Adult's Mathematical Thinking and Emotions - J. Evans (Routledge, 2000) WW

313 Pages·2000·1.02 MB·English

Adults’ Mathematical Thinking and
Emotions

The perpetual concerns about the teaching and learning of mathematics, and its use
in work and everyday life, relate to a number of issues:

•
doubts about the transferability of school learning to outside settings
•
declining participation in A-level and higher education mathematics courses
•
under-representation of certain groups, such as females, in mathematics study
•
the aversion of many people to mathematics generally.

This book addresses these issues through investigating the following:

•
the ways in which numerate thinking and performance of adults are context-
related
•
the inseparability of thinking and emotion, and the consequent ways in which
mathematical activity is emotional, and not simply cognitive
•
the understanding of mathematics anxiety in psychological, psychoanalytic and
feminist theories
•
social differences in mathematics performance, anxiety and confidence.

Drawing on works such as those of Jean Lave and Valerie Walkerdine, and ideas
from poststructuralism and psychoanalysis, this volume shows ways of reconceptu-
alising current debates in mathematics education, including its psychological and
sociological aspects. It points to ideas for practical applications in education and
training, such as clarifying the problems with the transfer of learning, and coun-
tering mathematics anxiety. It also illustrates a number of ways of fruitfully
combining quantitative and qualitative methodologies in educational research.

Jeff Evans is Principal Lecturer in Social Statistics at Middlesex University, and
teaches social and business statistics and research methods.

Studies in Mathematics Education Series
Edited by Paul Ernest
University of Exeter, UK

The Philosophy of Mathematics Education
Paul Ernest

Understanding in Mathematics
Anna Sierpinska

Mathematics Education and Philosophy
Edited by Paul Ernest

Constructing Mathematical Knowledge
Edited by Paul Ernest

Investigating Mathematics Teaching
Barbara Jaworski

Radical Constructivism
Ernst von Glaserfeld

The Sociology of Mathematics Education
Paul Dowling

Counting Girls Out
Girls and mathematics
Valerie Walkerdine

Writing Mathematically
The discourse of investigation
Candia Morgan

Rethinking the Mathematics Curriculum
Edited by Celia Hoyles, Candia Morgan and Geoffrey Woodhouse

International Comparisons in Mathematics Education
Edited by Gabriele Kaiser, Eduardo Luna and Ian Huntley

Mathematics Teacher Education
Critical international perspectives
Edited by Barbara Jaworski, Terry Wood and Sandy Dawson

Learning Mathematics
From hierarchies to networks
Edited by Leone Burton

The Pragmatics of Mathematics Education
Vagueness and mathematical discourse
Tim Rowland

Adults’ Mathematical Thinking and Emotions
A study of numerate practices
Jeff Evans

Adults’ Mathematical
Thinking and Emotions
A Study of Numerate Practices

Jeff Evans

London and New York

First published 2000
by RoutledgeFalmer
11 New Fetter Lane, London EC4P 4EE

Simultaneously published in the USA and Canada
by RoutledgeFalmer
29 West 35th Street, New York, NY 10001

RoutledgeFalmer is an imprint of the Taylor & Francis Group

© 2000 Jeff Evans

The right of Jeff Evans to be identified as the Author of this Work has
been asserted by him in accordance with the Copyright, Designs and
Patents Act 1988

All rights reserved. No part of this book may be reprinted or reproduced
or utilised in any form or by any electronic, mechanical, or other means,
now known or hereafter invented, including photocopying and
recording, or in any information storage or retrieval system, without
permission in writing from the publishers.

British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library

Library of Congress Cataloging in Publication Data
Evans, Jeff, 1944–
Adults’ mathematical thinking and emotions: a study of numerate prac-
tices/Jeff Evans.
p. cm. –– (Studies in mathematics education series; 15)
Includes bibliographical references and index.
1. Mathematics–Study and teaching (Continuing)–Psychological
aspects. 2. Adult learning. I. Title. II. Series.
QA11.E93 2000
510`.71
5––dc21 00-032306

ISBN 0–750–70913–8 (hbk)
ISBN 0–750–70912–X (pbk)

This edition published in the Taylor & Francis e-Library, 2001.

ISBN 0-203-18589-7 Master e-book ISBN
ISBN 0-203-18712-1 (Glassbook Format)

Contents

List of Figures
xi
List of Tables
xii
Series Editor’s Preface
xiv
Author’s Preface and Acknowledgements
xvi

1
Introduction: Mathematics, the Difficult Subject
1

Perpetual Concerns about Mathematics Learning and Use 1
Developing Ideas and Methodologies for the Study 4
Overview of the Book 7

2
Mathematical Thinking in Context Among Adults
9

Conceptions of Practical Mathematics and the Context 9
‘Numerical Skills’Approaches 10
The Cockcroft Report and ‘Functional’ Numeracy 11
Recent British Surveys of Adult Numeracy 13
Conceptual Map and Research Questions 15
Research Setting and Sample of Adults 16
Developing a Conceptual Map 17
Research Questions 17
Survey Results for Performance and Context 19
Overall Levels of Performance 19
Specification of Contexts of Performance: School
Mathematics and Practical Maths 23
Conclusions 25

3
Mathematics Performance and Social Difference
28

Gender Differences 28
Social Class Differences 30
Conceptual Map and Research Questions 33
Survey and Modelling Results for Gender Differences
in Performance 34

Survey and Modelling Results for Social Class Differences
in Performance 38
Conclusions 39

4
Affect and Mathematics Anxiety
42

Affect and Anxiety 43
Psychological Conceptions and Measures of Anxiety 45
Mathematics Anxiety, Measures and Relationships 48
Two Measures 49
Dimensions of Mathematics Anxiety 51
Mathematics Anxiety, Performance and Social Difference 53
Model A: Conceptual Map and Research Questions 54
Survey and Modelling Results: Contexts of Mathematics Anxiety 56
Initial Considerations 56
Factors of Mathematics Anxiety 57
Survey and Modelling Results: Social Differences and
Mathematics Anxiety 61
Survey and Modelling Results: Mathematics Anxiety and
Performance 63
Conclusions 65

5
Reflections on the Study So Far
69

6
Rethinking the Context of Mathematical Thinking
74

A Range of Views on the Meanings of Context and the
Possibilities of Transfer 75
The Turn to the Social: Sociocultural Approaches and
Situated Cognition 78
Situated Cognition: Jean Lave 80
The Turn to Representations: Street Mathematics and
Computer Microworlds 86
The Turn to Language: Structuralist and Poststructuralist
Approaches 94
Discourse and Boundaries: Basil Bernstein 95
Discursive Practice and Relations of Signification:
Valerie Walkerdine 96
Conceptualising Contexts, Practices, Boundaries and Bridges 99
Contexts and the Practices at Play 99
Relations Between Practices: Boundaries and Bridges 101
Conclusions 104

7
Rethinking Mathematical Affect as Emotion
107

‘No Emotion, Please! We’re Researching Mathematics’ 108
Model B: Process Conceptions of Affect and Anxiety in Mathematics 109
Model C: Approaches Informed by Psychoanalysis 113

viii
Contents

Basic Ideas: Freud and Lacan 113
Studies Done Within a Psychoanalytic Perspective 116
Model D: A Psychoanalytic Approach, Informed by
Poststructuralism 120
Cultural and Emotional Differences in Mathematical
Activity 121
Poststructuralist Views on the Gendering of Mathematics 127
Conclusions 130

8
Developing a Complementary Qualitative Methodology
135

Themes or Foreshadowed Problems 135
Focus and Methodology of the Interview 140
Psychoanalytic Insights in the Interview Process 141
Areas for Exploration and Developing Indicators 142
Doing the Interviews 145
Sampling Methods and Recruitment 145
The Conduct of the Interview 145
The General Reflexive Account 146
Overview of the Analysis of the Interviews 147
Summary 149

9
Reconsidering Mathematical Thinking and Emotion in Practice
150

Theme 1: Contexts of Thinking Ascribed in Terms of
Positioning in Practices
150
Theme 2: Inseparability of Task and Context 156
Theme 3: Gender and Social Class Differences in Performance
Related to Positioning 160
Abstract Calculation of 10 per cent 160
Calculation of 10 per cent Tip 162
Approximate and Exact Calculations of 9 per cent
Pay Increase 162
Theme 4: Numerate Thinking as Specific to the Subject’s
Positioning 165
Strategies Used: Best Buy Shopping Decision 165
Methods of Critical Evaluation 170
Theme 5: Emotion Pervades Mathematical Thinking –
‘Mathematics is Hot’ 171
Theme 6: Gender Differences in Expressing Anxiety 174
Conclusions 176

10
The Learners’ Stories
181

Overview of Themes to be Analysed 181
Case Studies 182
Jean’s Story 183
Ellen’s Story 186

Contents
ix