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