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Post 14 Inquiry - Further Response
A Further Response to the Post 14 Inquiry
This response consists of two parts of which the second develops some ideas on some key issues.
1. Comments on the minutes of the meeting at QCA on 31st March 2003
Italicised amendments have been added to the original version together with comments to highlight various points that do not reflect what was said. We are concerned that the minutes do not seem to us to represent a balanced and thoughtful account of the discussion we had. Moreover they do not appear to have been checked through and edited before being sent out.
2. Further ideas on three key issues:
- Mathematics Curriculum 14 - 19
- Recruitment and Retention of Teachers
- National Centre for Excellence in Mathematics Teaching
These three items were written by three different individuals and, although they have been modified in the light of comments from others in the responding group, the original format in which they were written has been retained.
Minutes of Meeting on 31st March 2003
Meeting with the Mathematics Association
Our correct title is: The Mathematical Association
31 March 2003
Present:
Barry Lewis, Doug French, Jane Imrie, Jennie Golding, Peter Thomas, Professor Adrian Smith and Dr Jack Abramsky, Lara Casher
The name of Sue Singer has been omitted here.
Aims of meeting
· To update the MA on Charles Clarke's announcement of a new National Centre for Excellence in Mathematics Teaching and explain the ramifications this has on the Inquiry's timetable and remit
· To invite the MA to think of ways to take the idea of a centre for mathematics forward, and think of what kind of model/structure is required to make these ideas happen.
· To discuss how to turn issues highlighted in the MA's submission into practical recommendations.
The MA's Submission
· Adrian Smith thanked the Mathematical Association (MA) for their submission which the Inquiry received on the 26th February 2003.
· Barry Lewis (President of the MA) explained how the information had been gathered; after an initial meeting was called, for any member of the association to attend, a small team was set up to collate the information gathered and produce the final report.
· The three main areas of concern that the MA highlighted were
1. Recruitment and retention of teachers
2. Pupils learning difficulties with mathematics
'Quality of teaching and learning of mathematics' would convey this area of concern more clearly.
3. Nature and frequency of Assessment
National Centre for Excellence in Mathematics Teaching
· Inquiry is to consider and evaluate options and make a recommendation to the Secretary of State in September.
· AS will be writing to a select number of organisations for input
Recruitment and Retention
· Embedding rights to CPD within teachers contracts; CPD also must give teachers time to reflect and talk to colleagues
· Time issue for teachers is crucial but very difficult to tackle if there is a shortage of teachers already
· The Centre alone is not going to deal with the problem of shortage of teachers and this is the most severe issue at present. Reducing student debt might be an incentive for some to go into teaching soon after graduation.
· Need to explore why people leave the profession
· Also need to explore how to bring in people with non-conventional qualifications and how to train them.
The point was made here that two year conversion courses have been running successfully in a number of universities for the past 16 years, but they have never been publicised widely and students are not funded for their first year.
· There are non-conventional routes that have been set up already but there are very split views on whether they are working. For example, 'golden hellos' may be attracting new teachers but is this method encouraging retention?
The first comment presumably refers to the Graduate Teacher Programme; the second is a different point because it relates to conventional routes.
Possible solution?
· Using post graduates, or even under graduates, as a teaching resource
Action Point for MA
· Consider the values of such a resource? i.e. how graduates/post graduates could be used, organised and trained.
Whilst this idea is worth exploring we see that its greatest potential lies in encouraging the participants to consider teaching as a long term career.
Specialist Schools
· Specialist Schools are a red herring - these are not necessarily chosen and funded because they are the best at the specialist subject
· The label of Specialist School rules out schools that may have a greater input in delivery with mathematics expertise
· It would be better to look at the role of Advanced Skills Teachers than at Specialist Schools
Compulsory Mathematics Post-14?
· It was agreed that mathematics should remain compulsory post-14
· Pupils would probably continue to do mathematics post-14 even if it wasn't compulsory because they wouldn't know what to do otherwise, and because of social pressures
· How would this fit in especially in relation to a Baccalaureate system?
· Would there be a need to have choice of what sort of mathematics one does?
· AS - a case could be made for three options of mathematics
1. Basic numeracy for citizenship
2. Quantitative literacy (data handling in combination with IT)
3. Real mathematics (abstract concepts)
· MA view: This is a false trichotomy. You need to consider the characteristics one needs to do mathematics
The point here is that to be successful the first two require conceptual understanding even if it is only of simple arithmetical ideas in the same way that the third requires an understanding of more abstract ideas. There is not a clear distinction between what is simple and concrete and what is hard abstract. Understanding and an ability to think independently are equally important at the simplest level.
· If pupils fail to make sense of mathematics then they will fail to have any conceptual understanding of what they are studying.
· Pupils need to be able to think independently at whatever level they are in mathematics. NB
· This again comes back to the need for a high level of teaching skills
· A teacher needs the same level of skill to teach the best pupils as well as the worst pupils. NB
Motivation
· Pupil motivation comes from teaching mathematics in terms of the real world. The issue is 'demotivation' and this is often down to poor pedagogy, shortage of highly qualified teachers or placing students in an inappropriate course
Whilst we accept that 'the real world' can be one valuable source of motivation for students, we would emphasise that it is neither the sole source of motivation nor the most important source of motivation. Success in making sense of ideas that engage students' imagination is the major source of motivation - puzzles and problems of all kinds drawn from within mathematics are at least as engaging for many as applications from the real world. A balance between the two is needed.
· Need to think where pupils are going to end up, and what skills they need to access their chosen routes
· Need to also look therefore at what employers are looking for
· Must be aware though of equal opportunities for pupils and how to avoid the danger that pupils from inner city schools are not pushed in to doing 'superficial' mathematics
· In giving different options of types of mathematics to study post-14, there is a worry that some pupils will be pushed down routes that will not develop their potential. NB
· Doug French was worried about courses which make pupils diverge at age 14. This concern was shared by others.
· Have to teach pupils to overcome hurdles i.e. only getting a C at GCSE grade
- Are there routes that encourage pupils to over come these hurdles and encourage them to go back to subjects they did not think they could achieve in?
Action point for MA
- Consider other routes that may be more appropriate
- If discussing other systems such as French or German Baccalaureate, look in detail at the pro and cons of these systems
Pedagogy
· National Numeracy Strategy and Key Stage 3 National Strategy are recognition by the government that if you want to improve attainment and learning in mathematics you must improve pedagogy
· In Europe, cultural attitudes are very different concerning the standard of mathematics in relation to the nature of pedagogy.
· There is a problem in the fact that teachers are not reflecting on how students learn/understand mathematics. They are more concerned with methods of class control and how to teach.
· Textbooks that have been written by exam boards and publishers are not providing teachers with innovative and creative material that encourage teachers to use new methods of teaching
This does not distinguish between writing and endorsing books. It omits our request for public endorsement to be banned and does not mention the commercial effects on other publishers and pressures on teachers caused by the existence of endorsed books.
· The School Mathematics Project (SMP), SMILE Mathematics, and Mathematics and Education in Industry (MEI) have all been innovative projects that produced interesting, well-tried, materials for teachers and developed INSET
The key characteristics of these projects have always been independence from central control, strong teacher involvement with teams of writers and materials that have been extensively piloted in schools. The words 'well-tried' give the wrong impression.
· KS3 National Strategy is very effective in ordinary and mediocre classrooms because it gives teachers a very clear structure of what to teach. The same applies to the National Numeracy Strategy
· However, some teachers feel deprofessionalised and too constricted by these strategies
· Most teachers will tell you that it is working though because they are achieving results
· Are results a good enough measure of success?
Assessment
· Testing narrows teaching/learning
· Assessment is too dominant and too frequent. Too much time is lost to examinations. In reality pupils are now are sitting high stakes examinations for four consecutive years. This is detrimental to the teaching of mathematics, as the sole aim has become to prepare pupils for tests so that targets are fulfilled rather than to keep pupils motivated and interested in mathematics
· Mathematics is very cumulative and constantly reinforcing itself, therefore the need to keep pupils interested in the subject, and motivated, is essential.
· There is still a concern that below grade C is seen as a failure. This is especially so in mathematics - why is this the case?
· Requirement for AS Mathematics as a qualification en route for A level mathematics should be dropped
Possible solutions?
· Single free standing mathematics qualifications
NB. This was discussed in some detail in the MA's submission
(Please see point 2.8)
Action point for MA
· Consider and demonstrate why mathematics is 'different' compared to other subjects
· Why a C grade at GCSE standard is still considered a failure?
· Is mathematics more difficult than other subjects? Can you demonstrate this?
Other issues
- Further Mathematics should be promoted more. FP1 should attract funding and UCAS points.
This point belongs with the comment about FSMQs above.
- The timing of external examination results in a lot of dead time at the end of the summer term
Follow up action points
· Adrian Smith will write formally to The Mathematical Association to request a further submission on the points raised in this meeting
· The Mathematical Association is to provide an evidence-based document that considers the points raised in this meeting, and in particular, why mathematics is 'different'.
Mathematics Curriculum 14 - 19
1.1 Qualifications should require command of the material covered. The achievement of a particular grade should require 80% facility on an appropriate test. The content specified should be appropriate in nature and size. Long content lists can give the appearance of high standards but lead to superficial rote training to get marks in examinations; the skills gained by learners should extend beyond the ability to answer stereotyped examination questions. Whilst the short-term goals that are available within a modular scheme can aid motivation, such schemes can lead to teaching and learning which is unduly focussed on assessment and learning of behaviours which jump the next hurdle but do not lay foundations for long-term success.
1.2 Learners must experience success yet learn to cope with difficulty. They should learn to think independently and not have their interest educated out of them. At present, there is too much telling; teachers need to be encouraged to develop a richer pedagogy. They need time to do this, both in and out of the classroom. Summative assessment, and preparation for it, takes up too much time to the detriment of learning and the formative assessment which assists it. The quantity of summative assessment, especially where it occurs before the exit point needs to be reduced substantially.
1.3 The need for separate pathways needs to be considered. If there are to be such pathways, the point or points of divergence need to be considered, as do possible routes between pathways. The creation of separate paths would raise issues of status and equal opportunities which would need to be addressed. Any scheme proposed would need to be able to be implemented within existing institutions with the current cohort sizes; although consortium arrangements can be of value in increasing curricular flexibility they have a mixed history: if used then it will be important to ensure that they are beneficial to the learners involved as well as their institutions.
2.1 GCSE should be recast as an assessment at the end of Key Stage 4 at age 16; alternative provision would be made for the other uses to which GCSE is put at present. The present headline measure of 5 GCSEs at Grade C or above would be recast as the equivalent of GCSE Grade C in the core subjects of English, Mathematics, Science and ICT. To avoid undue concentration on these subjects, there would be a statutory duty on institutions to provide a broader curriculum, including languages, humanities, and practical subjects, the themes of community, action and service, as well as critical thinking with an ethical side to encourage learners to engage with issues as active and responsible citizens.
2.2 Summative assessment in the four core subjects would be largely external, with Key Stage 4 Tests after the manner of the tests at the earlier Key Stages. In the non-core subjects, summative assessment would be largely internal with external moderation and, to varying extents depending on the nature of the subject, external verification tests. (In subjects, more than one model might exist.)
2.3 Mathematics would be divided into two subjects: a core subject and a non-core subject, here provisionally given the names Use of Mathematics and Mathematics. A Use of Mathematics qualification would be available at several Levels of the National Qualifications Framework. Nearly all students should take Use of Mathematics, at some level, and Mathematics should also be taken by at least 60% of the 14 - 16 cohort. The double subject would not require significant change or expansion to the existing National Curriculum, but would require much greater depth of understanding at each level with an enhanced ability to solve unstructured problems and to 'use and apply' the ideas within mathematical and other contexts. It is envisaged that the 16 - 19 curriculum would be broader than at present and subjects might be available as minor and major subjects (the exact size of these courses would depend on the overall model adopted for the 16 - 19 curriculum). There may well be benefit, in motivating learners, in qualifications designed for use post-16 having different titles from those for use at 16. Given that qualifications should indicate command of the material assessed, each should have only a short grading scale.
2.4 A chart outlining a possible scheme is appended. Details are given below.
2.5 Use of Mathematics would be the core course and include numeracy for citizenship and quantitative literacy. At the lower levels numeracy for citizenship would be emphasised and at the higher levels quantitative literacy. (Mathematical literacy should be interpreted in such a way as to ensure that all learners are exposed to something of the power and beauty of mathematics, as well as its utilitarian and immediate application.) It is hoped that Level 2 would be achieved by at least 60% by 16 and 80% by 18. At Level 3, there should be sufficient mathematical content to allow for smooth progression to Foundation Degrees of a substantially quantitative nature as well as providing a good background for a wider range of employment and further study.
2.6 Mathematics would be a non-core course. At both levels there would be external written assessment as well as opportunities for internal assessment. Alongside content appropriate for progression, it would develop problem-solving skills and contain elements of mathematical literacy. It is envisaged that the course would have a substantial take-up at Level 2, comparable to that for English Literature. At Level 3, study would be to the same depth as for the present AGCE Mathematics but the amount of content would be determined by the overall 16 - 19 structure. It is envisaged that Level 3 Mathematics would give smooth progression into a range of employment and degrees of quantitative where the mathematical demand was comparable to that for a B.Eng.
2.7 Further Mathematics should be available to give access to degrees in mathematics, the physical sciences and engineering (M.Eng) and to challenge and inspire the most able. The major course would not be a requirement for access to any course, but students pursuing it would be particularly well-prepared for the most demanding courses; it is likely that in many institutions that provision of the major course would involve elements of distance learning. Students at all institutions must be able to access the major course.
2.8 In the long-term, it is desirable that all study mathematics (as well as their native language) to age 18, but in the short-term priority must be given to ensuring a sufficient supply of teachers pre-16. It is envisaged that the transition to the universal study of mathematics post-16 would be gradual with Use of Mathematics courses being incorporated within vocational programmes.
3.1 The structure discussed above would need several years to be developed and trialled. In the meantime, there should be a period of stability so that teachers can concentrate on improving the quality of teaching and learning. For whatever system is introduced, its success will depend on how it is taught.
3.2 The present system makes very limited provision in mathematics for those post-16 who are not pursuing Level 3 courses. It is important that what provision that does exist (such as FSMQ Levels 1 and 2 and C+G Numeracy) remains available and funded, and that any new GCSE specifications make appropriate provision for post-16 learners.
3.3 The forthcoming much-needed reforms to GCE Mathematics are likely to lead to larger number of students for who some provision beyond A level GCE Mathematics is appropriate. The provision of GCE Further Mathematics varies, encouragement can be given by supporting distance-learning initiatives and by offering targets which are perceived as being manageable. To that end, it would be desirable if all GCE Mathematics units from the seventh to the twelfth could be certified as FSMQ Level 3 (so securing LSC funding and UCAS points); as a first step, the FP1 unit in the new specifications should be available in this mode.
Recruitment and Retention
1. Alternative Routes into Teaching
Opportunities should be available for people with degrees in non-mathematical subjects (including existing teachers of other subjects), who have an A level or equivalent in the subject, to train as mathematics teachers. A number of universities provide two year conversion courses for such people, and in some cases where people are not graduates, but have some HE level qualification, there are similar two year courses which lead to a degree. These conversion courses have never been widely publicised at a national level and students are not properly funded for their first year, although they do receive the training salary in their second year. A relatively modest outlay on publicity and funding in this area could make a very significant difference: students on these courses often say that they only heard about them by chance and many potential applicants are deterred for financial reasons.
Proposal 1.1
Pay at least the £6000 training salary to all trainees in the first year of two year conversion courses.
Proposal 1.2
Insist that the TTA advertises two year conversion courses in the national press and elsewhere. Advertisements should state all the institutions that offer the courses with relevant contact details for each. This would be much more effective, and a lot cheaper, than advertisements from individual institutions.
Proposal 1.3
Encourage institutions to offer conversion courses in those parts of the country where they are currently not available.
The table below shows the total number of students over the past 4 years who have successfully completed PGCE courses in a sample of five of the institutions which offer both one and two year PGCE courses. The numbers who attained that PGCE through a two year conversion course are given in brackets. The bottom row gives the percentage in each year across the five institutions who obtained their PGCE through a two year course. Numbers vary greatly from year to year, but usually constitute over 30% of the total output from the PGCE in the institutions involved.
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2000
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2001
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2002
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2003
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University of Birmingham
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25(7)
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29(9)
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28(11)
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37(16)
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University of Cambridge
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37(14)
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31(14)
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35(5)
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35(5)
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University of Hull
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15 (4)
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13 (4)
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18 (8)
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11 (6)
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University of Keele
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12 (3)
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19 (9)
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25 (14)
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16 (5)
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Manchester Metropolitan University
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35(11)
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35(15)
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42(16)
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41(13)
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Two year PGCE as percentage of total
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31.5%
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40.2%
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36.5%
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32.1%
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Most of these courses have been running since 1987. As further evidence, since 1989 (the first year of completion) until the current year, the number successfully completing the courses at Keele and Hull were 146 and 106 respectively, with comparable numbers in the other institutions.
The accompanying leaflet gives further information about the conversion course at the University of Hull.
Proposal 1.4
A coherent system should be established for retraining teachers of other subjects who wish to become mathematics teachers or who already teach mathematics.
MEI is currently piloting a project for updating teachers of other subjects in conjunction with Warwick University and funded by the Gatsby Foundation. Such initiatives should be extended more widely with proper funding for participants so that they have time to pursue the course effectively.
Ancillary Help in Mathematics Departments
Providing generous dedicated additional ancillary help within mathematics departments so that teachers can concentrate more of their energies on teaching can have beneficial effects on working conditions and morale.
Proposal 2.1
Every mathematics department should have ancillary help which is based within the mathematics department on the model of the laboratory technician in science.
The person (or persons) should be a member of the departmental team and answerable to the head of department. The role should be one of providing administrative support to all the teachers in the department particularly relating to managing resources, including ICT and other physical facilities of the department. Such a role could be combined with providing learning support, involving direct work with individual pupils under the direction of a qualified teacher, but that should not be allowed to detract from the other aspect of the role.
Proposal 2.2
Ancillary help concerned with learning support should be more readily available in mathematics with the individuals involved organised from within the department so that they are, as above, members of the departmental team.
We are very concerned that increased provision of teaching assistants should not be seen as a way of dealing with the teacher shortage. Paragraph 2.5 of the HLTA (Higher Level Teaching Assistants) DfES consultation document (April 2003) (paragraph 2.5) suggests a qualification in numeracy at level 2 in the NVQ framework is appropriate. We regard this as grossly inadequate for anybody providing learning support in mathematics at any level and are very concerned that this is being proposed for higher level teaching assistants. Mathematics teaching is the role of qualified mathematics teachers and, despite all the shortages, we would only expect learning support to be delegated to classroom assistants with an appropriate subject and pedagogical background and training. A level 2 qualification in Application of Number or Numeracy should not be regarded as equivalent to GCSE mathematics at grade C and above for this purpose.
Proposal 2.3
Training focussed on current good practice should be provided for all heads of department to ensure that ancillary help is used effectively for both resource management and learning support.
Proposal 2.4
Head teachers should be required to ensure that mathematics, as an important and problematic subject area, is given an enhanced allocation of dedicated ancillary help.
3. Pay and Conditions of Service
Proposal 3.1
Pay enhancements for mathematics teachers who are good classroom teachers should not necessarily entail additional responsibilities for those who would otherwise choose to devote most of their time to classroom teaching and, for heads of department, pay enhancement should not entail an additional whole school role.
Pay is a very significant issue because there are so many alternative employment possibilities for highly qualified graduates in mathematics and related subjects. Given the shortage of mathematics teachers it is important that they spend more time teaching mathematics and less time on other things, even if the balance is different than that for other teachers. Professional development bursaries, currently available to teachers in their 4th or 5th year of teaching, should be rapidly extended to all teachers.
Proposal 3.2
All teachers of mathematics in the 14 to 19 range, including schools, colleges and FE should be paid on the same pay scales to create a unified mathematics teaching profession with no 'poor relations'.
Proposal 3.3
All initiatives involving mathematics teachers, such as schemes to provide laptops, professional development opportunities, bursaries and scholarships, should include those teaching mathematics in the FE sector as well as those in schools and colleges.
Proposal 3.4
Reducing class sizes in mathematics significantly should be set as an important long term target.
There is much anecdotal evidence that class sizes in mathematics, and possibly English, tend to be higher than in other subjects and have been rising in recent years. This is partly a consequence of decisions made by individual schools and is exacerbated by mathematics departments very sensibly attempting to ensure smaller numbers in lower sets where pupils with learning difficulties and behaviour problems are placed. If the mean class size is over 30, something that is not uncommon, higher sets often have over 35 pupils without achieving a very significant reduction in the size of lower sets, which ought ideally to be below 20.
Reducing class size may have little measureable effect on attainment, but it would have very significant effects on the working conditions of teachers because it would reduce workload and the many stresses caused by poor pupil behaviour, both of which are exacerbated by large classes. It would also help in creating conditions where teachers could ensure more effective interaction and individual help. That would increase job satisfaction, enhance pupils' learning and improve attitudes towards mathematics.
We recognise that reducing class sizes is difficult to achieve in a situation where there is a serious shortage of teachers, but it should be recognised explicitly as an important long term goal.
Proposal 3.5
There should be much less central direction from government and its agencies, so that there can be greater stability in curriculum content and structures and greater trust in the professionalism of thoughtful and creative mathematics teachers so that they have the freedom and time to think, to innovate and to maintain their enthusiasm for the subject.
To quote from the Association's earlier response:
'Many thoughtful and creative teachers, both young future curriculum leaders and those with a wealth of experience, become disillusioned by constant superficial changes and interference which devour time and undermine professional judgement. Recent reforms have tended to reduce the freedom to innovate and give excessive emphasis to tests and targets to the detriment of stimulating interest, promoting positive attitudes and encouraging effective learning. These factors apply to teachers of all subjects, but mathematics is in a particularly vulnerable position because of the cumulative effect of the shortage of good teachers over a long period and, because, like English and Science, it is continually in the forefront of public attention and subject to constant criticism and change.'
National Centre for Excellence in Teaching Mathematics
How should it operate?
· The Centre should aim to support and enhance projects to develop mathematics pedagogy at all levels, including provision for a wide range of mathematical abilities.
· The Centre would have a small central office, not necessarily based in London. This would facilitate communication across Regional Centres, provide cross fertilisation of innovative practice and ensure coherent national and local provision of professional development opportunities.
· It should be structured with 8 or 9 Regional Centres, preferably based on existing mathematics education centres linked to LEAs or HE institutions, and should encourage links between all local providers.
· Practising teachers should have a major role in the Regional Centres. They should be employed as consultants or on short term secondments (1 or 2 years), so that they retain their links to the classroom, thus maintaining credibility and not adding to the shortage of good mathematics teachers. An alternative, or additional, way of involving teachers would be to appoint ASTs with their outreach defined as being via the Regional Centre. The nature of the staff employed is critical: they must be reflective and adventurous, dynamic and innovative, committed to the ideas of the Centre and they must have a broad and balanced understanding of mathematics education.
· The Centre must be coordinated in a coherent way with all other agencies - DfES, QCA, National Strategies, TTA and the whole range of providers of initial and in-service teacher training for mathematics teachers, including higher education, major projects such as SMILE, SMP and MEI and commercial organisations like SfE and Network Training.
· The National Strategies, Advisors and Numeracy Consultants should be brought under the umbrella of the Centre, so that teachers are not faced with yet more sources of information and advice with the accompanying documentation which has to be absorbed and assessed.
· Where there are areas of significant shortfall in subject and pedagogical expertise, funding should be available for sustained and substantial courses such as the 20 day primary mathematics courses, which have been among the most effective in-service provision in recent years.
· The central philosophy of the Centre should be enabling, not providing.
· The Centre should encourage 'bottom-up' development, supporting local initiatives, identifying local needs and using the strengths of local teachers and schools, including mathematics and computing specialist schools where appropriate.
· It should be outward looking, not inward looking: it is notable that the most significant initiatives in mathematics education have been driven by fiercely independent bodies such as MEI, SMP and SMILE. The Centre should seek to learn from the success of these projects in influencing classroom practice.
· Subject associations should have a leading role, both at a central and local level, because they are independent of particular powerful interests and they represent mathematics teachers directly with many active and innovative teachers across the country as members. The Mathematical Association is very keen to be involved in a steering group to work out how the Centre will function and to contribute to its development.
Funding
· It is vitally important that teachers have funded time to make use of the Centre. To minimise disruption to classes, generous payment to teachers for successful participation in courses outside school hours is the only short term way of ensuring that the Centre can have a substantial impact.
· Funds spent on central initiatives should be limited so that more money is available fro local initiatives and directly to teachers and schools to take advantage of what is offered through provision co-ordinated by Regional Centres.
· Ring-fencing of funds for approved initiatives should be kept to a minimum.
What should it do?
· It should aim to extend teachers' understanding of how students learn mathematics and help them to develop a range of effective teaching styles.
· It should also aim to extend teachers' mathematical background by providing courses in mathematics for teachers, as well as those in how to teach it: learning new mathematics revitalises teachers by reminding them how enjoyable mathematics can be.
· The Centre should form links across all sectors: primary, secondary, sixth form/FE colleges and HE.
· An initial priority should be training linked to improving learning opportunities at KS4, particularly for those students not served well by existing academic pathways.
· The Centre should accredit approved courses. Credits should be linked to enhanced increments for teachers completing courses.
· Accreditation will help to build a professional ethos of continuous learning and development throughout teachers' careers.
7.5.03.
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