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El. knyga: Foundations of Geometric Cognition [Taylor & Francis e-book]

  • Formatas: 188 pages, 3 Tables, black and white; 12 Line drawings, black and white
  • Išleidimo metai: 24-Sep-2019
  • Leidėjas: Routledge
  • ISBN-13: 9780429056291
  • Taylor & Francis e-book
  • Kaina: 161,57 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Standartinė kaina: 230,81 €
  • Sutaupote 30%
  • Formatas: 188 pages, 3 Tables, black and white; 12 Line drawings, black and white
  • Išleidimo metai: 24-Sep-2019
  • Leidėjas: Routledge
  • ISBN-13: 9780429056291

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers.

Foundations of Geometric Cognition

shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought.

Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.

Preface ix
Acknowledgments xv
1 Geometric thinking, the paradise of abstraction
1(44)
1.1 Introduction and synopsis of the chapter
1(1)
1.2 The geometric roots of mathematical thinking
2(8)
1.3 Geometric intuition as a philosophical locus classicus
10(7)
1.4 The development of geometric skills as a psychological problem
17(8)
1.5 Euclid in the classroom
25(6)
1.6 How cognitive science discovered and forgot Euclid
31(9)
1.7 Summary
40(1)
Notes
41(4)
2 The hardwired foundations of geometric cognition
45(36)
2.1 Introduction and synopsis of the chapter
45(1)
2.2 Hardwired sensitivity to geometry
46(7)
2.3 In search of a theoretical framework
53(9)
2.4 Causal factors: Core systems of geometry
62(4)
2.5 The evolutionary adaptiveness of core geometry
66(2)
2.6 Phylogeny of core geometry
68(4)
2.7 Ontogeny: Toward a new representational system
72(4)
2.8 Summary
76(2)
Notes
78(3)
3 Embodiment and abstraction
81(40)
3.1 Introduction and synopsis of the chapter
81(3)
3.2 The classic cognitive science of concepts
84(5)
3.3 The embodiment and its challenges
89(8)
3.4 Embodied theories of abstract concepts
97(6)
3.5 Are abstract concepts really embodied?
103(5)
3.6 Into the realm of abstraction: Through the body and beyond
108(7)
3.7 Summary
115(2)
Notes
117(4)
4 Cognitive artifacts and Euclid: Diagrams and formulae
121(22)
4.1 Introduction and synopsis of the chapter
121(3)
4.2 The lettered diagram as a cognitive artifact
124(6)
4.3 The professional language of geometry: Another cognitive artifact
130(4)
4.4 Where do the necessity and generality of Euclid's proofs come from?
134(5)
4.5 Summary
139(1)
Notes
140(3)
Conclusions and future directions for research 143(4)
References 147(28)
Index 175
Mateusz Hohol is Assistant Professor at Jagiellonian University, Kraków, and Postdoc at Polish Academy of Sciences (IPS PAS), Warsaw. His research focuses on the cognitive science of mathematics, especially on numerical and geometric cognition.