The Practice of Mathematics

Yvette Solomon

Routledge | 1989 | 211 páginas | rar - pdf | 6 Mb

link (password: matav)

The psychological description and explanation of how children learn to work with numbers is dominated by the theories of Piaget. Yvette Solomon suggests an alternative approach to the child's conception of number.

Contents

Acknowledgements

1. The development of the number concept as a field of psychological investigation

2. Why does Piaget's theory take its particular form? 9

The background to Piaget's explanation: the status and nature of mathematical propositions 10

Mathematics and genetic epistemology: the relation between logic and psychology 18

3. The child's conception of number 28

Piaget's criticisms of intuitionism and logicism 28

Piaget's synthesis of order and class 36

4. Piaget's account of the growth of understanding 43

Piaget's criticisms of empiricism and rationalism 43

Growth as a synthesis of genesis and structure 48

5. Does Piaget give an adequate account of growth? 66

The transition from weaker to stronger logics 67

Reflective abstraction and the growth of knowledge 70

'The individual constructs his world': Piaget's account of objective knowledge 75

6. Do number theorists give adequate accounts of knowing? 79

Piaget's essentialism 80

Bryant's work 89

Gelman and Gallistel' s work 99

7. Can a Piagetian perspective be defended? 109

Socio-cognitive conflict and the growth of knowledge 110

Information-processing theory and Piagetian theory: Case's 'neo-Piagetian' analysis 119

8. Knowing how and when to use numbers 131

Linguistic, non-linguistic and social contexts, and psychological experiments 131

The context of doing arithmetic 147

Understanding the context of doing arithmetic 150

9. 'The development of mathematical thinking ': entering into the social practices of number use 160

Analysing social practices 161

Entering into social practices 179

Notes 188

References 193

Index 200

Outros livros da mesma autora:

Mathematical literacy : developing identities of inclusion por Yvette Solomon Idioma: Inglês   Editora: New York : Routledge, 2009.

Mathematical relationships in education : identities and participation por Laura Black; Heather Mendick; Yvette Solomon;  Publicação de conferência Idioma: Inglês   Editora: New York : Routledge, 2009.