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Memorandum submitted by the National Centre for Excellence in the Teaching of Mathematics (NCETM) The National Centre for Excellence in the Teaching of Mathematics (NCETM) is a DCSF funded organisation which is charged with the task of providing effective strategic leadership for mathematics specific CPD. As such it aims to raise the professional status of all those engaged in the teaching of mathematics so that the mathematical potential of learners will be fully realised. Our response to this inquiry is therefore focused around our knowledge of the mathematics related needs of teachers emerging from Initial Teacher Training (ITT) and our understanding of what constitutes effective mathematics CPD for serving teachers. In responding to the Inquiry, we have focused on the parts of the questions which directly relate to our remit and have indicated these in bold. In summary, the NCETM suggests that · There is clear evidence of what constitutes effective teaching of mathematics and that assessments of the quality of teaching can be made against this. However this is not widely understood by non-specialist teachers or senior leaders in schools. · All student teachers who will teach mathematics should develop a deep understanding of the subject and its related pedagogy at a level that is at least consistent with the age of the pupils that they will be teaching. · It is unrealistic to expect that students will be able to develop the subject knowledge and pedagogical skills to equip them for teaching a broad range of pupils during their ITT and hence they need an entitlement and expectation of mathematics-specific CPD throughout their careers. Measuring quality1. There is substantial evidence of what constitutes effective mathematics teaching, which includes the Cockcroft report 'Mathematics Counts' (1982), A Study 'Effective Teachers of Numeracy' (1997), a review led by the NCETM 'Mathematics Matters' (2008), Ofsted's report 'Understanding the Score' (2008). Together these reports have identified the following characteristics of effective mathematics teaching: · Builds on the knowledge learners already have · Exposes and discusses common misconceptions and other surprising phenomena · Uses higher-order questions · Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work · Encourages reasoning rather than 'answer getting' · Uses rich, collaborative tasks · Creates connections between topics both within and beyond mathematics and with the real world, in particular drawing out connections between different representations of mathematics (e.g. graphical, numerical, algebraic) · Uses resources, including technology, in creative and appropriate ways · Confronts difficulties rather than seeks to avoid or pre-empt them · Develops mathematical language through communicative activities · Sets high expectations for pupils in mathematical challenge, achievement and enjoyment 2. These principles of effective teaching are widely accepted by teachers who have specialised in mathematics teaching and learning in their ITT or later in their career. There is however a gap between this recognition and acceptance and what happens in practice - given numerous classroom constraints. Based on research and other evidence the NCETM suggests that in order for these principles to be applied in practice, teachers must have · good mathematical subject knowledge, including a developed understanding of the links and connections within the subject; · an understanding and knowledge of effective mathematics specific pedagogy; · the skills to embed subject knowledge and pedagogy in practice. 3. The principles for effective mathematics teaching are less well known to the many non-specialist teachers of mathematics, including many primary teachers. 4. Ofsted provides very clear, appropriate and accessible guidance for measuring the quality of teaching generally and specifically for mathematics in 'Understanding the Score' Entry into the teaching profession5. The NCETM recognises that the essential characteristics of good teachers of all subjects are enthusiasm for the subjects that they are teaching, personal aptitude in the subject at an appropriate level and the ability to communicate effectively with students with differing aspirations and competences. In the particular case of mathematics, many teachers are unable to demonstrate all of these characteristics: the Ofsted report 'Understanding the Score' suggests that in secondary schools there is often a weakness in communicating mathematical ideas effectively, while primary school teachers often have gaps in their mathematics subject knowledge. 6. The large number of routes into teaching appears to be effective in attracting teachers into the profession. However, the NCETM has concerns that on school-based routes where there is only a short period of engagement with HEI provision, student teachers have insufficient opportunities to explore effective mathematics pedagogy or to deepen their own subject knowledge. This is a particular issue for primary trainees who arrive with the minimum GCSE grade C level of qualification in mathematics. We applaud the recommendations of the 2008 Independent Review of Mathematics Teaching in Early years Settings and Priimary (The Williams Mathematics Review) to raise the bar of entry level to Grade C in the proposed 2 GCSEs in mathematics and also to put in place one mathematics specialist in every primary school. 7. Limited available time for in depth study of mathematics and mathematics pedagogy during ITT for teachers who will teach the subject at some level is common to the majority of courses on offer. In most cases it would be unrealistic to expect additional provision. It is important that teachers recognise their ITT as the start of a career-long CPD path which should, if they teach mathematics, include opportunities to develop their personal and pedagogical understanding of the subject. In particular teachers are likely to need additional subject knowledge development to enable them to teach 'A' level mathematics, more in-depth study of how children learn mathematics to enable them to support children with Special Educational Needs or who are particularly gifted in the subject, the flexibility to recognise and use opportunities for developing mathematical thinking when working with very young children, or an understanding of adult learning when teaching Skills for Life qualifications. 8. There are related issues in further education, where there is little evidence of subject specific teaching and assessment in ITT for QTLS, unless the trainee is aiming to teach Skills for Life qualifications, in which case, there are specific Mathematics (numeracy) courses. The delivery of ITT
9. The NCETM values opportunities to work in partnership with ITT providers as this builds trainee teachers' appreciation of the need, and the opportunities available for engaging in continuing professional development as they begin their careers. In many ITT institutions future teachers of mathematics are introduced to the NCETM web-based tools that enable them to identify their subject-specific and pedagogical needs and can support them in locating appropriate CPD provision to meet these needs. These have been made available to all ITT institutions, and a number of ITT colleagues have supported their development. CPD provision
10. The need to 'support, sustain and enhance current teachers of mathematics through CPD and other teaching and learning resources' has been emphasised in three ACME reports[1]. In addition this was noted in the 2004 Smith Report on post-14 mathematics education 'Making Mathematics Count' which led to the establishment of the NCETM. Indeed the then DfES responded to the Smith report as follows: Necessary components of effective CPD For all teachers, at every stage of their career, there are three aspects of continuing professional development (CPD) · developing a depth of personal subject knowledge to underpin teaching and learning · enhancing their repertoire of subject specific teaching methods and pedagogy · applying general strategies for teaching and learning All three aspects contribute to all subjects but the need for them varies across disciplines. Research shows that for mathematics in particular the subject specific elements are critical in raising levels of pupils' interest and attainment. Similarly the Williams Mathematics Review noted the limited opportunity and willingness for primary teachers to engage in mathematics CPD and recommended that a programme should be developed in order to ensure that every primary school has at least one 'Mathematics Specialist' teacher with the ability to support the development of all teachers within the school. While this will be a large-scale and well-coordinated programme, all teachers will continue to have CPD needs which need to be addressed in a more systematic way. The NCETM agrees with the view of both of these reports that all teachers should be expected and enabled to engage in CPD throughout their careers, as is the case in other professions, in order to maintain a 'license to practice', and commends the developments in the FE sector where teachers are required to undertake a minimum of 30 hours CPD in order to maintain their QTLS status. 11. The NCETM takes the view that ITT cannot fully prepare students for all of the tasks that they will undertake during their teaching career. Consequently it is important that all teachers have opportunities to engage with high-quality CPD throughout their careers in order to increase and refresh their subject and pedagogical knowledge and to enable them to embed these in practice. While any form of CPD willingly undertaken by a teacher will enhance her practice to some extent, the greatest impact is achieved when this is closely matched to needs that may have been identified by the teacher herself or by a colleagues who have the opportunity to assess her practice. The NCETM self-evaluation tools and personal learning space have been designed to support this process. A range of factors commonly influence the choice of CPD undertaken and the opportunity to take part. These include cost, time commitment, what is on offer from known providers and the priorities of the school as a whole. This frequently results in fragmented provision and uptake amongst teachers. Head teachers are in a position to organise their schools so mathematics teachers obtain the support needed - issues that enhance recruitment and retention. 12. Currently there is no entitlement or responsibility for teachers to engage in CPD once they have achieved Qualified Teacher Status (QTS). In order for teachers to have appropriate CPD opportunities in any subject or aspect of education, school and college leadership must have an understanding of the value of teacher CPD in improving the learning of their students and the ability to assess what the needs of the teachers are. In the case of secondary and tertiary Mathematics, the NCETM has concerns that senior leaders often fail to recognise the impact that improving mathematics pedagogy can have on the quality of students' learning and their attitudes towards the subject, while in primary schools head teachers often have insufficient knowledge of mathematics to be able to recognise ineffective or inaccurate teaching of the subject. These factors suggest that there is a need for school and college leaders to work with colleagues so as to be able to present a vision for mathematics and its development for their school. 13. The NCETM has been appointed to lead on the coordination of mathematics-specific CPD as part of the Government's STEM Programme and is establishing a National Mathematics CPD Committee. The work of the committee will be informed by stakeholder groups and key agencies, including the NCETM Regional Advisory Committees. The Committee will identify gaps in provision and facilitate and promote a more coordinated CPD offer for teachers in schools and colleges through encouraging these groups and agencies to work in partnership. February 2009 References
Many of the reports and documents referred to in this submission are available to view online. We have included electronic links to these documents where this is the case. ACME (2002) Continuing Professional Development for teachers of mathematics. ACME (2006) Ensuring effective Continuing Professional Development for teachers of mathematics in primary schools Askew, M., Brown, M.,
Rhodes, V., Johnson, D. and Wiliam, D. (1997), Effective Teachers of Numeracy: Final Report. Cockcroft, W. (chair), (1982). Mathematics Counts: Report of the Committee
of Enquiry, DCSF (2004) Making Mathematics Count: the Report of Professor Adrian Smith's Inquiry into Post-14 Mathematics Education. NCETM (2008) Mathematics Matters: Final Report. Ofsted, (2008), Mathematics: Understanding the Score [1] Continuing Professional Development for teacher of mathematics (ACME Dec 2002) Report on Ensuring a high quality, localised infrastructure for the Continuing Professional Development of teachers of mathematics (ACME July 2005) Ensuring effective Continuing Professional Development for teachers of mathematics in primary schools (ACME Sept 2006) |