The Post-14 Mathematics Inquiry

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The Report

Table of contents
Exec. Summary
Chapter 1
Chapter 2

Chapter 3
Chapter 4
Chapter 5
Chapter 6
Appendix 1

Appendix 2
Appendix 3
Appendix 4

Press Releases
About the Inquiry
Who's involved

Making Mathematics Count

The Report of Professor Adrian Smith's Inquiry into Post-14 Mathematics Education

Executive Summary

Purpose of the post-14 mathematics education inquiry
Overview of the report
The importance of mathematics
Supply of teachers of mathematics
Current mathematics pathways
Action on current and future pathways
Support for the teaching and learning of mathematics
National and regional support infrastructure

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 past decade, not only in science and engineering areas, but also in the financial services and ICT sectors. In addition to the supply problem, the report identified concerns expressed by employers about the mismatch between skills acquired during formal education and those required in the workplace.

  • The Roberts report concluded that this mismatch of supply and demand is leading to skills shortages that will adversely affect the Government’s productivity and innovation strategy. These shortages will become increasingly serious unless remedial action is taken. The report raised a number of concerns about the image and perception of science and engineering among young people. It concluded that many young people have a poor experience of science and engineering education. It also concludes that many have a poorly informed view of career opportunities arising from the study of science and engineering.
0.4 SET for Success was concerned with these generic issues across the range of science and engineering and its overview and recommendations for the most part apply to all the relevant individual disciplines.
0.5 However, it has been widely recognised that mathematics occupies a rather special position. It is a major intellectual discipline in its own right, as well as providing the underpinning language for the rest of science and engineering and, increasingly, for other disciplines in the social and medical sciences. It underpins major sectors of modern business and industry, in particular, financial services and ICT. It also provides the individual citizen with empowering skills for the conduct of private and social life and with key skills required at virtually all levels of employment.
0.6 In addition, many of the generic problems identified across science and engineering in SET for Success manifest themselves most acutely in the area of mathematics. For example: there has long been deep concern about the supply of appropriately qualified mathematics teachers in secondary schools and colleges; there has also been considerable concern about many young people's perception of mathematics as being "boring and irrelevant" and "too difficult, compared with other subjects".
0.7 These and other specific concerns about mathematics in its own right led the Government to conclude that there was a need for a closer examination of current mathematics education provision. The intention to set up this independent Inquiry into Post–14 Mathematics Education was announced by the Chief Secretary to the Treasury, on 23 July 2002. The appointment of the Chair of the Inquiry was announced on 25 November 2002.
0.8 The Terms of Reference of the Inquiry were announced at the same time.
They were:
To make recommendations on changes to the curriculum, qualifications and pedagogy for those aged 14 and over in schools, colleges and higher education institutions to enable those students to acquire the mathematical knowledge and skills necessary to meet the requirements of employers and of further and higher education.
0.9 This Inquiry was commissioned by the UK Government and we therefore focus our recommendations on the UK Government’s areas of responsibilities. Responsibility for mathematics education is devolved to all three devolved administrations, but the degree of common ground with England varies markedly across the territories of the UK as do territorial perceptions of the nature of the problems they face regarding mathematics education. This has meant that much of our analysis and many of our recommendation refer more directly to England than to Wales, Northern Ireland and Scotland. It is hoped, however, that many elements of this report will be useful to all the devolved administrations, as well as to the Department for Education and Skills (DfES) for England.

Overview of the report

0.10 The Post–14 Mathematics Inquiry has identified three key issues of major concern:
  • the shortage of specialist mathematics teachers, particularly in England and Wales;
  • the failure of the current curriculum, assessment and qualifications framework in England, Wales and Northern Ireland to meet the needs of many learners and to satisfy the requirements and expectations of employers and higher education institutions;
  • the lack of resources, infrastructure and a sustained continuing professional development culture to support and nurture all teachers of mathematics.
0.11 The main body of the report consists of six chapters:
  • Chapter 1 reviews the very special nature and importance of mathematics and the need for more young people to acquire greater mathematical skills;
  • Chapter 2 reviews problems related to the supply of mathematics teachers;
  • Chapter 3 provides a detailed account of current 14–19 mathematics pathways in the UK;
  • Chapter 4 reviews the fitness for purpose of current pathways and
  • considers possible action on current and future mathematics pathways;
  • Chapter 5 considers the issues of how we could provide better support for the teaching and learning of mathematics;
  • Chapter 6 details possible national and regional support infrastructure for the teaching and learning of mathematics.

The importance of mathematics (chapter 1)

0.12 The Inquiry regards it as vital that society fully recognises the importance of mathematics: its importance for its own sake, as an intellectual discipline; for the knowledge economy; for science, technology and engineering; for the workplace; and for the individual citizen.
0.13 All this underlines the importance of ensuring a sufficient supply of young people with appropriate mathematical skills. However, we currently face a situation of long term decline in the numbers of young people continuing to study mathematics post–16 in other than Scotland. The Inquiry draws attention to possible factors underlying this decline.
  • the perceived poor quality of the teaching and learning experience;
  • the perceived relative difficulty of the subject;
  • the failure of the curriculum to excite interest and provide appropriate motivation;
  • the lack of awareness of the importance of mathematical skills for future career options and advancement.

We examine these particular issues in greater detail in later chapters and make a number of recommendations.

0.14 We believe it to be crucial that the importance of mathematics is more clearly and visibly recognised within Government and its agencies. We also believe that the current division of responsibilities in England between the DfES and the Learning and Skills Council (LSC) for schools and colleges, respectively, creates an obstacle to providing a coherent strategy for mathematics education throughout the 14–19 stage. The Inquiry therefore recommends that a high level post be created in the DfES with dedicated subject specific responsibility for mathematics and that the DfES and LSC create a high level joint forum for overseeing a coherent strategy for mathematics education.
0.15 We are also concerned about the lack of a national body to champion the cause of mathematics and mathematics education to Government the DfES, the devolved administrations and others, and to ensure that the potential contributions of mathematics to the economy and society are appreciated at the highest levels. The Advisory Committee for Mathematics Education (ACME) already plays this role to some extent in relation to mathematics education and we envisage an extended role for ACME in taking forward a number of this report’s recommendations. However, there is no corresponding body to speak on behalf of the mathematics community to Government and others on strategic issues relating to general research and industrial reach-out role of mathematics in the economy and society. The Inquiry recommends that ACME be provided with enhanced support in order to play an active role in helping to take forward the recommendations of this Inquiry and that a corresponding body be set up to speak on behalf of the mathematics community on strategic issues relating to research and knowledge transfer in mathematics.

Supply of teachers of mathematics (chapter 2)

0.16 The shortage of specialist mathematics teachers teaching mathematics is the most serious problem we face in ensuring the future supply of sufficient young people with appropriate mathematical skills. We think it likely that there is a current shortfall of around 3,400 specialist mathematics teachers in maintained secondary schools in England. We also note a recent survey finding that over 30 per cent of those currently teaching mathematics do not have a post A-level qualification in mathematics.
0.17 A further finding from the Inquiry that has concerned us is that there are apparently very significant numbers of teachers in schools qualified to teach mathematics who do not teach mathematics. If the figures we have are accurate, some 25 per cent of teachers in schools in England qualified to teach mathematics are employed in tasks other than teaching mathematics. This seems to the Inquiry to raise serious issues about current school level resource management and to merit at least some further investigation. The Inquiry recommends that the DfES undertake a review of school level resource management of qualified mathematics teachers in England and consider, in particular, whether current career paths and rewards are providing appropriate incentives for qualified mathematics teachers to continue teaching mathematics.
0.18 The above recommendation refers to incentives to those already in the system. In trying to recruit qualified mathematicians into teaching, we are competing with other employment opportunities for mathematicians that in recent years have increasingly offered career prospects that are perceived as considerably more attractive than teaching: the finance industry provide one obvious example. In this regard, the Inquiry has come to the same conclusion as the Roberts review: namely, that ultimately market forces will have to be recognised in setting remuneration levels for teachers in shortage subjects. We are aware that the Roberts recommendation was not accepted. However, we do not believe the issue can continue to be ignored. The Inquiry therefore recommends to the DfES that the issue of enhanced financial incentivesfor teachers of mathematics (and subjects with similar recruitment difficulties) be reconsidered.
0.19 The scale of the problem of the shortfall of specialist teachers is analysed in detail in Chapter 2 of the report. However, the Inquiry has found it very frustrating not to be able to arrive at a clear overall picture of current and future needs for mathematics teachers in schools and colleges due to irregular and radically incomplete official data collection, particularly in the Further Education sector. The Inquiry makes recommendations to the DfES and the LSC about future data collection and its importance for policy. In particular, in setting appropriate targets for the future recruitment of mathematics teachers and for monitoring progress towards meeting the shortfall.
0.20 The serious magnitude of the current problem can be appreciated from the fact that to solve the problem of the shortfall we would need to attract into teacher training over 40 per cent of the annual UK output of mathematics graduates for each of the next several years.
0.21 Such a solution is not, of course, available. However, there are many current schemes and initiatives in place aimed at boosting the numbers entering mathematics teacher training. These include enhancement courses, which enable those without appropriate existing mathematics qualifications to acquire these as a first step to training as a mathematics teacher. They also include schemes for encouraging more undergraduates to consider a teaching career. The Inquiry strongly supports all such measures undertaken by the Teacher Training Agency and supported by the DfES and makes recommendations for increased funding, where appropriate, to further encourage the expansion of mathematics teacher training places. The Inquiry also recommends further support for schemes aimed at fast track careers for outstanding mathematics teachers.
0.22 We acknowledge the concerns of respondents to the Inquiry that schemes involving enhancement courses will necessarily be attracting potential entrants to the teaching profession with very varying levels of mathematical knowledge. In this connection, we have identified one area where we think a radical rethink in the approach to the certification of teachers could both help to increase the supply of those able to teach some part of the mathematics curriculum and also allay the fears of those who are concerned about the possible lack of mathematical knowledge of entrants to teaching coming through this route. The Inquiry recommends that consideration be given to the introduction of new mathematics teacher certification schemes which award certification to teach mathematics only up to certain specified levels, eg Key Stage 3.

Current mathematics pathways (chapter 3)

0.23 These are reviewed in some detail as necessary background to our subsequent discussion of concerns expressed to the Inquiry about current provision and the steps that might be taken to improve the situation.

Action on current and future pathways (chapter 4)

0.24 The work of the Post–14 Mathematics Inquiry has proceeded in parallel with deliberations of the Working Group on 14–19 Curriculum and Qualifications reform in England and similar initiatives in Wales. The Inquiry has not regarded itself as constrained by the thinking emerging from the Progress and Interim Reports of the Working Group, but it has clearly been of interest to the Inquiry to keep in mind the issue of the compatibility of its own thinking with that of the Working Group. We do not believe that any of the short-term or longterm changes we recommend will cause any problems when it comes to designing detailed pathways in mathematics compatible with the kind of framework envisaged by the Working Group. More positively, we strongly support the Working Group’s wish to see a move away from rigid, age-related, one-size-fits-all arrangements.
0.25 It is clear that the overwhelming majority of respondents to the Inquiry no longer regard current mathematics curricula, assessment and qualifications as fit for purpose.
0.26 So far as GCSE is concerned, public perception, in line with school and college league tables, regards a Grade C as the “success” threshold. However, within the current three-tier arrangements for mathematics the lower (Foundation) tier can only lead to at most the attainment of a Grade D. As a result, the 30 per cent of the age cohort entered for this tier are pre-destined to "fail". The Inquiry believes this to be a perverse arrangement and would wish to see a new structure in place as soon as possible. A two-tier GCSE is currently being piloted. The Inquiry recommends that, subject to successful piloting, we move as soon as possible to a two-tier system for GCSE mathematics in England, Wales and Northern Ireland.
0.27 Respondents to the Inquiry also report the universal perception among teachers and pupils that the amount of effort required to obtain the single GCSE in mathematics is similar to that needed to obtain the two awards in English or the double award in science. This further reinforces pupils' view of mathematics as a disproportionately hard subject and undoubtedly influences pupils' subject choices post–16. The Inquiry recommends that immediate consideration be given to re-designating GCSE mathematics as a double award.
0.28 There is much concern and debate about the positioning of Statistics and Data Handling within the current mathematics GCSE, where it occupies some 25 per cent of the timetable allocation. On the one hand, there is widespread agreement that the Key Stage 4 curriculum is over-crowded and that the introduction of Statistics and Data Handling may have been at the expense of time needed for practising and acquiring fluency in core mathematical manipulations. Many in higher education mathematics and engineering departments take this view. On the other hand, there is overwhelming recognition, shared by the Inquiry, of the vital importance of Statistics and Data Handling skills both for a number of other academic disciplines and in the workplace. The Inquiry recommends that there be a radical re-look at this issue and that much of the teaching and learning of Statistics and Data Handling would be better removed from the mathematics timetable and integrated with the teaching and learning of other disciplines (eg biology or geography). The time restored to the mathematics timetable should be used for acquiring greater mastery of core mathematical concepts and operations.
0.29 In addition to the anxiety referred to above about the undesirable effects of the current arrangements for the lower attaining 30 per cent of the age cohort, respondents to the Inquiry have expressed considerable concern that we do not sufficiently stretch and motivate the top 10 per cent. The Inquiry agrees and believes it to be vitally important that we nurture and encourage the very best mathematical talent. The Inquiry therefore recommends that attention be given to making special provision in mathematics for these more able pupils, both at GCSE and GCE levels.
0.30 Towards the more vocational end of the spectrum, respondents to the Inquiry have expressed considerable concerns regarding mathematics provision and the delivery of mathematics teaching within and relating to the Government's Key Skills agenda. There is a widespread feeling that it would be timely to consider rationalising the provision available through Application of Number, Free Standing Mathematics Qualifications, AS Use of Mathematics and Adult Numeracy qualifications. The Inquiry agrees and recommends that such a review be undertaken as soon as possible.
0.31 There is widespread recognition that the Curriculum 2000 reforms which led to a new post–16 structure based on AS and A2 levels have been a disaster for mathematics. The original AS/A2 split simply did not work. Students could not cope with the material within the laid down timetable and in the first year of operation the pass rate for AS mathematics was only just over 70 per cent, compared with over 90 per cent in many other subjects. The consequence was that the image of mathematics has suffered badly again and entries in the following two years have been some 20 per cent down on pre–2000 numbers. Given the UK’s long-standing concern about the small numbers continuing with mathematics post–16, this further serious decline in the supply chain is very serious indeed. There are also concerns about the nature and frequency of assessment for AS/A2. The Inquiry supports the remedial measures that are being put in place to try to mitigate the AS/A2 problems in mathematics and recommends reconsideration of the frequency and style of assessment. However, the Inquiry regards it as vitally important that numbers of entries in future years be closely monitored and, if there is no significant improvement, we recommend that radical measures – including financial incentives – be considered to address the issues of increasing post–16 take up of mathematics.
0.32 So far as the longer-term re-design of mathematics 14–19 pathways is concerned, we explore a number of ideas encapsulating differing suggestions emanating from the mathematics community. We have set out a number of principles that we are clear should inform the design of new pathways in order to avoid the perceived defects of the current arrangements. We do not believe that a one-size-fits-all model is appropriate. We wish to see a highly flexible set of interlinking pathways that provide motivation, challenge and worthwhile attainment across the whole spectrum of abilities and motivations, but avoid the danger of returning to the O-level/CSE "sheep and goats" divide. We are clear that the new design should be underpinned and supported by extensive trialling and piloting and that a wide cross-section of the mathematics community be given maximum opportunity to participate in and influence the process of re-design. The Inquiry therefore recommends that an open bidding process be adopted to identify and commission several groups to carry out curriculum and assessment development studies as a preliminary to identifying a preferred pathways model to form part of the eventual reformed 14–19 structure in England.

Support for the teaching and learning of mathematics (chapter 5)

0.33 The Inquiry believes that whatever the longer-term prospects of increasing the supply of specialist mathematics teachers, we must do everything possible to support and nurture those teachers currently teaching mathematics in schools and colleges. They need and deserve the very best support we can provide. Much of this chapter therefore focuses on the need for various forms of Continuing Professional Development (CPD) for teachers of mathematics and the need to radically change our culture of expectations in relation to CPD in England, Wales and Northern Ireland. The situation in Scotland is already changed. The Inquiry recommends that formal responsibility for and entitlement to fully funded CPD be introduced as soon as possible into the professional terms and conditions of service of teachers of mathematics in schools and colleges in England, Wales and Northern Ireland. The Inquiry further recommends that additional remuneration be linked to successful completion of accredited CPD activities.

National and regional support infrastructure
(chapter 6)

0.34 We present detailed arguments in favour of delivering CPD and other forms of support for teachers of mathematics through a national and regional infrastructure. We believe this provision to be of the utmost importance in sustaining, nurturing and enhancing current provision of mathematics teaching. The Inquiry strongly recommends that in England this support infrastructure take the form of a National Centre for Excellence in Mathematics Teaching, together with nine Regional Mathematics Centres. The Inquiry recommends that this infrastructure incorporate existing CPD provision, including the mathematics strand of the current Key Stage 3 Strategy.
0.35 In addition to supporting the delivery of CPD, the Inquiry believes that such an infrastructure should provide both strategic co-ordination of and local support for a wide range of other important networking and resource provision for the support of the teaching and learning of mathematics. The Inquiry makes firm recommendations relating to: the provision of an expert resource for dissemination of educational research and development findings, including those relating to the use of ICT; networking and mentoring relationships involving local schools, colleges, higher education and business; the incorporation of relevant existing mathematics support activities and initiatives, including the work of the Open University, the Learning and Teaching Skills Network, the Specialist Schools Network and the National Research and Development Centre for adult literacy and numeracy.


0.36 The Inquiry has identified three broad areas of considerable concern:
  • the shortage of specialist mathematics teachers;
  • the failure of the current curriculum and qualifications framework to meet the requirements of learners, higher education and employers, and to ensure that sufficient numbers of young people continue with mathematics post–16;
  • the need to support, sustain and enhance current teachers of mathematics through CPD and other teaching and learning resources.
0.37 The recommendations set out in this report provide a series of practical measures designed to begin to reverse the problems and concerns we have identified. The Inquiry believes that implementing these recommendations will provide a crucial first step towards ensuring a future supply of sufficient young people in the UK with appropriate mathematical skills.

1 The large majority of the recommendations were endorsed by Government in Investing in Innovation in July 2002 and significant funding has been ommitted to both schools and universities in areas such as science laboratories, equipment, studentships and assistantships.

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