Geometry as Objective Science in Elementary School Classrooms

Mathematics in the Flesh

Nonfiction, Reference & Language, Education & Teaching, Educational Theory, Philosophy & Social Aspects, Teaching, Teaching Methods
Cover of the book Geometry as Objective Science in Elementary School Classrooms by Wolff-Michael Roth, Taylor and Francis
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Author: Wolff-Michael Roth ISBN: 9781136732201
Publisher: Taylor and Francis Publication: May 9, 2011
Imprint: Routledge Language: English
Author: Wolff-Michael Roth
ISBN: 9781136732201
Publisher: Taylor and Francis
Publication: May 9, 2011
Imprint: Routledge
Language: English

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.

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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.

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