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.

chapter |11 pages


Of Hands, Flesh, and Mind

part |68 pages

Toward a Theory of Mathematics in the Flesh

chapter |3 pages

Introduction to Part A

chapter 1|16 pages

What Makes a Cube a Cube?

A Phenomenological Overture

part |114 pages

Stories of Mathematics in the Flesh

chapter |4 pages

Introduction to Part B

chapter 4|24 pages

The Flesh, Distractions, and Mathematics

chapter 5|27 pages

Coordinating Touch and Gaze

Re/Constructing a Mystery Object

chapter 7|38 pages

Doing Time in Mathematical Praxis

part |72 pages

Emergence of Geometry—An Objective Science

chapter |3 pages

Introduction to Part C

chapter 8|30 pages

Ethno-Methods of Sorting Geometrically

chapter 9|12 pages

Reproducing Geometry as Objective Science

chapter 10|17 pages

Rethinking Mathematical Conceptions

chapter |7 pages