1st Edition
Geometry as Objective Science in Elementary School Classrooms Mathematics in the Flesh
This study examines the origins of geometry in and out of the intuitively given everyday lifeworlds of children in a second-grade mathematics class. These lifeworlds, though pre-geometric, are not without model objects that denote and come to anchor geometric idealities that they will understand at later points in their lives. Roth's analyses explain how geometry, an objective science, arises anew from the pre-scientific but nevertheless methodic actions of children in a structured world always already shot through with significations. He presents a way of understanding knowing and learning in mathematics that differs from other current approaches, using case studies to demonstrate contradictions and incongruences of other theories – Immanuel Kant, Jean Piaget, and more recent forms of (radical, social) constructivism, embodiment theories, and enactivism – and to show how material phenomenology fused with phenomenological sociology provides answers to the problems that these other paradigms do not answer.
Introduction: Of Hands, Flesh, and Mind A. Toward a Theory of Mathematics in the Flesh Introduction to Part A. 1. What Makes a Cube a Cube? A Phenomenological Overture 2. From Intellectualist Metaphysics to Embodiment Epistemologies 3. Material Life as the Organizing Principle of Knowing B. Stories of Mathematics in the Flesh Introduction to Part B. 4. The Flesh, Distractions, and Mathematics 5. Coordinating Touch and Gaze: Re/Constructing a Mystery Object 6. Emergence of Measurement as the Realization of Geometry 7. Doing Time in Mathematical Praxis C. Emergence of Geometry – An Objective Science Introduction to Part C. 8. Ethno-methods of Sorting Geometrically 9. Reproducing Geometry as Objective Science 10. Rethinking Mathematical Conceptions. Epilogue: From the Flesh to Society in the Mind
Biography
Wolff-Michael Roth is Lansdowne Professor of Applied Cognitive Science at the University of Victoria. He researches knowing and learning related to mathematics and science across the entire life span. His recent publications include Language, Learning, Context (Routledge, 2010), Science Education from People for People (Ed., Routledge, 2010), and Re/Structuring Science Education (Ed., Springer, 2010).
