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Adult Numeracy: Review of Research and Related Literature

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Adult Numeracy: Review of Research and Related Literature Research Review Adult numeracy: review of research and related literature Diana Coben, University of Nottingham with contributions by: Dhamma Colwell; Sheila Macrae; Jo Boaler, Margaret Brown and Valerie Rhodes; King’s College, London November 2003 This report is funded by the Department for Education and Skills as part of Skills for Life: the national strategy for improving adult literacy and numeracy skills. The views expressed are those of the author(s) and do not necessarily reflect those of the Department. Published by the National Research and Development Centre for Adult Literacy and Numeracy This report may be downloaded as a PDF document from the NRDC website at www.nrdc.org.uk We welcome feedback on the content and accessibility of this publication. This should be sent to: Publications NRDC Institute of Education 20 Bedford Way London WC1H 0AL. Telephone: +44 (0)20 7612 6476 Fax: +44 (0)20 7162 6671 email: [email protected] ISBN 0 9546492 0 6 © Crown Copyright 2003 Extracts from this publication may be used or reproduced for non-commercial, research, teaching or training purposes on condition that the source is acknowledged. NRDC is a consortium of partners led by the Institute of Education, University of London (see back cover for a list of members) and is part of the Bedford Group for Lifecourse and Statistical Studies at the IoE. www.ioe.ac.uk/bedfordgroup Design: chapmandesign Photography: Phillip Meech Print: Bradell Adult numeracy: review of research and related literature Diana Coben, University of Nottingham with contributions by: Dhamma Colwell; Sheila Macrae; Jo Boaler, Margaret Brown and Valerie Rhodes; King’s College, London CONTENTS ACKNOWLEDGEMENTS 5 EXECUTIVE SUMMARY 7 INTRODUCTION 8 The scope of the review 8 Adult numeracy - conceptual issues 9 (Adult) mathematics education as a research domain 21 Epistemologies of mathematics and mathematics education 26 Absolutist and fallibilist epistemologies of mathematics 26 Constructivist and sociocultural epistemologies of mathematics education 26 Feminist epistemologies 27 Ethnomathematics 28 Reviews of research 30 Survey evidence of adults’ numeracy skills 32 The International Adult Literacy Survey (IALS) 34 The Adult Literacy and Lifeskills Survey (ALL) 35 Concluding remarks on surveys 36 NUMERACY IN CONTEXT 38 Context and transfer 38 Investigating the use of mathematics in everyday life by Dhamma Colwell 40 The implications for mathematics and numeracy education 44 Mathematics and employment 47 Financial literacy 50 Concluding remarks on context and transfer 53 LEARNING AND TEACHING ADULT NUMERACY 54 Issues in learning and teaching adult numeracy 54 Policy and provision of adult numeracy in England: Skills for Life and Key Skills 55 Curriculum development and approaches to teaching and learning 58 Elements of mathematics 64 Assessment 66 Literacy, language and ICT in relation to numeracy 68 Multiple intelligences 72 Critical pedagogies 72 Adult numeracy learners 73 Adults with learning difficulties and disabilities 74 Gender 74 Age 76 Teacher education for adult numeracy 77 Effective Teachers of Numeracy project by Sheila Macrae 83 Data sources 83 Some findings from the project 84 The National Numeracy Strategy in Primary schools by Sheila Macrae 85 The three-part lesson 86 Oral/mental starter 86 Main teaching session 87 Plenary phase 88 Evaluation of the National Numeracy Strategy 88 Leverhulme Numeracy Research Programme by Sheila Macrae 90 Conclusion 90 FACTORS AFFECTING LEARNING 92 Affective factors - attitudes, beliefs and feelings 92 Attitudes to mathematics by Jo Boaler, Margaret Brown and Valerie Rhodes 93 A. Factors influencing pupils’ attitudes to mathematics 93 Introduction 93 1. Gender 94 2. Teaching, learning and the curriculum 95 3. Confidence 96 B. Choice of mathematics post-16 97 C. Changes in attitude effected by special initiatives 98 D. Influence of societal attitudes to mathematics 99 E. Relationship between participation in science and mathematics and improved national economic performance 100 Mathematics anxiety by Sheila Macrae 100 Mathematics anxiety in the primary school 101 Mathematics anxiety in the secondary school 102 Mathematics anxiety in adults 103 Dyscalculia and the functioning of the brain in mathematical activity by Dhamma Colwell 104 The functioning of the brain in mathematical activity 104 Dyscalculia 106 Dyscalculia: Incidence 106 Dyscalculia: Assessment 106 Dyscalculia: Symptoms 107 Implications for adult numeracy teaching and learning 108 METHODOLOGICAL ISSUES 110 Methodological issues in research on adult numeracy 110 Mixed methods 111 Experimental/intervention studies including randomised controlled trials 112 Ethnographic approaches 112 Practitioner research 113 WHAT DO WE KNOW AND WHAT DO WE NEED TO KNOW ABOUT ADULT NUMERACY - AND WHAT SHOULD WE DO ABOUT IT? 115 Conceptualising numeracy 115 Surveying numeracy 115 Designing and implementing policies for adult numeracy 115 Teaching and learning adult numeracy 115 Seeing the wood for the trees: numeracy in situ 116 Researching adult numeracy 117 Developing teachers of adult numeracy 117 Learning adult numeracy 118 Building capacity in adult numeracy 118 REFERENCES 119 Adult numeracy: review of research and related literature 5 Acknowledgements I am grateful to many people who have made suggestions, provided references and answered queries, including Professor Margaret Brown, Professor John Bynner, Dr Jeff Evans, Tessa Griffiths, Dr Jeremy Hodgen, Dr Betty Johnston, Dr Michael Rice, Dr Katherine Safford- Ramus, Dr Jon Swain, Dr Alison Tomlin, Dr Karin Tusting, Dr Tine Wedege, Professor Alison Wolf; also participants at the following events and conferences: I London Language and Literacy Unit (LLLU) 4th National Numeracy Conference, London, May 10, 2002 I The Summer Institute, Montreal, Canada, June 27-29, 2002 I FENTO/ABSSU Dissemination Events in Birmingham, London and Newcastle, April-July, 2002 I The 9th international conference of Adults Learning Mathematics - A Research Forum (ALM9), Uxbridge, July 17-20, 2002 I Skills for Life conferences in Manchester and London, November 2002 I NRDC/CCER International Conference, Nottingham, March 20-22, 2003 I Expert seminar, King’s College London, 24 June, 2003. Special thanks also to those who have given invaluable technical assistance: to Jem Dowse and Dave Vout, Institute of Education computer technicians, to Vanessa Gordon, NRDC Administrator. Diana Coben September 2003 Note on authorship Text in the report is by Diana Coben except where otherwise indicated: the sections on ‘Dyscalculia and the functioning of the brain in mathematical activity’ and ‘Investigating the use of mathematics in everyday life’ are by Dhamma Colwell; the sections on ‘Mathematics anxiety’, ‘The National Numeracy Strategy in schools’, ‘The Effective Teachers of Numeracy project’ and ‘The Leverhulme Numeracy Research project’ are by Sheila Macrae. The section on ‘Attitudes to mathematics’ is by Jo Boaler, Margaret Brown and Valerie Rhodes. This is extracted, with permission, from an unpublished report on attitudes to mathematics, science and technology by a group from King’s College London (Osborne et al. 1997). Some editing of these texts has been done by Diana Coben in order to make the report cohesive. Dedication For Callimachus, Librarian of Alexandria, the father of bibliography. Adult numeracy: review of research and related literature 7 Executive Summary I Adult numeracy is fast-developing but under-researched, under-theorised and under- developed. It is a deeply contested concept which may best be considered as mathematical activity situated in its cultural and historical context. Research and capacity-building are required in: theory; policy; teaching and learning; teacher education; communication between stakeholders; international comparative studies. I Surveys reveal low levels of adult numeracy in England, with deleterious effects on individuals, the economy and society. The measurement of adult numeracy skills is problematic, especially for adults with lower ability levels (including special educational needs and dyscalculia) and/or reading or language difficulties. I The need for adult numeracy/mathematical skills, including the communication of information based on mathematical data, is being progressively extended throughout the workforce as a result of the pressure of business goals and the introduction of IT. Employees increasingly need to have broader general problem-solving skills, interrelating IT with mathematics. I Research on adults’ ‘numerate practices’ suggests that they are diverse – as are learners themselves - and deeply embedded in the contexts in which they occur and that ‘transfer’ of learning between contexts may be problematic, posing a challenge for teachers attempting to relate the curriculum to learners’ contexts. I Evidence on the impact of adult numeracy tuition is sparse and unreliable. Detailed studies are required, including longitudinal studies. School sector projects employing constructivist theories of learning and with a ‘connectionist’ orientation to teaching and learning, making connections with the world beyond the classroom and with other elements of mathematics, demonstrate improvements in attitude and attainment. I Adult numeracy teacher education is currently undergoing major transformation. Some teachers’ inadequate subject knowledge is a continuing concern. Studies with children suggest that: initial and ongoing teacher education increases subject knowledge, facilitates career
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