Making Mathematics Count The report of Professor Adrian Smith’s Inquiry into Post-14 Mathematics Education February 2004 Printed by The Stationery Office Limited 2/04 937764 CONTENTS Page Foreword V Executive Summary 1 Purpose of the post-14 mathematics education inquiry 1 Overview of the report 3 The importance of mathematics 3 Supply of teachers of mathematics 4 Current mathematics pathways 6 Action on current and future pathways 6 Support for the teaching and learning of mathematics 8 National and regional support infrastructure 9 Conclusion 9 Chapter 1 The Importance of Mathematics 11 Mathematics for its own sake 11 Mathematics for the knowledge economy 11 Mathematics for science, technology and engineering 11 Mathematics for the workplace 12 Mathematics for the citizen 13 Increasing mathematical skills 13 This report 14 The special position of mathematics 14 Territorial responsibilities 15 Government departments and agencies 15 The mathematics education community 16 Chapter 2 The Supply of Teachers of Mathematics 19 The need for qualified teachers of mathematics 19 Teacher shortages and their effect on students’ performance 20 The shortfall of specialist mathematics teachers in secondary schools 22 The shortfall of specialist mathematics teachers in colleges 28 The shortfall of ITT mathematics trainers 28 Teacher vacancies 30 Teacher age-profiles and forecasts of future supply requirements 32 The decline in post-16 take up of mathematics 34 Teacher recruitment 36 i Teachers’ Remuneration 49 A summary of additional comments on teacher supply in Wales, Northern Ireland and Scotland 50 Chapter 3 Current Mathematics Pathways 53 The National Curriculum (pre-16) 53 The curriculum post-16 55 Mathematics qualifications: current progression routes within mathematics 56 A summary of structures, qualifications and developments in Wales, Northern Ireland and Scotland 71 Chapter 4 Action on Current and Future Mathematics Pathways 81 The Working Group on 14-19 Curriculum and Qualifications Reform 81 Current concerns over GCSE Mathematics in England 82 Concerns over key skills and Application of Number (AoN): FSMQs and AS Use of Mathematics 87 Concerns relating to GCE Mathematics 92 Concerns with Adult Numeracy 95 Possible Future Pathway Models for Mathematics 14-19 96 Chapter 5 Support for the Teaching and Learning of Mathematics 105 Continuing Professional Development (CPD) for teachers of mathematics) 105 The need for subject-specific CPD 107 The ACME report 109 CPD content and delivery 112 Key requirements and tasks of a support infrastructure 120 Chapter 6 National and Regional Support Infrastructure 127 Existing and potential providers, networks and initiatives 127 The role of the Numeracy and Key Stage 3 Strategies 128 The role of Higher Education in supporting Schools and Colleges 131 The role of Specialist Schools 135 The role of voluntary initiatives 137 Support of teachers of adult numeracy 141 Evaluation and dissemination of research in mathematics education 141 ii Remit and responsibilities of the national and regional centres 142 Funding requirements for the NCETM and the RMCs 144 The governance of the NCETM and the RMCs 147 The location and management of the NCETM and the RMCs 150 Appendix 1 List of Recommendations by Chapter 151 Appendix 2 Background, Terms of Reference and Steering Group 163 Appendix 3 Glossary 165 Appendix 4 National Qualifications Framework 171 iii iv FOREWORD The Rt. Hon. Charles Clarke, MP Secretary of State for Education and Skills Sanctuary Building Great Smith Street London SW1P 3BT February 2004 I am pleased to present to you the report of the Post-14 Mathematics Inquiry. I am grateful to have been given the opportunity to lead this Inquiry and would like to thank the many organisations and individuals who provided me with such a wealth of invaluable facts, figures, opinions and advice. I would particularly like to thank the members of my Steering Group for their patient support and wise counsel; my expert advisers for their tutorial advice, and my secretariat for their professional support. All have contributed enormously to my report. In carrying out this UK Inquiry, I have been mindful of the fact that responsibility for mathematics education is devolved to all three devolved administrations. The degree of common ground with England varies markedly across the territories of the UK, as do territorial perceptions of the problems they face regarding mathematics education. I should therefore make clear that, for the most part, my analyses and recommendations refer more directly to England than to Scotland, Northern Ireland and Wales. Nevertheless, I hope that many elements of the report will be useful to all the devolved administrations. Mathematics is of central importance to modern society. It provides the language and analytical tools underpinning much of our scientific and industrial research and development. Mathematical concepts, models and techniques are also key to many vital areas of the knowledge economy, including the finance and ICT industries. Mathematics is crucially important, too, for the employment opportunities and achievements of individual citizens. The Inquiry has therefore found it deeply disturbing that so many important stakeholders believe there to be a crisis in the teaching and learning of mathematics in England. There are three major areas of concern. First, we have a curriculum and qualifications framework that fails to meet the mathematical requirements of learners, fails to meet the needs and expectations of higher education and employers and fails to motivate and encourage sufficient numbers of young people to continue with the study of mathematics post-16. Secondly, we have a serious shortage of specialist mathematics teachers in schools and colleges and this is having an adverse effect on pupils’ learning experiences. v Thirdly, there is a lack of support infrastructure, both at national and local levels, to provide continuing professional development and resources, including ICT, in support of excellence in the teaching and learning of mathematics. My report makes a number of recommendations for addressing these problems. Some, I believe, can be implemented straightaway and would produce immediate improvements. Others require more radical, longer-term changes. So far as the curriculum and qualifications framework is concerned, it is timely that the publication of the report of this Inquiry follows so closely after the publication of the Interim Report of the Working Group on 14-19 Curriculum and Qualifications Reform. The Post-14 Mathematics Inquiry strongly welcomes and endorses the broad philosophy of the Working Group’s proposals. I believe that the proposals I make in this report for designing new pathways for mathematics are fully compatible with the Working Group’s proposals for the overall 14-19 framework. So far as support for the teaching and learning of mathematics is concerned, the Inquiry believes it to be vital that we provide teachers of mathematics in schools and colleges with greatly enhanced resources and with sustained access to professional support and development. Specifically, I propose a model of national and local infrastructure that I believe will enhance the mathematics teaching environment, nurture and support individual teachers of mathematics and encourage collectively in mathematics departments in schools and colleges a renewed sense of confidence and professionalism. The implementation of the recommendations set out in this report will begin the process of averting the crisis in mathematics education. I commend these recommendations to you. I am also copying this letter to Jane Davidson in Wales, Jane Kennedy in Northern Ireland and Peter Peacock in Scotland. Professor Adrian Smith, FRS vi EXECUTIVE SUMMARY Purpose of the Inquiry 0.1 At the time of Budget 2001, the Government commissioned a review into the supply of people with science, technology, engineering and mathematical skills. In the context of the Government’s strategy for improving the UK’s productivity and innovation performance, this reflected a concern that the supply of scientists and engineers should not constrain the UK’s future research and development and innovation capability. The review was carried out for the Chancellor of the Exchequer by Sir Gareth Roberts, who published his report, SET for Success: The supply of people with science, technology, engineering and mathematical skills, in April, 2002.1 0.2 The Roberts report examined the supply of science and engineering skills in the UK in the specific contexts of the biological sciences, the physical sciences, engineering, mathematics and computer science. It presented a number of findings relating to the difficulties faced by employers in recruiting appropriately qualified scientists and engineers and raised a number of issues about the development of science and engineering skills in schools, colleges and higher education. 0.3 The report noted that although, relative to many other countries, the UK has a large and growing number of young people studying science and engineering, this overall growth has masked a decline in the numbers studying the physical sciences, engineering and mathematics. For example, the report drew attention to the drop during the 1990s of nearly 10 per cent in the numbers taking A-level mathematics in England. At the same time, the report also noted that the demand for graduates and postgraduates in these strongly mathematically oriented subjects has grown significantly over the