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

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About the Inquiry
Who's involved

Making Mathematics Count

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

Chapter 1 - The Importance of Mathematics

Mathematics for its own sake
Mathematics for the knowledge economy
Mathematics for science, technology and engineering
Mathematics for the workplace
Mathematics for the citizen
Increasing mathematical skills
This report
The special position of mathematics
Territorial responsibilities
Government departments and agencies
The mathematics education community

Mathematics for its own sake

1.1 Mathematics provides a powerful universal language and intellectual toolkit for abstraction, generalization and synthesis. It is the language of science and technology. It enables us to probe the natural universe and to develop new technologies that have helped us control and master our environment, and change societal expectations and standards of living. Mathematical skills are highly valued and sought after. Mathematical training disciplines the mind, develops logical and critical reasoning, and develops analytical and problemsolving skills to a high degree.

Mathematics for the knowledge economy

1.2 Mathematics is of central importance to modern society. It provides the vital underpinning of the knowledge economy. It is essential in the physical sciences, technology, business, financial services and many areas of ICT. It is also of growing importance in biology, medicine and many of the social sciences. Mathematics forms the basis of most scientific and industrial research and development. Increasingly, many complex systems and structures in the modern world can only be understood using mathematics and much of the design and control of high-technology systems depends on mathematical inputs and outputs.

Mathematics for science, technology and engineering

1.3 Ensuring an adequate supply of people with science, technology, engineering and mathematics skills is at the heart of the UK Government’s strategy for innovation and productivity and was the subject of the recent important Roberts report (April 2002), SET for Success: the supply of people with science, engineering and mathematics skills.
1.4 The report documents the declining numbers of young people continuing post-16 with education in subjects with high mathematics content other than in Scotland, where numbers have increased substantially in recent years as a result of the introduction of new National Qualifications in 1999, which provided a wider range of qualifications. The UK is almost alone in Europe in not making some form of mathematics a compulsory part of the post-16 curriculum. Currently, less than 10 per cent of the age cohort in England continues with mathematics post-16; and less than 10 per cent of those who do continue go on to do a mathematics degree.
1.5 Against this background, the Roberts report provides a wealth of data and analysis in support of the need for greater numbers of trained young people with appropriate mathematical skills. In particular, it provides evidence from employment rates, salary levels and surveys of employers' recruitment experience that demonstrates that graduates and postgraduates in strongly mathematical subjects are in increasing demand in the UK economy. The report concludes that skills shortages in areas requiring high levels of mathematical knowledge are resulting from the disparity between the growing demand for such skills and the declining numbers of graduates in the relevant disciplines. These shortages constitute a threat to the Government’s innovation and productivity strategy and to the future strength and success of the UK economy.

Mathematics for the workplace

1.6 Although the role of mathematics in underpinning science, technology and engineering is reasonably well recognized and acknowledged in the UK, the fundamental and all-pervasive role of mathematics throughout the rest of the economy is typically not well understood. To the layman it can appear that mathematics for the workplace has become less important because "everything is now done by computers". The clear message to the Inquiry from a wide range of leading industries and businesses is that this is absolutely not the case.
1.7 Major employers in the engineering, construction, pharmaceutical, financial and retail sectors have all made clear to us their continuing need for people with appropriate mathematical skills. In particular, employers highlight the shortage of statisticians. Advanced economies need an increasing number of people with more than minimum qualifications in mathematics to stay ahead in international competitiveness and, in particular, to effectively exploit advances in technology. An adequate supply of young people with mastery of appropriate mathematical skills at all levels is vital to the future prosperity of the UK.
1.8 Requirements for mathematical skills in the workplace have been examined in detail in a recent report, Mathematical Skills in the Workplace (Celia Hoyles, Alison Wolf, Susan Molyneux-Hodgson and Philip Kent – June 2002, Institute of Education and STMC). A key finding of the study was that although the ubiquitous use of information technology in all sectors has changed the nature of the mathematical skills required, it has not reduced the need for mathematics. The authors of the report refer to these mathematical skills and competencies, framed by the work situation and practice and the use of IT tools, as “mathematical literacy”. The term partly reflects the skills needed by individuals in relation to business goals, but also reflects the need to communicate mathematically expressed decisions and judgements to others. On the basis of detailed case studies, the report concludes that there is an increasing need for workers at all levels of organisations to possess an appropriate level of mathematical literacy.

Mathematics for the citizen

1.9 The acquisition of at least basic mathematical skills – commonly referred to as "numeracy" - is vital to the life opportunities and achievements of individual citizens. Research shows that problems with basic skills have a continuing adverse effect on people’s lives and that problems with numeracy lead to the greatest disadvantages for the individual in the labour market and in terms of general social exclusion. Individuals with limited basic mathematical skills are less likely to be employed, and if they are employed are less likely to have been promoted or to have received further training.

Increasing mathematical skills

1.10 From all perspectives, the UK needs more young people with greater mastery of higher levels of appropriate mathematics skills than is currently the case. To achieve this, we need three things to happen:
  • first, that more young people continue longer with the study of mathematics;
  • secondly, that we have a clear view of what are, at any given level, the appropriate mathematical skills to be acquired and what constitutes mastery of these skills;
  • thirdly, that, having agreed the latter, the teaching and learning process and environment effectively encourages and promotes the mastery of these skills.
1.11 In the current non-compulsory environment, the first requirement in paragraph 1.10 leads us to consider the issue of the numbers of students choosing to continue with mathematics post-16. This leads us to consider the factors that influence student choice post-16 and how these might be modified. Factors influencing student choice are complex and not well understood, although certain themes emerge anecdotally from focus groups:
  • the influence of the teacher is clearly important; in particular, poor teaching is likely to turn students off mathematics;
  • the perceived difficulty of mathematics relative to other subjects is also important both to schools (concerned with league tables) and to individual students (concerned with university entrance);
  • separate from perceived difficulty, the content of the course may be perceived to be boring or irrelevant, or insufficiently stimulating or challenging;
  • lack of awareness of the link between career options and subject choices may also play a role, both for teachers and students.
1.12 The second requirement leads us to consider issues of curriculum, assessment and qualifications and whether these are currently fit for purpose.
1.13 The third requirement leads us to consider issues relating to learning pathways, teaching resources and pedagogy (including the use of ICT) and whether these are currently fit for purpose.

This report

1.14 In this report, we address these issues in the following way.
  • Chapter 2 reviews problems related to the supply of specialist mathematics teachers and makes a number of recommendations;
  • Chapter 3 sets the scene for a discussion of curriculum, assessment and qualifications issues with a detailed account of current 14-19 mathematics pathways in the UK;
  • Chapter 4 reviews in detail a number of the concerns expressed to the Inquiry about the fitness for purpose of current pathways and makes a number of recommendations for short- and mediumterm improvements and changes;
  • Chapter 4 goes on to make a longer-term recommendation about preparation for a more radical re-think of mathematics pathways in the context of the kinds of overall changes to the 14-19 landscape that might emerge, for example in England, from the Working Group on 14-19 curriculum and qualifications reform;
  • Chapter 5 considers the issues of how we could better support, in the very broadest sense, the teaching and learning of mathematics;
    in particular, how we could better support those involved in the teaching of mathematics at all levels through various forms of Continuing Professional Development;
  • Chapter 6 presents a blueprint for a national infrastructure to oversee and deliver such support for the teaching and learning of mathematics.

The special position of mathematics

1.15 In considering these issues, the Inquiry has inevitably had to relate the concerns of mathematics both to other disciplines and to the wider concerns of schools and the education system. This has led us to become increasingly concerned that there is insufficient recognition, in many quarters, of the fact that mathematics is in many respects "special" and that we must be prepared to consider, particularly in terms of organisation, structures, and investment, that different approaches and prioritisation may be required for mathematics.
1.16 There are positive senses in which mathematics is special. First, by virtue of its fundamental nature as a universal abstract language and its underpinning of the sciences, technology and engineering, mathematics has a claim to an inherently different status from most other disciplines. Secondly, as we have set out above, mathematics is fundamentally important in an all-pervasive way, both for the workplace and for the individual citizen.
1.17 But there are also negative senses in which mathematics is special. In particular, in the UK there is a widespread view, among both parents and students, that the subject itself is "difficult" and "boring" and presents disproportionate challenges in the school and college setting, both in terms of the workload and the achievability of high grades. Another, unfortunate, negative sense in which mathematics is special derives from the very serious shortage of specialist mathematics teachers, particularly in maintained secondary schools and colleges in England and Wales.

Territorial responsibilities

1.18 Within the territories of the UK, there is a varied pattern of devolution of responsibilities for different aspects of mathematics education. Scotland has a completely devolved system and all responsibilities lie ultimately with the Scottish Executive. Northern Ireland also has fully devolved responsibilities, but its curriculum and qualification structure is very similar to that of England and Wales and it has historically approached issues of teachers’ pay and conditions with a view to generally maintaining parity with England and Wales. Wales no longer has a common curriculum with England, although the current arrangements are still very similar to the previous joint arrangements. It has responsibilities for its own targets for teaching training and for Continuing Professional Development, but responsibility for teachers' pay and conditions remains with the Department for Education and Skills (DfES). Engalnd, Wales and Northern Ireland share a common qualifications system.

Government departments and agencies

1.19 This report makes a number of detailed recommendations. However, we are necessarily addressing our recommendations to existing government departments and agencies and have inevitably been led to reflect on whether these are currently organised and constituted in a manner best suited to acknowledging and taking forward our very special concerns about mathematics. We have outlined above the complex division of devolved responsibilities among the four territories of the UK but restrict our further discussion of this issue to England.
1.20 In particular, respondents are concerned about what they see as current obstacles in England to taking forward subject-specific agendas within the education system. For example, the Inquiry has observed, with considerable concern, that there is no high-level post in the DfES in England with dedicated subject-specific responsibility for mathematics. We are also very concerned that in England the split of responsibilities between secondary schools (DfES) and Sixth Form and FE Colleges (LSC) presents a potential obstacle to joinedup thinking and action regarding 14-19 mathematics educational strategy. This prompts our first recommendation.
Recommendation 1.1

The Inquiry recommends that in England a high-level post be created in the DfES with dedicated subject-specific responsibility for mathematics. The Inquiry further recommends that in England a joint forum be created between the DfES and the LSC through which high-level officers in the DfES and LSC with subject-specific responsibilities for mathematics are charged with overseeing coherent strategy for 14-19 mathematics education.


The mathematics education community

1.21 It has also become clear during the course of this Inquiry that although almost everyone can be regarded as an important stakeholder in mathematical education, there are currently very few forums for effective communication among major stakeholders. We make some recommendations in Chapters 5 and 6 that attempt to address this issue at a local level, but a broader issue remains.
1.22 The Advisory Committee for Mathematics Education (ACME) is a recently formed body, empowered by the Royal Society and the mathematics professional bodies and learned societies that come under the umbrella of the Joint Mathematics Council to speak on behalf of the mathematics community on matters in England pertaining to mathematics education. In any particular case, the involvement of ACME, augmented by professional representatives from the territories as and when appropriate, could provide a direct and manageable mechanism for involving a large part of the professional stakeholder community. We believe this to be an important and valuable role for ACME to play and have made explicit suggestions for ACME's involvement in a number of the Inquiry's recommendations. However, the current scale of funding for ACME would not support this expanded role. This prompts our next recommendation.
Recommendation 1.2

The Inquiry recommends that, in order to enable ACME to play an important extended role, including taking forward a number of the Inquiry's recommendations, substantial Government funding be made available to ACME. We recommend that this be channelled, as is existing funding, through the Royal Society, in order to enable ACME to retain its standing as an independent voice acting on behalf of the mathematics education community.


The wider mathematics community

1.23 However, the Inquiry is aware that ACME is empowered only to represent the wider mathematics community on matters of mathematics education. Respondents to the Inquiry have covered a much wider constituency of stakeholder interests; in particular, those in the mathematics community primarily concerned with mathematics research and/or the outreach of mathematics to business and industry.
1.24 Many of these respondents to the Inquiry have noted the lack of a single high-level body - comparable, say, with the Science Council or the Engineering and Technology Board - that could make representations to the DfES, or to Ministers when appropriate, on strategic level issues relating to the discipline of mathematics and its role in the economy and society. The Inquiry believes that such a body would be invaluable in advising on taking forward the issues and recommendations presented in this report and in sustaining subsequent strategic discussions on the future of mathematics in the UK. This prompts the following recommendation.
Recommendation 1.3

The Inquiry recommends that the UK mathematics learned and professional societies form an Advisory Committee on Mathematics Research and Industry (ACMRI), which would be empowered to speak on behalf of the community to Government and others on strategic level issues concerning the role of mathematics in the economy and society, complementing ACME's role in relation to mathematics education. The Inquiry suggests that it would be valuable to also have a joint Advisory Committee for Mathematics (ACM), formed from representatives of ACME and ACMRI, to speak on behalf of the community on general strategic issues concerning mathematics.

Chapter 2->

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