Make Sense 5.6 The Emergence of Sense 5.7 Who Is the Subject that Makes Sense? References Chapter 6: Genesis of Mathematical Reasoning 6.1 Connecting Claims and Evidence in Geometrical Reasoning 6.1.1 Developmental Context 6.1.2 Claim, Evidence, and Burden of Proof 6.1.3 The Lesson Fragment 6.2 Participating in an Event of Mathematical Reasoning 6.3 Mathematical Mind as Society of Occasions 6.4 Society of Occasions and Concept Formation References Chapter 7: Affect in the Mathematical Mind 7.1 A Monist Initiative to Integrate Affect and Intellect 7.2 The Drama in/of a Mathematics Lesson 7.3 Unity of Affect and Intellect 7.4 Affect Permeates Experience: Drama 7.5 Later Vygotskian and Evental Perspectives 7.6 Tenets of a Unitary Theory References Part III: Integrations Chapter 8: The Thinking Body of Mathematics 8.1 Performing Analogies 8.1.1 Bouncing Ball 8.1.2 Piston 8.1.3 Rubber Band and Wire 8.2 Bodily Diagramming 8.3 Thinking, Communicating, and the Body 8.3.1 Thinking and Communicating 8.3.2 Diagrams Without Originary Grammars 8.3.3 The Sense of the Body Is the Body of Sense 8.4 The Thinking-Body-as-Event References Chapter 9: Experience, Mathe matics, and Mind 9.1 Experience 9.1.1 Perezhivanie: A Cultural–Historical Perspective 9.1.2 Experiential Continuity: A Pragmatist Take 9.2 Materials for Thinking about Experience 9.3 Through the Lens of Experience 9.3.1 Experiencing: Dynamic Unity of Person and Environment 9.3.2 Self-Movement, Continuity, and Novelty 9.3.3 From Experiencing to an Experience 9.3.4 Intersubjective Speech and Sense-Constitutive Field 9.3.5 Affect and Feeling 9.3.6 The Question of the Subject 9.4 Consciousness, Mind, and Experience References Appendix Transcription Conventions Index