Foundations of geometric cognition

Description

Cover Half Title Title Page Copyright Page Dedication Contents Preface Acknowledgments 1. Geometric thinking, the paradise of abstraction 1.1 Introduction and synopsis of the chapter 1.2 The geometric roots of mathematical thinking 1.3 Geometric intuition as a philosophical locus classicus 1.4 The development of geometric skills as a psychological problem 1.5 Euclid in the classroom 1.6 How cognitive science discovered and forgot Euclid 1.7 Summary Notes 2. The hardwired foundations of geometric cognition 2.1 Introduction and synopsis of the chapter 2.2 Hardwired sensitivity to geometry 2.3 In search of a theoretical framework 2.4 Causal factors: Core systems of geometry 2.5 The evolutionary adaptiveness of core geometry 2.6 Phylogeny of core geometry 2.7 Ontogeny: Toward a new representational system 2.8 Summary Notes 3. Embodiment and abstraction 3.1 Introduction and synopsis of the chapter 3.2 The classic cognitive science of concepts 3.3 The embodiment and its challenges 3.4 Embodied theories of abstract concepts 3.5 Are abstract concepts really embodied? 3.6 Into the realm of abstraction: Through the body and beyond 3.7 Summary Notes 4. Cognitive artifacts and Euclid: Diagrams and formulae 4.1 Introduction and synopsis of the chapter 4.2 The lettered diagram as a cognitive artifact 4.3 The professional language of geometry: Another cognitive artifact 4.4 Where do the necessity and generality of Euclid’s proofs come from? 4.5 Summary Notes Conclusions and future directions for research References Index