The Post-14 Mathematics Inquiry

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Making Mathematics Count

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

Chapter 5 -  Support for the Teaching and Learning of Mathematics

Continuing Professional Development (CPD) for teachers of mathematics
The need for subject-specific CPD
The ACME report
CPD content and delivery
Key requirements and tasks of a support infrastructure

Continuing Professional Development (CPD) for teachers of mathematics

5.1 The Government has recognized in setting up this Inquiry that there is an urgent need to improve the mathematical skills of the general population. There are concerns about both numbers and quality and, in particular:
  • the relatively low numbers of school pupils continuing mathematics post-16 through to the age of 19 and beyond;
  • a declining trend in the number of students obtaining degrees in Higher Education courses in disciplines with substantial mathematical content; and
  • the under-supply of appropriately qualified teachers of mathematics, which is exacerbated by the high demand in other sectors of the economy for the skills of mathematically qualified graduates.
5.2 In previous chapters of this report, we have examined ways in which the future supply of appropriately qualified mathematics teachers entering the profession might be increased and ways in which the numbers of pupils continuing with mathematics post-16 might be increased.
5.3 We now turn to the issue of support for staff currently teaching mathematics in schools and colleges. We consider possible forms of support to update and enhance subject knowledge and pedagogy and to sustain enthusiasm and commitment. Respondents to the Inquiry have noted with concern that, in contrast to many other professions, there is not a strong tradition of Continuing Professional Development (CPD) among teachers in England, Northern Ireland and Wales.
5.4 The situation is somewhat different in Scotland, where local authorities have a stronger tradition of delivering CPD for teachers and CPD responsibilities and entitlements have been incorporated into a formal agreement, A Teaching Profession for the 21st Century, which followed the report of the McCrone Inquiry (January 2001) into professional conditions of service for teachers in Scotland.
5.5 The agreement in Scotland included the following:
  • teachers shall have an ongoing commitment to maintain their professional expertise through an agreed programme of CPD;
  • an additional contractual 35 hours of CPD per annum will be introduced as a maximum for all teachers, which shall consist of an appropriate balance of personal professional development, attendance at nationally accredited courses, small scale school based activities or other CPD activity; this balance will be based on an assessment of individual need taking account of school, local and national priorities and shall be carried out at an appropriate time and place;
  • every teacher will have an annual CPD plan agreed with her/his immediate manager and every teacher will be required to maintain an individual CPD record;
  • it was recognized that a framework for professional development will take some time to deliver and therefore teachers would work towards but not be expected to meet the full commitment until August 2003;
  • the aims of the agreement are to enhance opportunities available to all teachers and minimize teachers undertaking work that is a not directly related to their key role in teaching and learning; it was also agreed that CPD should be a condition of service, and every teacher should have a commitment to it;
  • local authorities will undertake to review their provision within the arrangements for the development of a national register of approved CPD providers, and consideration should be given to the role of a national agency such as Learn Direct Scotland in this regard: not all CPD will necessarily be accredited, but there should be maximum opportunity for accreditation.
5.6 In view of these recent developments in Scotland, most of what follows in this chapter – with some exceptions, which we shall clearly flag – should be taken to refer to the situation in England, Northern Ireland and Wales.
5.7 The clear message to the Inquiry from many sources is that there is a need for a radical change in culture regarding CPD in the teaching profession in England, Northern Ireland and Wales. Ideally, it is felt that every teacher should have a personal professional development plan, to which both teacher and school commit in writing, placing obligation for ongoing CPD on them both, as in Scotland. Indeed, the McCrone agreement is seen by many to be a minimal model to which the rest of the UK should aspire.
5.8 The Inquiry believes that CPD is important for all teachers in all subjects. We therefore welcome all recent moves in the UK toward a strategy for more systematic CPD provision. In particular, we welcome the General Teaching Council’s (GTC) introduction of the Teachers’ Professional Learning Framework (TPLF) in England, which offers a map of professional development experiences. Teachers will use the TPLF to plan their individual development needs. Headteachers, CPD co-coordinators, Local Education Authority (LEA) advisers and others will use the TPLF to develop CPD policy strategy and facilitate networks of professional learning. The General Teaching Council for Wales (GTCW) is considering a similar initiative for teachers in Wales, as is the recently established General Teaching Council for Northern Ireland (GTC(NI)).
5.9 In Wales, some funding for CPD is provided directly through the GTCW. General funding for CPD is included as an element within the “Grants for Education, Support and Training” (GEST) programme, which is funded 60% directly by the Assembly and 40% by the Welsh LEAs from funds included in the overall revenue settlement. It is intended that CPD be explicitly linked to the newly introduced performance management arrangements in Wales, which will identify individual teacher’s development needs. Schools will set their own priorities within the scope of the scheme. Currently, there is no requirement for subject specific CPD and no money is ring-fenced for individual subjects. The Inquiry understands that funds could be used for subject specific CPD, but that the Welsh Assembly Government would not wish to be centrally prescriptive about priorities.
5.10 In Northern Ireland, statutory responsibility for CPD for teachers lies with the Education and Library Boards (ELBs). Each ELB has a Curriculum Advisory and Support Service (CASS), with teams of officers, including those for mathematics, who provide support to schools in both subject specific and more thematic whole-school areas. The CCEA also has a role in relation to the provision of support materials for teachers in Northern Ireland. There is now in place in Northern Ireland a fully integrated programme of initial teacher education, induction and early professional development, as well as the Professional Qualification for Headship programme. Further developments are under consideration by the GTC(NI).
5.11 We have already noted the different situation regarding CPD entitlement and provision in Scotland.

The need for subject-specific CPD

5.12 The Inquiry welcomes increasing evidence of greater emphasis on and commitment to CPD for teachers throughout the UK. However, we note that most of these developments are not specifically aimed at systematic and sustained subject specific CPD.
5.13 A teacher’s overall competence involves three separate elements: subject matter knowledge and confidence, general pedagogical skills and subject specific pedagogical skills Overwhelmingly, concerns expressed to the Inquiry about the current overall state of mathematics teaching in schools and colleges in England have focused on subject matter knowledge and subject specific pedagogy. The Inquiry shares these concerns.
5.14 Separate from recent developments in support of generic CPD for teachers, the Inquiry therefore believes that a large-scale programme of subject specific CPD for teachers of mathematics in England, Northern Ireland and Wales is an urgent priority in its own right. This message has been strongly reinforced in relation to teachers of mathematics in England by the December 2002 report, Continuing Professional Development for Teachers of Mathematics, from the Advisory Committee on Mathematics Education (ACME PR/01), which we shall discuss in more detail later in this chapter.
5.15 We have not received the same unequivocal message in relation to the situation in Northern Ireland and Wales. However, responses to the Inquiry from Northern Ireland indicate clear needs for both subject matter and pedagogy CPD. In particular, teachers in Northern Ireland expressed the view that more mathematics subject specific CPD would be desirable. We have also been informed of the view of the ACCAC that issues relating to teachers of mathematics are seen in Wales as the key to raising standards in mathematics. We believe therefore that much of the following general discussion of the situation in England will be found to be relevant to Northern Ireland and Wales.
5.16 The ACME report concluded that the most effective way to provide support and raise the quality of mathematical provision in schools in England would be to expand CPD substantially for teachers of mathematics throughout the system.
5.17 Pre-14, a start on this has already been made in England through the National Numeracy Strategy in primary schools, and the mathematics strand of the Key Stage 3 Strategy for 11-14 year olds in secondary schools. Although formally outside the remit of this Post-14 Inquiry, we shall consider the work of these strategies later in more detail in paragraphs 6.4-15.
5.18 In Northern Ireland, the Northern Ireland Numeracy Strategy (NINS) has raised the profile of CPD for teachers of mathematics. The NINS is focusing on three inter-related strands of support, provided by CASS, for primary and post-primary teachers of mathematics: leadership and management, learning and teaching and the use of ICT. It has provided targeted funding for teachers of mathematics (including all primary school teachers), facilitated closer working among the five ELBs and sought to provide a consistent message on the development and support of mathematics across the different phases of compulsory schooling. All teachers of mathematics are entitled to two days of professional development, typically supported by in-school development work. Other elements of the strategy include support for numeracy coordinators and heads of mathematics departments.
5.19 Respondents to the Inquiry overwhelmingly endorse the general analysis set out in the ACME report and support the report’s conclusions regarding the fundamental need for a substantial increase in the provision of appropriate CPD for teachers of mathematics. The Inquiry also strongly supports the broad thrust of the recommendations set out in the ACME report. Chapter 2 of this Post-14 Mathematics Inquiry report has discussed the urgent need to address the problem of recruitment of sufficient numbers of suitably qualified mathematics teachers. The ACME report makes clear that there is also an urgent need to provide infrastructure to support the retention and enhancement of existing teachers of mathematics in schools and colleges.
5.20 The ACME report recommendations provide the underpinning of the Inquiry’s own recommendations later in this chapter for the establishment of a national support infrastructure for teachers of mathematics. We therefore summarize the key elements of the ACME report in some detail in the following section.

The ACME report

5.21 The ACME report is clear that programmes of CPD in mathematics should recognize the need for the broadening and deepening of mathematical knowledge, as well as of subject specific pedagogy. The report is also clear that such CPD programmes are needed both for teachers of mathematics with strong mathematics qualifications and for those with less strong qualifications, the latter including teachers who have been recruited from other subjects to teach some mathematics.
5.22 To improve retention in the profession, there is a need to revive and sustain the enthusiasm of existing qualified teachers of mathematics, as well as a need to support and develop them throughout their teaching careers. In addition, it is felt by many that a programme of CPD aimed at qualified mathematics teachers might encourage currently inactive mathematics teachers to return to the profession. Overall, in addition to retaining and attracting greater numbers of mathematics teachers, the belief is that a successful CPD programme would lead to a more motivated and enthusiastic teaching force in mathematics, with improved subject matter and subject related pedagogical expertise. The report is clear that there is a need for CPD for teachers of mathematics at all stages of their careers, whatever their knowledge and experience.
5.23 The report recognises and the Inquiry accepts that it is not possible for ITT to provide future teachers of mathematics with all they should know about the subject they will teach, how pupils learn it or how to teach it effectively. There is therefore a need for mathematics specific CPD, which is available from the beginning of their careers for all Newly Qualified Teachers (NQTs) of mathematics.
5.24 The technical nature of mathematics and the subtle interconnections of different elements of the curriculum can pose problems for teachers whose understanding of the subject is partial and limited. There is therefore a particular requirement for CPD for those teachers who teach mathematics, but who are not well-qualified or experienced in terms of mathematics background. This could relate to both newly qualified mathematics teachers and to experienced teachers who were not specifically trained as mathematics teachers.
5.25 It is seen as equally important for the health of the profession that experienced and well-qualified mathematics teachers are given the opportunity to refresh their skills and to renew their enthusiasm for the subject. Teachers of mathematics need not only to deliver curricula, but also to adapt their teaching methods and style to the changing needs of pupils. They also have to engage with new materials and advances in technology, and to learn from advances in research on pupil learning and on teaching practice in mathematics.
5.26 School and college mathematics does not remain static. Content, applications and assessment evolve. In addition, changes in technology impact both on the subject matter and on possible modes of teaching and learning. The last 30 years have seen major curriculum changes as a result of advances in technology and pedagogy, as well as an evolving perception of what is important in the subject. This evolution and change is particularly marked in the discipline of mathematics. In recent years, this has resulted in the introduction of significantly more data handling, statistics, and investigational work. There is therefore also an ongoing need for CPD for more experienced mathematics teachers. Indeed, many respondents to the Inquiry have emphasized that a mathematics teacher’s education needs to be seen as a career-long process.
5.27 However, until now, apart from the work of the Numeracy and Key Stage 3 Strategies in England and the NINS in Northern Ireland, there has been very little properly resourced support for teachers of mathematics to meet this need. This is consistent with a culture in which teachers in England and Northern Ireland have not seen professional development in their subject as a right or an obligation and, until recently, the employing authorities have not seen lifelong CPD as a priority.
5.28 The Inquiry believes that teachers of mathematics in schools and colleges in England, Northern Ireland and Wales should have an expectation and a responsibility to engage in CPD throughout their working careers, together with an entitlement to time and resources, including funding, alongside a system of accountability and rewards. Current provision for teachers of mathematics in secondary schools and Sixth Form Colleges is clearly inadequate.
5.29 Respondents to the Inquiry have suggested that provision for teachers of mathematics in FE Colleges has been even worse. We are encouraged therefore by the joint work currently being undertaken by the DfES and the LSC aimed at improving classroom practice and promoting active learning in mathematics in FE. An important central element of this work is to enable FE teachers to develop and reflect on their practice with specialist support.
5.30 The inquiry is convinced of the need for a radical culture change in relation to subject specific CPD for all teachers of mathematics. It has been suggested to us that such a culture change is required for all teachers throughout the educational system. However, this takes us well beyond the remit of this Inquiry. Given the terms of reference of the Inquiry, the recommendation that follows therefore refers only to teachers of mathematics. We note, however, that a similar message is conveyed in Recommendation 2.6 of the SET for Success report.
Recommendation 5.1

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.

5.31 The ACME report envisages that it may be necessary to encourage teachers of mathematics to engage in CPD, and to reward in some way those who do so – for example by salary increments on completion of accredited components of CPD. The report also suggests that building up a CPD portfolio should become an important part of career progression, and the key to higher salaries and promotion. The Inquiry fully endorses this conclusion.
5.32 In relation to the problem of mathematics teacher supply, many respondents have noted that the obvious economic market solution is to provide higher salaries and more attractive career paths for teachers in shortage subjects. The Inquiry is sympathetic to this argument, but some respondents are concerned about the threats that this might pose to collegial working within schools and colleges. We remain convinced that the issue of differential salaries will ultimately have to be faced. However, we see no sign of this happening in the immediate future and would therefore not wish to pursue this at the expense of achieving similar practical ends more quickly by other means in the context of teachers of mathematics. We therefore make the following recommendation, which echoes Recommendation 2.5 of SET for Success (a recommendation made in relation to science teachers in general).
Recommendation 5.2

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.

CPD content and delivery

5.33 The ACME report and many respondents have provided the Inquiry with a wealth of detailed analysis of issues relating to the content and delivery of CPD. We summarize in what follows many of the key issues raised.
5.34 A point emphasized to us over and over again is that it is essential for teachers of mathematics to have sufficient subject knowledge to challenge and develop the full range of the pupils they teach. Broadening and deepening mathematical knowledge and understanding are essential. Teachers should also be encouraged to have greater awareness of different representations and links within mathematics, as well as awareness of links to other subjects where mathematics plays a role.
5.35 For teachers of mathematics, an important part of broadening their knowledge of subject specific pedagogy is appreciating how pupils learn mathematics, the role of questioning and response, and the potential obstacles to learning that students are likely to face. Teachers also need to become increasingly aware of key ideas and new approaches to promoting mathematical reasoning in ways appropriate to a diverse range of students with differing abilities and motivations.
5.36 Teachers should also have the opportunity to reflect upon different approaches to delivering the mathematics curriculum. This should include how it is structured in terms of progression within each separate topic, the links between topics, and the way topics are introduced and revisited in different contexts. Many have emphasized the need for a shift of emphasis towards the processes of “doing mathematics” and away from “learning outcomes”. Experts also cite the importance and value of formative assessment as an aid to future learning and understanding.
5.37 Professional development needs to be differentiated according to the diverse needs of teachers of mathematics. Individual teachers have different combinations of pedagogical skills, mathematical knowledge and experience of teaching. For this reason, subject specific CPD provision should be sufficiently flexible to respond to the individual needs of teachers and enable teachers to identify how these needs can best be met. A range of provision must therefore be available at different stages of teachers’ careers and at different points in their mathematical development.
5.38 The ACME report and respondents to the Inquiry have identified distinct categories of teachers of mathematics with potentially differing CPD needs, while recognizing that within each of these categories there will, of course, be considerable variations in individual teachers’ backgrounds, goals and needs:
  • primary school mathematics co-coordinators;
  • primary schoolteachers generally;
  • secondary school heads of mathematics or aspiring heads of mathematics;
  • secondary school specialist mathematics teachers;
  • secondary school non-specialist mathematics teachers, defined as those teaching mathematics whose main subject specialism is not mathematics or a closely aligned discipline; and
  • FE lecturers in mathematics and numeracy skills;
  • FE heads of mathematics or curriculum coordinators, or those aspiring to these roles;
  • those involved in teaching adult numeracy.
5.39 In addition, there are other specialized groups of teachers with an involvement in mathematics teaching, including those working with pupils with special educational needs and in adult learning.
5.40 The Inquiry would also wish to draw attention to the need for mathematics CPD for teachers of other subjects – for example, geography, biology and physics – and for those involved in teaching vocational subjects in FE colleges. The Inquiry believes that this is crucially important and will become increasingly important as the 14-19 curriculum and qualifications structure moves towards greater integration of subjects. It will also be an important prerequisite for genuinely integrating the teaching and learning of mathematical skills with vocational subjects – for example, in modern apprenticeships.
5.41 The ACME report reviews the types of training and professional development that have been available previously. The types of professional development currently on offer range from day courses, usually relating to national strategic initiatives, right through to extended programmes leading to higher degrees. Examples are given below in the panel Types of professional development now on offer. Current financial support can range from full-cost, mainly for the day courses, to little or nothing for the extended programmes.
5.42 The clear view of respondents to the Inquiry is that there is now an urgent need to take stock and interconnect these developments, to plug gaps in provision, and to seek to identify what is effective for different groups in order to plan sustained portfolios of subject related CPD that will meet the diverse needs of teachers of mathematics. The ACME report envisages the following kinds of provision, some or all of which might include courses leading to accreditation:
  • courses for NQTs;
  • courses for those in the first year of holding a co-coordinating/ leading post;
  • courses for each group in their second or third year of teaching or holding a co-coordinating/leading post;
  • a more diverse range of focused courses for teachers with more than 5 years’ experience in their current role.

Types of professional development now on offer to teachers of mathematics

1. Award-bearing courses run by Higher Education Institutions. These may lead to diplomas, MAs or PhDs and may also involve professional associations. The focus varies, but is likely to include mathematics, statistics, teaching and learning and associated research. They are often funded by the individual participating teachers and might be undertaken by either part- or full-time study. The numbers of teachers involved are small.

2. In-school development. Each school should have a policy on CPD and a person responsible for coordinating and managing mathematics education. There is likely to be a plan for development in mathematics, which includes use of external courses and inschool shared development. This may be supported by the materials provided by the National Numeracy and KS3 Strategies.

3. Courses run by the National Numeracy Strategy at primary level. Consultants in each LEA run both nationally prescribed and locally developed courses. A key course is the five-day course, which includes both subject content and pedagogy. Within each LEA, certain courses are for ‘intensive’ schools (selected by the LEA as being those who would most benefit from support) while some are for all schools. There are also short courses run for coordinators.

4. Courses run by the KS3 Strategy (11-14). Consultants in each LEA run both nationally prescribed and locally developed courses. These have included courses for heads of department and KS3 coordinators, which include developing skills in leading departments. A four day course has been run for less experienced teachers of KS3 mathematics, which includes both subject content and pedagogy. Recent courses include teaching of ratio and proportion and geometrical reasoning, as well as approaches to lower attaining pupils. These all provide materials for departmental meetings to support discussion of content and pedagogy. Within each LEA, certain courses are for ‘intensive’ schools while some are for all schools.

5. In-school development for numeracy. LEA consultants work in ‘intensive’ schools to help embed ideas from the courses and to develop skills in teaching and planning. They may work with individual teachers, pairs of teachers or provide training sessions for all teachers of mathematics. This work generally embraces subject content and pedagogy, and action planning.

6. Demonstration lessons by Leading Mathematics Teachers (LMTs). In primary schools, LMTs are identified within each LEA who will demonstrate lessons in their own schools to teachers from other schools. A similar scheme has been introduced in mathematics departments in secondary schools for KS3. Advanced Skills Teachers in both phases will demonstrate lessons and work with teachers in the ‘learning’ teachers’ classrooms.

7. Courses run by examination boards. These are mainly sources of information dissemination at KS4 and 16-19 levels. Examination boards usually run courses focused on changes to specifications or assessment methods. There is a small percentage uptake of these courses, but they influence an opinion-forming sector of the mathematics teaching profession.

8. Conferences/working seminars run by professional subject associations and LEAs. These are usually at weekends or in school holidays. There are also regular local meetings of professional subject associations as well as annual conferences.

9. Other organisations (including private sector). These run courses for mathematics teachers on topics such as managing the curriculum, assessment, teaching more able or less able pupils, managing behaviour, etc.

10. Government initiatives. These are often cross-subject developments arising as part of Government initiatives such as the Gifted and Talented strand of the Excellence in Cities initiative and the transition work of Education Action Zones. There has also been significant investment in ICT training for secondary mathematics teachers through the new opportunities fund.

5.43 Additionally, there is a need for provision concentrating on particular areas of mathematics, such as statistics and data handling, applications and modelling, diagnostic and formative assessment, working with gifted pupils or those with special needs, new initiatives in curricula or in resources, as well as the integration of ICT. We understand that the KS3 Strategy is currently intending to focus on increased use of ICT in mathematics and the teaching of algebra, following on devfelopment work initiated by the QCA.
5.44 Respondents to the Inquiry echo the conclusion of the ACME report that short courses are most effective when time is subsequently made available for teachers in schools and colleges to reflect on what has been learnt, to seek the best ways of implementing ideas and methods in the classroom and to reflect on these practices in an informed way. The report is also clear that teachers need opportunities to reflect on curricular materials and methods in order to encourage the development of professional practice rather than just the reinforcement of current methods. For this to be achieved, teachers need support from experts or mentors with a perspective either of mathematics or of the teaching and learning of mathematics, which is wider than delivery of immediate curriculum goals.

Key elements of a CPD programme

5.45 The ACME report therefore envisages two elements in a CPD programme:
  • part should be personalized, to address individual teachers’ needs and support them in developing their own versions of the understanding of mathematics and mathematics teaching.
  • part should be generalized, so that teachers can place their theories and actions within a wider perspective, but also see how they might influence their own practice in the classroom, school or college.
5.46 We have noted that the ACME report stresses the need for professional development programmes that engage teachers in reflective practice in their own school and college classrooms, so that their knowledge and practice continue to grow and evolve. The ACME report envisages that this process can be encouraged in three ways.
5.47 First, teachers have a great deal to learn from observing colleagues and skilled practitioners in their own and in other schools and colleges. A system of peer mentoring would be beneficial, provided there is appropriate time and support. Peer mentoring should be both supportive and developmental, enabling lesson observation and discussion of teaching practice to become more commonplace in schools and colleges and more acceptable to teachers. To further stimulate discussion and reflection on practice, teachers should also be strongly encouraged to join a national professional subject association. Such organizations might be encouraged to develop career structure grades for mathematics teachers as part of their membership structure.
5.48 Secondly, professional development requires resources. The ACME report emphasises that the critical resource is time. Teachers need frequent and regular opportunities to try out ideas and approaches with their pupils and to discuss their experiences with specialists in mathematics and specialists in teaching and learning mathematics, as well as with other mathematics teachers. However, there is currently very little non-contact time in schools and colleges. The ACME report is clear that key individuals in leadership roles must be given time to spend working alongside teachers to develop good practice, as well as managing their departments effectively. The report therefore suggests that there must be timetabled time for teachers to meet regularly to discuss the teaching of mathematics.
5.49 Thirdly, the report notes that within schools and colleges there is a shortage of money for professional development generally and that, in practice, shortterm issues tend to take priority. Outside the earmarked funding for the NN and KS3 strategies, in England funding for CPD for teachers of mathematics currently has to compete within schools with other requests. The ACME report concludes that current levels of resource are woefully inadequate to even begin to address current concerns relating to mathematics CPD needs.
5.50 The ACME report is therefore clear that the mathematics teaching profession will not develop a culture of CPD unless sustained and improved funding is made available. The Inquiry wholeheartedly endorses this conclusion.
5.51 The report also makes the important observation that when teachers participate in communities of practice that support their CPD, the effects of CPD can be sustained more easily. Some of this will occur naturally in school and college communities, but often is more effectively developed in wider communities based in LEAs, or around Education and Mathematics departments in Higher Education Institutions (HEIs), or around professional subject association groups. Respondents to the Inquiry have overwhelmingly supported this view. They have also pointed out that creating synergies across all these parts of the mathematics community would have the added advantage of engaging more of the community in facing up to the challenge of providing support for teachers of mathematics, including the provision of quality CPD.
5.52 Many have noted, however, that there is a currently a shortage of individuals with appropriate experience and expertise to offer training, support and guidance to teachers of mathematics. This concern has also been echoed by respondents commenting on the situation in Scotland, where there are no longer local authority Advisers in Mathematics to coordinate the work of school departments. One possibility put forward in the report, building on structures already in place in some areas, is to set up a cadre of “expert teachers”. However, respondents have emphasized the importance of ensuring that individuals identified as “expert teachers” have the appropriate academic background to provide support for subject-specific CPD, particularly for teachers of 14-19 year olds. It is envisaged that “expert teachers” would remain classroom based, but would also form part of a network of local resource centres for teachers of mathematics. (See Recommendation 6.14.) The Inquiry notes with concern that since the transfer of responsibility for FE to the LSC, teachers of mathematics in FE currently do not have access to the equivalent of LEA advisers.
5.53 The ACME report sees a key aim of these local centres to be that of bringing together mathematics teachers, mathematics educators and research mathematicians. The aim would be to encourage the development in each locality of a community of mathematics teachers from primary, secondary, Sixth Form and FE Colleges, and HE, providing local infrastructure to support provision of resources and information for teachers of mathematics in schools and colleges. The Inquiry believes this to be an important and long overdue development.
5.54 In terms of current provision, the ACME report identifies fragmentation, lack of coherence and gaps in CPD provision for teachers of mathematics. Elements of CPD do already exist, provided by university education departments, subject associations, curriculum development bodies and training companies. Recently, the QCA has also initiated such provision through its six regional groups developing materials for algebra and geometry for the KS3-4 curriculum. However, the report notes that there is currently no overall supporting infrastructure to provide strategic direction and coordination.

The need for national and local support infrastructure

5.55 ACME studied models of CPD in operation through such support infrastructure in France through the IREMs (Instituts de Recherche sur l’Enseignement de Mathematiques, literally translated as Research Institutes for Mathematics Teaching), and in Israel through the Weizmann Institute. The conclusion of the ACME report is that there is a pressing need for such national and local infrastructure in the UK to provide strategic leadership and coordination of mathematics CPD. The Inquiry wholeheartedly agrees with this conclusion.
5.56 The report’s recommendation is that a centre of excellence for mathematics teaching be established to define strategic objectives for CPD and oversee their local implementation. On 13 March, 2003, at a conference jointly hosted by ACME and the DfES to examine best international practice in CPD, the Secretary of State for Education and Skills announced that he was in broad agreement with ACME’s proposals to develop CPD for teachers of mathematics. The Secretary of State also took the opportunity to extend the remit of the Post-14 Mathematics Inquiry, requesting that the Inquiry examine possible options for the organization and funding of what he referred to as a ‘National Centre for Excellence in Mathematics Teaching’ (NCEMT) and recommend to him, as part of its report, a preferred option.
5.57 The Secretary of State indicated that such a Centre should:
  • cover all ages from pre-school, through universities and adult learning;
  • provide teachers with curriculum support, opportunities to explore different teaching approaches, exciting classroom materials and access to good quality training and development;
  • link with Specialist Schools and through them, with their local partner schools, and universities to create strong subject specialist networks;
  • work to support the Numeracy Strategy in primary schools and the mathematics strand of the Key Stage 3 Strategy in secondary schools.
5.58 The Inquiry endorses the need for a national support infrastructure for mathematics teaching in the strongest possible terms and welcomes the support and encouragement of the Secretary of State in taking this forward.
Recommendation 5.3

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.

5.59 In view of the Secretary of State’s clear indication that support should be provided for teachers of mathematics across the entire age spectrum, the following sections of the report no longer focus primarily on post-14 mathematics education.

The effective delivery of CPD

5.60 There has been considerable debate about the most effective forms in which to deliver CPD for teachers of mathematics. Respondents to the Inquiry have drawn our attention to some of most widely quoted research evidence currently available on the effectiveness of typical forms of CPD provision and strategies. The Inquiry notes, in particular, the following general criticisms of in-service education set out in Fullan, 20011:
  • one-shot workshops are a widely used format, but are often ineffective;
  • in-service programmes are rarely directed to the individual needs and concerns of participants;
  • follow-up support for ideas and practices introduced during inservice programmes is rarely provided;
  • follow-up evaluation occurs infrequently;
  • most programmes involve teachers from a number of different schools and colleges, but the potential different impact of positive and negative factors in the individual teacher’s local environment is typically not factored in to the programme;
  • there is an inadequate conceptual basis underlying the planning and implementation of in-service programmes in order to ensure their effectiveness.
5.61 Cascade training, in particular, is widely identified as a weak link in CPD programmes. In particular, the Evaluation Report of the Key Stage 3 Pilot and Strategy (DfES, 2003) identifies some dissatisfaction with this form of training, although the training in general was well received. The report notes that:
“Not everyone was positive about the training: over a fifth (21%) of the teacher survey respondents did not find the training by local education authority consultants effective, and more than a quarter (27%) felt that it had not prepared them well for teaching... There was some evidence of dissatisfaction with two aspects of the training: perceived rigidity of some of the presentations and reliance on cascade training”.

The criticisms of the cascade approach primarily concerned lack of time and the opportunity to cascade training adequately in schools. There is also a view that the effectiveness of the cascade process diminishes as one moves down the cascade chain.

5.62 Joyce, 19912, makes an important distinction between two key elements of staff development activities – the workshop and the workplace. The workshop (the traditional CPD course) is where understanding is developed, demonstrations are provided of the teaching strategy under consideration and practice takes place in a non-threatening environment. However, if the skills acquired in the workshop are to be transferred to the workplace – that is, the classroom and the school – on-the-job support is required. Respondents have argued that in the context of CPD for teachers of mathematics, there should be a shift away from reliance on the cascade model towards schoolbased team initiatives in which members of a mathematics department work together in the school context, with an expert mathematics teacher acting as the leader or facilitator. The latter role is a key one and we return to the important issue of ensuring an adequate supply of such individuals in Recommendation 6.13.
5.63 This implies a “diffusion” rather than “delivery” model of CPD and is regarded by many respondents as a far more effective way of implementing real change in classroom practice. Such an approach to CPD, placing emphasis on autonomy and professionalism, is described by some respondents as seeking to “involve teachers in change” rather than seeking to “change teachers”. However, as we have noted earlier such an approach requires dedicated time and input from appropriately skilled and reflective people within the school. Resources are clearly needed to support such a model.
5.64 The Inquiry accepts that this implies changes to the workplace and the way in which staff development is organised in schools. In particular, it means that opportunity must be provided for immediate and sustained practice, collaboration and peer review and support. Above all, there is the need to provide time for informed reflection with expert colleagues. One of the strongest messages from the evaluation of the Key Stage 3 Strategy (DfES, 2003) is the importance of time if meaningful change is to occur. Creating time for the CPD provided under the Strategy was a problematic issue for virtually all schools. Almost all of the evaluation survey respondents reported that it had been difficult to find time to develop practice, 65 per cent of school strategy managers identifying the key challenge as that of providing sufficient time for CPD related activities. These difficulties have proved particularly acute in schools facing overall mathematics teacher recruitment and retention problems.
5.65 The Inquiry accepts that these changes will be difficult to achieve in the workplace without, in most cases, quite radical alterations to the way in which schools are organised. There is a real need for more creative solutions to the problems of time and timing that beset on-the-job training. This further emphasizes the need to formalize CPD rights and requirements in contractual form (Recommendation 5.1).

Key requirements and tasks of a support infrastructure

5.66 The ACME report recognises the need to create both a national centre and local centres to support and deliver CPD for mathematics teachers. Respondents to the Inquiry have overwhelmingly echoed the need for both national and local support infrastructure. In general, respondents would wish the role of the national centre to be that of:
  • identifying and co-coordinating national strategy for the support of the teaching and learning of mathematics;
  • interfacing with Government and its agencies, employer groups, learned societies and professional bodies to ensure effective delivery of that strategy;
  • working to influence Government, employer and public perception of the importance and high priority of the study of mathematics both to the individual and society.
5.67 More specifically, respondents would wish the role of the centre to include some or all of the following:
  • provision of advice, resources and information in support of all aspects of the teaching of mathematics, including the use of ICT and distance learning materials;
  • coordination of the development, dissemination, delivery and accreditation of mathematics CPD;
  • provision of guidance on emerging research and development in relation to mathematics teaching and learning.
5.68 We shall consider in detail in Chapter 6 possible options for the remit of a national network involving local centres. Meanwhile, we note that most respondents to the Inquiry on this issue have argued strongly for the establishment of a network of regional centres, in addition to the establishment of a national centre. In addition, the overwhelming view of respondents is that the support infrastructure should not be based on a single institution or agency, however selected, but should be a consortia-based network with central strategic direction. In particular, those with knowledge and experience of the work of the pre-14 strategies have argued strongly that a network of regional centres is essential. Without such a local network, respondents are agreed that the majority of teachers will feel too remote from a national centre to become involved in developments.
5.69 In general, respondents see the role of regional centres to be that of coordinating local support delivery and providing both regional focus and regional awareness – eg by interfacing with the Regional Development Agencies (RDAs), employers, education authorities, institutions and training providers. The Inquiry also believes that links between local education providers and RDAs will become increasingly important and that this further strengthens the case for regional as well as national support infrastructure.
5.70 More specifically, respondents would wish the role of regional centres to include some or all of the following:
  • provision of a forum for links and joint working among local education providers and employers;
  • development of formal working relationships with LEAs and regional directors of the national strategies;
  • support for local networks of teachers, linking schools, colleges and higher education;
  • support for and coordination of local delivery of CPD and other support for the teaching and learning of mathematics.
5.71 We shall return later to a consideration of options regarding the role of regional centres as part of national support infrastructure. However, we note that whatever form of structure is adopted the following key mathematics subject specific needs have been identified over and over again in responses to the Inquiry:
  • to raise informed awareness of the wider applications of mathematics – in science and technology, in society, in everyday life, in the workplace and in other subjects;
  • to extend the base of research-based evidence on teaching and learning strategies;
  • to encourage and facilitate interaction throughout the wider mathematics community on an ongoing basis;
  • to ensure that teachers at all levels are actively engaged in networking;
  • to expose teachers to material on modern developments in mathematics, the scope of its application and the wide range of employment possibilities;
  • to ensure confidence and security in teachers’ mathematical and pedagogical knowledge and to encourage the use of a wide range of teaching styles;
  • to ensure that teachers are fully informed about the role and potential of ICT to enhance the teaching and learning of mathematics and have access to state-of-the-art hardware and software;
  • to provide scholarships and secondments for teachers to extend their knowledge and understanding of issues in mathematics education;
  • to provide time for teachers to explore and reflect on mathematics for its own sake;
  • to link with the National College of School Leadership (NCSL) to provide quality training and advice for experienced, new or aspiring heads of mathematics departments;
  • to provide local management and peer support, through responsive teams at school and local level, for teacher-centred selfdiagnosis of development needs;
  • to integrate CPD with curriculum development and enhancement activity;
  • to integrate CPD with classroom/school-based research and development work at national, regional/local/schools levels;
  • to develop an entitlement for each school and each individual teacher of an allocation of resources for CPD, including time;
  • to ensure that CPD is an ongoing experience throughout the course of each teacher’s career;
  • to offer accreditation for CPD courses in a way that will allow teachers to collect credits in flexible ways;
  • To develop kite-marked accreditation systems for CPD.
5.72 In terms of a longer term research and development agenda for the new infrastructure, respondents have identified the following key areas:
  • the development of new 14-19 pathways;
  • the development of more critical pedagogies, based on developing mathematical comprehension, communication and argumentation;
  • the development of new approaches to assessment, including diagnostic and formative assessment;
  • the development of new approaches to mathematics teaching and the curricula to take account of developments in technology and in usage;
  • the development of mathematics teaching for and with other subjects and as part of vocational programmes, such as modern appenticeships.
5.73 Continuing professional development in mathematics is currently provided by the NN and KS3 strategies, by higher education, by LEAs, by schools and colleges for their own staff and by private providers, particularly in vocational areas. There are some instances of schools providing professional development for staff in other schools – for example, Beacon schools, schools with Advanced Skills Teachers and Leading Mathematics Teachers. However, at present, there is no national registry of all the continuing professional development opportunities available. Respondents see a need for an infrastructure that would set up a database to keep track of and quality access all externally provided CPD in mathematics. Following on from this, work could be commissioned in close collaboration with the best providers to enhance, develop and promote CPD in mathematics. Many respondents would like to see this lead on to kite-marking of provision.
5.74 As we have indicated, respondents to the Inquiry have overwhelmingly endorsed the important conclusion of the ACME report that there is a need for both a national centre and local centres. The national centre is seen as essential to provide strategic direction and coordination of expertise in all aspects of the support of the teaching and learning of mathematics, as well as to provide a focus for close working with national stakeholders. Respondents have also argued that regional centres are essential to provide accessible delivery of CPD, coordinate local support networks for teachers of mathematics and provide a focus for close working with RDAs, LEAs and other existing local networks and stakeholders. The Inquiry wholeheartedly endorses this conclusion.
5.75 We have considered the option of only creating a new central structure to oversee all post-14 CPD, with direct delivery through some form of local consultant network, essentially following the model of the existing strategies. This would have the attraction of avoiding creating a formal network of regional centres. However, we believe there to be two major problems with this approach.
5.76 First, the breadth and range of subject matter and subject specific pedagogy across the post-14 agenda is considerably greater and more diverse than that covered by the primary and KS3 strategies. We do not believe it would be possible to achieve coverage of the entire post-14 agenda – including GCSE, AS- and A-level, Further Mathematics, and the whole spectrum of vocational and key and basic skills mathematics courses and qualifications through a manageable network of local consultants. Furthermore, even if sufficient and appropriate expertise could be identified, given the scale of the post-14 mathematics agenda, following the model of the existing strategies is likely to have the undesirable effect of removing a very large number of some of the best qualified teachers from day-to-day post-14 mathematics teaching in the school and college setting.
5.77 Secondly, we have been entirely convinced by the argument that we need to build and sustain local networks of support, bringing together schools, colleges, HE and other stakeholders, including the RDAs and local employers. The absence of an integrated network of all relevant stakeholders is a serious current weakness. As many respondents have impressed on us, this is not just a prerequisite for culture change in relation to CPD and sustainable on-going support and mentoring of teachers of mathematics. It is also a prerequisite for addressing the current lack of involvement of HE and employers with local mathematics teachers and for raising the profile and awareness of mathematics. We are currently failing to harness the full range of available expertise and resource and to share and disseminate knowledge and best practice. Greater involvement of these important stakeholders would provide considerable added value, both in terms of additional expertise and resources and also in raised awareness on all sides – and, in particular, among careers advisers – of the all-pervasive importance and applicability of mathematics. The Inquiry is led to conclude that a network of regional centres is essential.
Recommendation 5.4

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.

5.78 In responses to the Inquiry, there has been an indication of interest from Northern Ireland and Wales in developing centres that would in part play a similar role to English regional centres, but would also have a strategic role in relation to specific local concerns arising in the Northern Ireland and Wales systems. In the case of Northern Ireland, the NINS Steering Group (which has representatives from key stakeholders in NI) has informed the Inquiry that they “would be strongly in favour of a regional mathematics centre”. Scotland will consider at a later stage whether or how future developments of CPD for teachers of mathematics in Scotland might relate to or interact with such an infrastructure in England.

1 Fullan, M. (2001). The meaning of Educational Change, New York, Teachers College Press

2 Joyce, B. (1991), Co-operative Learning and Staff Development. Teaching the Method with the Method, Co-operative Learning 12(2)

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