Edited by Paul Ernest

Studies in Mathematics Education Volume 3

The Falmer Press, 1994.

This book embodies a far-reaching interdisciplinary enquiry into philosophical and reflective aspects of mathematics and mathematics education. It also addresses the central problem of the philosophy of mathematics education, concerning the impact of conceptions of mathematics on educational practice. It combines fallibilist and social philosophies of mathematics with exciting new analyses from post-structuralist and post-modernist theorists, offering both reconceptualisations and critiques of mathematics and mathematics education. The outcome is a set of new perspectives which bring out the human face of mathematics, as well as acknowledging its social responsibility. Many of the chapters are from leading thinkers in the field, and the result is an important contribution to current debate. The book makes contributions of four types:

Reconceptualising the Philosophy of Mathematics

1. Reuben Hersh, Fresh Winds in the Philosophy of Mathematics

2. David Bloor, What can the Sociologist of Knowledge say about 2+2=4?

3. Paul Ernest, The Dialogical Nature of Mathematics

4. Thomas Tymoczko, Structuralism and Post-Modernism in the Philosophy of Mathematics

Post-Modernist and Post-Structuralist Approaches

5. Valerie Walkerdine, Reasoning in a Post-Modern Age

6. Brian Rotman, Mathematical Writing, Thinking and Virtual Reality

7. Anna Tsatsaroni and Jeff Evans, Mathematics: The Problematical Notion of Closure

8. David Jardine, On the Ecologies of Mathematical Language and the Rhythms of the Earth

9. Paul Dowling, Discursive Saturation and School Mathematics Texts: a strand from a language of description

10. Jeff Vass, The Dominance of Structure in 'Post-Structural' Critiques of Mathematics Education

11. Tony Brown, Describing the Mathematics you are a part of: A Post-structuralist account of Mathematical Learning

The Human Face of Mathematics

12. Philip J. Davis, Mathematics and Art

13. Hao Wang, Skolem and Gödel

14. George Gheverghese Joseph, Different Ways of Knowing: Contrasting styles of argument in Indian and Greek Traditions

The Social Context of Mathematics and Education

15. Sal Restivo, The Social Life of Mathematics

16. Mairead Dunne and Jayne Johnston, Research in Gender and Mathematics Education: the Production of Difference

17. Ubiratan D'Ambrosio, Ethnomathematics, the Nature of Mathematics and Mathematics Education



Edited by Paul Ernest

Studies in Mathematics Education Volume 4

The Falmer Press, 1994.

This book offers a panorama of complementary and forward looking perspectives on the learning of mathematics and epistemology from leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings new analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its teaching and learning. The book both surveys current research and indicates orientations for fruitful work in the future. It is essential reading for anyone interested in theoretical developments in mathematics education.

Constructivism and the Learning of Mathematics

1. Ernst Von Glasersfeld, A Radical Constructivist View of Basic Mathematical Constructs

2. Leslie P. Steffe and Ron Tzur, Interaction and Children's Mathematics

3. Robert Thomas, Radical Constructive Criticisms of Von Glasersfeld's Radical Constructivism

4. Stephen Lerman, Articulating Theories of Mathematics Learning

5. Michael Otte, Is Radical Constructivism Coherent?

6. Paul Ernest, Social Constructivism and the Psychology of Mathematics Education

7. Erick Smith,

8. Katherine Crawford, The Context of Cognition: The Challenge of Technology

Psychology, Epistemology and Hermeneutics

9. David Pimm, Another Psychology of Mathematics Education

10. Dick Tahta, On Interpretation

11. Philip Maher, Potential Space and Mathematical Reality

12. Tony Brown, Towards a Hermeneutical Understanding of Mathematics and Mathematical Learning

13. Falk Seeger and Heinz Steinbring, The Myth of Mathematics

Enquiry in Mathematics Education

14. Stephen I. Brown, The Problem of the Problem and Curriculum Fallacies

15. John Mason, Enquiry in Mathematics and in Mathematics Education

16. Marjorie Siegel and Raffaella Borasi, Demystifying Mathematics Education through Inquiry

17. Charles Desforges and Stephen Bristow, Reading to Learn Mathematics in the Primary Age Range

History, Mathematics and Education

18. Francesco Speranza, The Idea of 'Revolution' as an Instrument for the Study of the Development of Mathematics and its Applications to Education

19. Anna Sfard, Mathematical Practices, Anomalies, and Classroom Communication Problems.