Windows on Mathematical Meanings: Learning Cultures and Computers / Edition 1

by Richard Noss, Celia Hoyles

Overview

This book is the culmination of some ten years' theoretical and empirical investigation. Throughout this period, we have come into contact with many who have stimulated our thinking, some of whom belong to the community of Mathematics Educators. Our membership of that community has challenged us to make sense of some deep issues related to mathematical learning, especially the cognitive and pedagogical faces of mathematical meaning­ making. Alongside this community, we are privileged to have been part of another, whose members are centrally concerned both with mathematics and educa­ tion. Yet many of them might reject the label of Mathematics Educators. This community has historically been clustered around what is now called the Epistemology and Learning Group at the Massachusetts Institute of Technol­ ogy. Their work has focused our attention on cognitive science, ethnography, sociology, artificial intelligence and other related disciplines. Crucially, it has forced our awareness of the construction of computational settings as a crucial component of the struggle to understand how mathematical learning happens. We have sometimes felt that few have tried to span both communities. Indeed, an analysis of the references in the literature would, we are sure, reveal that the two communities have often ignored each other's strengths. One reason for writing this book is born of our hope that we might draw together Mathematics Educators and mathematics educators, and assist both communities in recognising that there are insights that might be derived from each other.

Product Details

ISBN-13:	9780792340737
Publisher:	Springer Netherlands
Publication date:	06/30/1996
Series:	Mathematics Education Library , #17
Edition description:	1996
Pages:	278
Product dimensions:	6.14(w) x 9.21(h) x 0.24(d)

Table of Contents

1. Visions of the mathematical.- 1. Reshaping mathematics, revisioning learning.- 2. Computers.- 3. …and cultures.- 4. Windows on methodologies.- 2. Laying the Foundations.- 1. Introduction.- 2. Meanings in mathematics education: a brief survey.- 3. Vignette: The N-task.- 4. The influence of setting on mathematical behaviour.- 5. Street mathematics.- 6. A way out of the cul-de-sac?.- 7. Rethinking abstraction.- 3. Tools and technologies.- 1. Computers and educational cultures.- 2. A preliminary case for programming.- 3. The development of a programming culture.- 4. Micro worlds: the genesis of the idea.- 5. Opening windows on microworlds.- 6. Objects and structures.- 4. RatioWorld.- 1. What do we — and learners — know?.- 2. Building an alternative methodology.- 3. The data set.- 4. The microworld activities and student responses.- 5. Quantitative windows on learning.- 6. Reflections.- 5. Webs and situated abstractions.- 1. Reviewing the foundations.- 2. Webs of meaning.- 3. Domains of situated abstraction.- 6. Beyond the individual learner.- 1. Extending the web.- 2. Collaborative activity in mathematics.- 3. A study of groupwork.- 4. Opening new windows.- 7. Cultures and change.- 1. Innovation and inertia.- 2. Visions of Logo.- 3. Myths and methodologies: a case study of Logo research.- 4. The struggle for meanings.- 8. A window on teachers.- 1. Investigating teachers’ attitudes and interactions.- 2. Teachers making meanings.- 3. Connections and cultures.- 9. A window on schools.- 1. The background to the case study.- 2. The teachers’ voices.- 3. The students’ voices.- 4. Meanings in conflict.- 10. Re-visioning mathematical meanings.- 1. Reviewing the scene.- 2. Epistemological revisions: six examples.- 3. Reconnecting mathematics and culture.- References.

Editorial Reviews

Scholars from the University of London draw on their individual and collaborative research to present an innovative approach to teaching mathematics. Using the computer as a window into the process of mathematical meaning-making, they introduce the concept of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social, and cultural forces. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"Noss and Hoyles take on the field of Mathematics Education as a whole to develop a coherent theoretical framework that will encompass its psychological, social, pedagogical and epistemological dimensions. Their pages abound with socratic flies to torment anyone who claims to understand concepts like abstract, concrete, formal, common-sensical and even mathematics, without the context of an elaborated theory. At the same time they present the most elaborated theoretical discussion to date of how the computer presence might contribute to the development of the field."

Seymour Papert, Massachusetts Institute of Technology

‘I would say that the book is very readable, and contains a number of interesting details as well as the construction of a theory. It is one important step in developing a theoretical framework for the use of technology in mathematics education.'

Nordic Studies in Mathematical Education, 3 (1997)

From the Publisher