The Post-14 Mathematics Inquiry

Table of contents
Foreword
Exec. Summary
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Appendix 1
Appendix 2
Appendix 3
Appendix 4

Chapter 1: The importance of mathematics

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 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 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: The supply of teachers of mathematics

The Inquiry recommends that the DfES undertake a review of school level resource management of qualified mathematics teachers in England. This review should include an assessment of whether current career paths and rewards provide appropriate incentives for qualified mathematics teachers to continue teaching mathematics. The LSC might wish to consider a similar exercise regarding the deployment of qualified mathematics teachers in colleges.

The Inquiry recommends that the DfES and the LSC work together and with the TTA to review the frequency and scope of data collection relating to mathematics teacher and teacher trainer numbers and qualifications. They should seek to agree a data collection strategy that will provide the evidence base for a coherent policy approach to the supply of appropriately qualified teachers for the teaching of mathematics across all secondary schools, sixth form and further education colleges, and of appropriately qualified ITTmathematics trainers. In particular, the Inquiry recommends that:

1. a revised form of SSCSS, requiring a mandatory response, should be designed and undertaken as soon as possible to cover not only secondary schools, including those in the independent sector, but also sixth form and furthereducation colleges and providers of mathematics ITT;
2. categories of response be redefined, along similar lines to the Cockcroft categorisation, to provide a clearer indication of teacher qualifications;
3. the breakdown of qualifications should be available separately for the those teaching key skills, KS3, KS4 and post–16;
4. in view of the current critical position in regard to provision of teachers of mathematics and the need for close monitoring of policy initiatives to improve recruitment and retention, at least the first three new surveys should be undertaken every two years.

The Inquiry recommends that at the earliest possible opportunity forecasts of future teacher training number requirements for mathematics teachers be re-examined in the light of:

• the estimate we have suggested of a current shortfall of at least 3,400 qualified mathematics teachers in secondary schools;
• the age profile findings from the 2002 SSCSS;
• and taking into account the current position and future needs of independent schools, Sixth form and FE Colleges, in addition to secondary schools.

The Inquiry recommends that the DfES give high priority to encouraging and funding a significant increase in the number of mathematics graduates admitted to the Fast Track Scheme and, in particular, a significant increase in the number of mathematics ASTs.

The Inquiry recommends that the current TTA enhancement programmes for graduates be evaluated carefully and that additional resources be made available to support and reinforce successful programmes in mathematics. The Inquiry further recommends that the TTA should consider introducing enhancement programmes that offer non-graduate career changers opportunities, including bursaries, to complete graduate mathematics course and secure QTS. The Inquiry recommends that, subject to appropriate quality assurance, the DfES give high priority to providing any extra resources required by the TTA in expanding mathematics enhancement programmes.

The Inquiry recommends that consideration be given to the introduction of new mathematics teacher certification schemes, aimed at increasing the overall supply of teachers appropriately qualified to teach at least some part of the curriculum.

The Inquiry recommends that a significant number of places in the Student Associate Scheme be earmarked for undergraduates on degree courses in mathematics or courses involving a substantial component of mathematics. We encourage the TTA to work closely with the Committee of the Heads of Departments of Mathematical Sciences (HoDMS) and others in higher education to continue to raise the level of awareness of the scheme among relevant undergraduates.

The Inquiry recommends that more must be done to address the issue of pay and other incentives to teachers of mathematics and other shortage subjects (see, also, Recommendation 5.2).

Chapter 4: Action on current and future mathematics pathways

The Inquiry recommends that, subject to the present pilot being fully and successfully evaluated, immediate consideration be given by the QCA and its regulatory partners to moving as soon as is practicable to a two-tier system of overlapping papers for GCSE Mathematics in England, Wales and Northern Ireland. The Inquiry recommends that the regulatory authorities try to recruit more schools and colleges to take part in preimplementation piloting after summer 2004.

The Inquiry recommends that, at the earliest possible opportunity, consideration should be given by the QCA and its regulatory partners to re-designating GCSE Mathematics, appropriately modified if necessary, to merit a double award at level 2. This re-designation should be considered in tandem with the possible move to a two-tier system (see Recommendation 4.1).

The Inquiry recommends that there should be an immediate review by the QCA and its regulatory partners of the quantity of coursework in GCSE mathematics and, in particular, the data handling component, with a view to reducing the amount of time spent on this specific element of the course. (See, also, Recommendation 4.4)

The Inquiry recommends that there should be an immediate review by the QCA and its regulatory partners of the future role and positioning of Statistics and Data Handling within the overall 14–19 curriculum. This should be informed by: (i) a recognition of the need to restore more time to the mathematics curriculum for the reinforcement of core skills, such as fluency in algebra and reasoning about geometrical properties and (ii) a recognition of the key importance of Statistics and Data Handling as a topic in its own right and the desirability of its integration with other subject areas (see, also, Recommendation 4.11).

The Inquiry recommends that the QCA and its regulatory partners should be funded to develop an extension curriculum and assessment framework for more able pupils at Key Stages 3 and 4. This extension curriculum should be firmly rooted in the material of the current Programmes of Study, but pupils should be presented with greater challenges. These should involve harder problem solving in non-standard situations, a greater understanding of mathematical inter-connectedness, a greater facility in mathematical reasoning (including proof) and an ability to engage in multi-step reasoning and more open-ended problem solving (see, also, Recommendation 4.11).

The Inquiry recommends that QCA and its regulatory partners undertake a comparative review and make appropriate re-designations as necessary, to ensure that claimed equivalences of levels of mathematics qualifications are well founded.

The Inquiry recommends that the QCA and its regulatory partners undertake an immediate review of current problems of delivery, content, assessment and availability of courses at levels 1– 3 provided by FSMQs, AS Use of Mathematics, AoN and Adult Numeracy. The aim of the review should be to identify scope for improvements in and potential rationalisation of this provision, including opportunities for more systematic integration of ICT in teaching and learning, as part of the longer-term design of a new 14–19 pathway structure for mathematics (see, also, Recommendation 4.11).

The Inquiry recommends that the effects of the introduction of the revised specifications for GCE be closely monitored by the QCA and its regulatory partners as a matter of high priority and that funding be made available to support this. If there is no significant restoration of the numbers entering AS and A2 mathematics within the next two or three years, the Inquiry believes the implications for the supply of post–16 qualified mathematics students in England, Wales and Northern Ireland to be so serious that consideration should be given by the DfES and the relevant devolved authorities to offering incentives for students to follow these courses. One possible form of incentive could take the form of financial incentives to HEIs to include AS or A-level mathematics as a prerequisite for certain degree courses. Another possibility might be to offer financial incentives directly to students following such course in HEIs, possibly through fee waivers or targeted bursaries.

The Inquiry recommends that the QCA and its regulatory partners conduct an immediate review of the frequency and style of current GCE assessment, with a view to reducing the time spent on external examinations and preparation for examinations.

The Inquiry recommends that there should be an immediate review by the DfES, LSC and the relevant devolved authorities of measures that could be taken to support and encourage current GCE course provision for the most able mathematics students. In particular, we believe there is a need to ensure that there are no funding disincentives in schools and colleges for providing access to Further Mathematics and the Advanced Extension Award in Mathematics We also believe that consideration should be given employing the same incentives as suggested in Recommendation 4.8.

The Inquiry recommends that funding be provided to the QCA and its regulatory partners to commission, through an open bidding process, up to three curriculum and assessment development studies of variants of these pathway models and approaches, including trialling, feedback and modification and an assessment of the workload implications. These studies should take on board developments arising from Recommendations 4.4, 4.5 and 4.7. The aim of this exercise will be to inform the selection of a preferred pathway model to form part of the reformed 14–19 structure in England and possible parallel developments in Wales and Northern Ireland. Given the importance of ensuring the widest possible involvement and commitment of the mathematics community to the outcome, the Inquiry recommends that the regulatory authorities work in partnership with ACME and mathematics community representatives from Wales and Northern Ireland, and that the DfES and relevant devolved authorities provide appropriate funding to support this.

Chapter 5: Support for the teaching and learning of mathematics

The Inquiry recommends to the DfES and the LSC, and the devolved authority in Northern Ireland, that formal responsibility for and entitlement to fully funded CPD be introduced as soon as possible into the professional conditions of service for teachers of mathematics in schools and colleges in England, Wales and Northern Ireland. In the light of what we perceive to be far greater problems with the teaching of mathematics in England and Wales as compared with Scotland, the Inquiry further recommends that the number of contractual hours of CPD in such formal entitlement in England and Wales be significantly greater than the provision made in the agreement A Teaching Profession for the 21st Century in Scotland.

The Inquiry recommends to the DfES and the LSC that additional remuneration be linked to mathematics teachers’ successful completion of accredited CPD activities and opportunities, thereby rewarding those teachers of mathematics who make particular efforts to improve further their subject knowledge and teaching effectiveness.

The Inquiry recommends that there be long-term investment in a national infrastructure to oversee the provision of subject specific CPD and other forms of support for teachers of mathematics, tailored to the needs of teachers of mathematics, both specialist and non-specialist, including leaders in mathematics teaching. A detailed discussion of possible options for such infrastructure support will follow in paragraphs 6.56-78, together with the Inquiry’s recommended option.

The Inquiry recommends that the national support infrastructure for the teaching and learning of mathematics take the form of a national centre providing strategy and coordination, together with regional centres providing local support and networking.

Chapter 6: National and regional support infrastructure

The Inquiry recommends that the work of the National Numeracy Strategy and the mathematics strand of the KS3 Strategy be continued and built upon, and that resources for mathematics are ring-fenced for any future form of successor to these strategies for KS1-3.

The Inquiry recommends that the existing mathematics strand of the KS3 Strategy be incorporated into the national support infrastructure and that the existing funding for this strategy be brought under the auspices of the infrastructure. The Inquiry also recommends that serious consideration be given to similarly incorporating the National Numeracy Strategy. The Inquiry further recommends that, on incorporation, a review of the content and delivery of the strategies be carried out under the auspices of the new infrastructure.

The Inquiry recommends that a programme be established to pay selected volunteer undergraduate and postgraduate students in disciplines with high mathematical content to support teachers of mathematics in schools and colleges. Payment should be on a competitive basis with other sources of employment open to such students. The precise nature of the support role should be for schools, colleges and universities to decide locally. (See also Recommendation 6.14, ninth bullet point.) It will be important to ensure that those participating have the appropriate skills and training.

The Inquiry recommends that the remit of the new national support infrastructure include responsibility for auditing existing ICT provision for mathematics in schools and colleges, assessing the need and potential for future ICT provision in support of the teaching and learning of mathematics and advising the DfES and the LSC on ICT investment requirements for mathematics in schools and colleges.

The Inquiry recommends that the national support infrastructure provide appropriate resources to enable the Committee of Heads of Departments of Mathematical Sciences in HEIs in the UK (HoDoMS) to work together with the LTSN Mathematics, Statistics and Operations Research Network to seek ways to promote sustainable closer links between HEI mathematics (and other relevant) departments and mathematics teachers in their local schools and colleges.

The Inquiry recommends that in the detailed planning of the national support infrastructure for the teaching and learning of mathematics particular attention should be given to involving the relevant experience and expertise of the Open University.

The Inquiry recommends that overall strategy for and coordination of the networking and other CPD developments relating to the mathematics elements of specialist schools be brought under the auspices of the national support infrastructure for the teaching and learning of mathematics.

The Inquiry recommends that the remit of the national infrastructure include responsibility for encouraging and evaluating independent initiatives in the teaching and learning of mathematics and for funding and managing dissemination of successful initiatives more widely across the school and college system. The Inquiry recommends that the overall resources provided for the national and regional centres include specific funding for this purpose.

The Inquiry recommends that the national infrastructure work with SETNET to improve the provision of mathematics enrichment and careers advice resources provided through SETNET and that appropriate funding be made available either through SETNET or the national infrastructure to support this development.

The national infrastructure for the support of the teaching and learning of mathematics should set up formal collaborative links with the NRDC, with a view to exploring how best to support teachers of adult numeracy.

The Inquiry recommends that the remit of the national infrastructure for the support of the teaching and learning of mathematics include the responsibility and resource for providing a national forum for the evaluation, synthesis and dissemination of research and development findings in the field of mathematics education in order to provide an evidence base to inform policy and practice.

The Inquiry recommends that the national infrastructure for the support of the teaching and learning of mathematics consist of:

• a National Centre for Excellence in the Teaching of Mathematics (NCETM) to provide expert advice, resources and information in support of the teaching of mathematics, and to oversee the funding for the development and dissemination of mathematics CPD provision at a strategic level and to coordinate its operation nationally;
• a network of Regional Mathematics Centres (RMCs) to encourage the formation of local communities of teachers of mathematics and relevant stakeholders across all phases and to oversee and coordinate local delivery of CPD.

The Inquiry recommends that the NCETM should:

• provide a forum to bring together all major groups and agencies involved in mathematics education, including from England the DfES, National Strategies, QCA, Ofsted, LEAs, HEIs, LSC, SSCs, ACME, ITT providers, together with equivalent groups and agencies from those territories which choose to be part of the NCETM;
• work with the GTC, TTA and other appropriate groups, including the relevant groups from those territories which choose to be part of the NCETM, to ensure national cohesion in mathematics CPD provision and accreditation;
• incorporate the current CPD work and funding of the NN and KS3 Strategies;
• work closely with the RMCs to provide a centre of expertise for research and development and the commissioning and dissemination of CPD and learning and teaching materials, including distance learning materials and materials to enhance the teaching of mathematics through the use of ICT;
• work closely with the RMCs to ensure an adequate supply of “expert teachers” to provide mentoring and support to local schools and colleges;
• coordinate and monitor CPD delivery provided by the RMCs;
• provide a national forum for the evaluation, synthesis and dissemination of research and development findings in the field of mathematics education;
• provide a database and act as an archive for exemplary teaching and learning and CPD resources and research and development findings;
• support and encourage the further development and dissemination of existing mathematics enhancement and distance-learning initiatives;
• foster international links and collaborative exchanges in relation to research and development in mathematics education.

The Inquiry recommends that the RMCs should:

• be located one in each of the 9 English regions as defined by RDAs, with possible additional national centres in Wales, Northern Ireland and Scotland;
• have formal close working relationships in England with local LEAs and Numeracy and KS3 Strategy regional directors, and with equivalent bodies and individuals from those territories which choose to establish a RMC;
• provide a forum for school, college, FE and HE local links and joint working;
• provide a forum for links and joint working among education providers and teachers, and employers, including RDAs, local LSCs, SETNET, Education and Business Partnerships and equivalent territorial agencies;
• provide support for local networks within the regional networks, building on existing local networks, including mathematics teacher associations, mathematics specialist schools networks, the LTSN for Mathematics, the regional and local activities of the mathematics professional and learned societies, the OU and other HEIs;
• work with the NCETM to deliver CPD regionally/locally for teachers of mathematics (including those teaching other disciplines or vocational subjects) and those who support mathematics teaching across all age groups;
• work with the NCETM to provide a regional/local CPD research and development and dissemination capability in mathematics education;
• provide a regional/local source of expert advice and information on all aspects of the teaching of mathematics;
• provide infrastructure support for quality assured schemes for bringing HE students into the classroom (see, also, Recommendation 6.3);
• together with the NCETM, develop and promulgate programmes and projects aimed at raising the profile of mathematics with pupils, teachers, careers advisers, parents, employers and the public.

The Inquiry recommends that, in addition to the transfer of funding from the existing strategies, the funding provision for the first five years of the NCETM should be of the order of £7M in year 1, £4.5M in years 2, 3 and £2M in years 4, 5, giving a total of £20M over 5 years.

The Inquiry recommends that, in addition to the transfer of funding from the existing strategies, the funding provision for the first five years of the RMCs should be at least of the order of £27M in year 1 and £26.6M in years 2, 3, 4, 5, giving a total of some £133.4M over 5 years.

The Inquiry recommends that, following an appropriate process of consultation, as the first step towards the establishment of the centres for England the DfES appoint and provide a secretariat for a council, to be responsible for overall policy and priorities for the NCETM and RMCs within the remit identified in the Inquiry’s Recommendations 6.13 and 6.14. The Inquiry further recommends that the DfES channel funding for the NCETM and the RMCs through the council, which should be accountable to the DfES for its use. The council should represent the wide range of stakeholders we have identified and the Inquiry recommends that over half of the membership should be appointed on the advice of ACME.

The Inquiry recommends that the locations and managements of the NCETM and the RMCs in England be selected by a process which invites consortia bids to deliver the agendas set out in Recommendations 6.13 and 6.14 and to provide appropriate management and administrative infrastructure for the running of the centres. Consortia will need to incorporate an appropriate range of national and local stakeholders. This bidding process should be overseen by the DfES, advised by the appointed governing council for the NCETM and the RMCs.