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Continuing ProfessionalDevelopment for teachers ofmathematics

JMCJoint Mathematical Council

Supported by the Gatsby Charitable Foundation

ACME Continuing Professional Development for teachers of mathematics | December 2002 | iii

page

Preparation of this report v

Executive Summary vii

1 Introduction 11.1 Rationale for ACME’s CPD project 11.2 The need for CPD in mathematics teaching 11.3 The present situation 2

2 A CPD programme for teachers of mathematics 32.1 Key components of a well-planned CPD programme 32.2 Starting from needs: a coherent programme for a diverse community 32.3 Entitlement, accountability and rewards 4

3 A support network for CPD provision 53.1 Within the school or college 53.2 Setting up a local and a national infrastructure for CPD 5

4 Conclusion 7

Annex 1: List of contributors 9

Annex 2: Professional development currently available for teachers of mathematics 10

Annex 3: Case studies of CPD opportunities that would become available 12

Bibliography 15

Continuing Professional Development for teachers ofmathematics

Contents

ISBN 0 085403 587 7

Copyright © ACME 2002Requests to reproduce all or part of this document should be submitted to:ACMEThe Royal Society6–9 Carlton House TerraceLondon SW1Y 5AG

ACME Continuing Professional Development for teachers of mathematics | December 2002 | v

Preparation of this report

This report has been prepared by the Advisory Committee on Mathematics Education (ACME).

The members of ACME are:

Sir Chris Llewellyn Smith FRS (Chair) University of Oxford

Chris Belsom Ampleforth College, York

Annie Gammon Sir John Cass Foundation and Redcoat Church ofEngland Secondary School, London

Professor Celia Hoyles Institute of Education, University of London, and Chairof the Joint Mathematical Council of the UK

Professor J Chris Robson University of Leeds

Dr Sue Sanders University of Wales Swansea

Nick von Behr Committee Secretary, The Royal Society

The Government recognises that there is an urgentneed to improve the mathematical skills of the generalpopulation. There are concerns about both numbersand quality. In particular, we note:

• the poor uptake of school pupils continuingmathematics through to the age of 19 and beyond;

• the reduced numbers of students qualifying forHigher Education courses in numerate disciplines,especially science and engineering and, this year, inmathematics; and

• the under-supply of appropriately qualifiedmathematics teachers, which is exacerbated by thehigh demand for the skills of mathematicallyqualified graduates.

These concerns are linked, in that the teachers oftomorrow are drawn from the pupils and students oftoday. The Advisory Committee on MathematicsEducation (ACME) believes that radical steps need to betaken now in order to break into this closed loop. Itcontends that one of the most effective ways to do so andto raise the quality of mathematical provision in schoolswould be to expand substantially Continuing ProfessionalDevelopment (CPD) for teachers of mathematics. Itbelieves this would revitalise skills throughout teachingcareers, and would re-enthuse and help retain existingteachers of mathematics.

Recommendations

After consultation with both the mathematicscommunity and bodies involved in the professionaldevelopment of teachers, ACME has now produced this,its first self-initiated report, on CPD for teachers ofmathematics,which makes the followingrecommendations:-

1. We recommend that the Government should initiateurgently the process of developing and funding along-term programme of CPD for teachers ofmathematics that can meet their needs at variousstages of their careers. To help launch this initiative, theGovernment should first: obtain relevant data on boththe number of teachers of mathematics needed overthe next 10 years and the qualifications of existingteachers; commission a survey of current CPDproviders in mathematics; and convene a series ofseminars to examine international best practice in CPDfor teachers of mathematics.

2. We recommend that CPD for teachers of mathematicsshould contain an element of broadening and

deepening of mathematical knowledge. This shouldcomplement an appreciation of how pupils learn, anda comparison of varied methods of teaching,mathematics. The weighting of each of thesecomponents will vary from course to course accordingto teachers’ and schools’ needs and goals. A survey ofteachers of mathematics to elicit their views on CPDwould help to determine these needs fully.

3. We recommend that part of any CPD programmeshould be structured so as to allow opportunities torelate theory to practice in the classroom, and toprovide time for informed and collaborative reflectionwith peers and with those with appropriate expertise.

4. We recommend that teachers of mathematics shouldbe expected to engage in CPD throughout theirworking careers. This implies an entitlement to timeand funds, alongside a system of accountability andrewards.

5. We recommend that teachers of mathematics must begiven an allocation of time and resources to enablecoherent planning and development to take place atan institutional level. There is currently a crisis inmathematics teaching, and some funding tied to CPDfor teachers of mathematics must be provided directlyto schools and colleges. The Government shouldcommission a study to quantify both teacher in- andout-of-school training entitlement and the resourceimplications for schools of making such an allocation.

6. We recommend that a network of Local MathematicsCentres (LMCs) should be developed to encourage thegrowth of a community of teachers of mathematicsacross all phases and to provide a source of expertadvice, resources and information. The Governmentshould commission a feasibility study of how LMCsmight function and then set up a pilot centre involvingteachers, Local Education Authority staff andacademics from mathematics and educationdepartments.

7. We recommend that a National Academy for Teachersof Mathematics should be established to have astrategic overview of CPD at a national level and to co-ordinate its operation locally. The Government shouldcommission a feasibility study to set out a range ofoptions with costings and then seek private sponsorsfor funding.

8. We recommend that some CPD funding should bemade available directly to teachers of mathematics toenable them to undertake substantial professionaldevelopment according to their individual needs andgoals.

ACME Continuing Professional Development for teachers of mathematics | December 2002 | vii

Executive Summary

We wish to clarify our terminology. First, we note thatthere are what we will call ‘training’ programmes. Theseare specifically targeted and might last for a day or a fewdays. They might concern, for example, theimplementation of a new assessment scheme orcurriculum, or understanding some new legislationwhich has implications in schools or colleges. Next,there are what we will term ‘professional development’courses such as a short course on using the graphicscalculator to introduce linear functions and equations ora short course on some branch of statistics. By aContinuing Professional Development (CPD)programme, we mean a sustained and developmentalprogramme: this could comprise different sets ofprofessional development and some training puttogether so as to be progressive over time to reflect ateacher’s needs (e.g. a 20-day mathematics coursespread over one year, followed by a course in leadership,a masters course, or several courses on the use ofdifferent software for teaching mathematicsculminating in an in-depth study of IT and geometry).Thus a CPD programme in mathematics typically willcontinue over years, planned by the teacher incollaboration with a head of department, a HeadTeacher or a mathematics co-ordinator or others withexpertise, with the aim of enhancing the knowledge,skills and enthusiasm of the teacher.

1.1 Rationale for ACME’s CPD project

The Government recognises the importance ofimproving the overall mathematical expertise of thegeneral population. In his significant report to HMTreasury, Sir Gareth Roberts (Roberts 2002) noted theinsufficient numbers applying to take degrees inmathematics and the major numerate disciplines, andthe worrying drop in the proportion of pupils takingmathematics A2 following the introduction ofCurriculum 2000. Added to these problems is theexisting acute shortage of mathematics teachers andthe fact that the under-supply of numerate graduatesmakes it difficult to recruit new teachers of mathematicswith good quality mathematical backgrounds1. A closedloop has been created, with not enough of today’spupils and students turning into tomorrow’smathematics teachers.

After taking evidence and following broadconsultation within the mathematics community (seeAnnex 1), The Advisory Committee on MathematicsEducation (ACME) believes that the most effective

way to break into this closed loop is to offer asubstantial programme of CPD aimed specifically atexisting teachers of mathematics in primary andsecondary schools. Whilst we believe CPD isimportant for all teachers in all subjects and whilst werecognise that the DfES is moving toward a strategyfor increased teacher professionalism, neverthelesswe stress that the current state of mathematicsthroughout the system makes a large-scale, coherent,carefully focused programme of CPD in mathematicsa matter of urgency and national priority.

Such a programme, which should have equal emphasison teachers of mathematics with or without a strongmathematics qualification, would improve the teachingof mathematics, re-enthuse existing teachers ofmathematics and support and develop themthroughout their teaching careers This re-invigorationwill improve their retention in the profession. Inaddition, we anticipate that a programme of CPD willencourage and assist those teachers who have beenrecruited from other subjects to teach somemathematics, and will facilitate the return to theprofession of individuals from the pool of non-activemathematics teachers.

Thus a successful CPD programme would yield a moremotivated and enthusiastic teaching force inmathematics as well as having the potential to increaseits size and expertise. Such improvements would, inturn, help to alleviate the other problems noted in thepreceding paragraphs.

1.2 The need for CPD in mathematics teaching

There is a natural need for CPD among all NewlyQualified Teachers (NQTs), since it is impossible for InitialTeacher Training (ITT) to provide future teachers with allthey should know about the subject they will teach,how pupils learn it and how to teach it effectively; andthere is a need for CPD for more experienced teachers inall subjects.

However, the technical nature of mathematics and thesubtle links within it mean that there is a specialrequirement for CPD among those who teachmathematics, both the newly qualified and the highproportion of experienced teachers who do not have anappropriate mathematics background and whoseunderstanding of the subject itself may therefore belimited.

ACME Continuing Professional Development for teachers of mathematics | December 2002 | 1

1 Introduction

1 DfES statistics from January 2002 show mathematics as the top shortage subject with 17% of all classroom teacher vacancies in maintainedsecondary schools; while DfES statistics from 1996 (the most recent available) show that only 40% of teachers of mathematics in maintainedsecondary schools had a degree in mathematics.

In addition to these particular cases, it is vitallyimportant for the health of the profession thatexperienced and well-qualified mathematics teachersare also given the opportunity to revitalise their skillsand to renew their enthusiasm for their subject. Further,teachers of mathematics need not only to delivercurricula, but also to adapt them to pupils’ needs, tocustomise curricula and assessment frameworks to theirpractice, to deal with new materials and advances intechnology, and to learn from advances in research onpupil learning and on teaching practice in mathematics.Indeed, a mathematics teacher’s education should beseen as a professional continuum, a career-long process.

1.3 The present situation

A review of initiatives over the past three decades wascompiled by ACME to give a background to the types oftraining and professional development which werepreviously available (including noting the culturalexpectations of the profession at the time, whetherparticipation was voluntary or directed, and their lengthand depth) and those in place in 2001/02 (see Annex 2).

It is clear from this review that there has been a shift inprovision away from longer accredited courses towardsshort course provision, mainly centrally managed anddelivered and largely geared to lower grades. The typesof professional development now on offer range fromday courses (usually around national initiatives) toextended programmes leading to higher degrees, with

financial support ranging from full-cost (mainly for theformer) to little or nothing for the latter. TheGovernment has put in place well-resourced training forthe implementation of the National Numeracy Strategy(NNS) and Key Stage 3 (KS3) Strategy. Primary or KS3training is common to all teachers in that sector whohave had the chance to attend so far. This training hasgenerally been well received and has had the effect ofboosting some professional development for allteachers of mathematics within schools. Additionallythe Government has put in place an array of initiativesfor supporting mathematics teachers. However, we areaware of an urgent need to take stock and interconnectthese developments, to plug gaps in provision, and toseek to identify what is effective for different groups ofteachers in order to plan sustained portfolios of CPDthat will meet the diverse needs of teachers ofmathematics.

We recommend that the Government shouldinitiate urgently the process of developing andfunding a long-term programme of CPD forteachers of mathematics that can meet their needsat various stages of their careers. To help launchthis initiative, the Government should first: obtainrelevant data on both the number of teachers ofmathematics needed over the next 10 years andthe qualifications of existing teachers; commissiona survey of current CPD providers in mathematics;and convene a series of seminars to examineinternational best practice in CPD for teachers ofmathematics.

ACME2 | December 2002 | Continuing Professional Development for teachers of mathematics

In this section we outline the desirable ingredients of aCPD programme that we envisage will meet thechallenges set out earlier.

2.1 Key components of a well-planned CPDprogramme

We wish to see more professional development forteachers of mathematics that seeks to broaden anddeepen mathematical knowledge and to integrate thiswith study of pupils’ learning and with teachingapproaches. The notion of ‘unpacking’ mathematics tofocus on the processes of doing mathematics ratherthan only on learning outcomes is crucial. Some coursesmay start with introducing mathematical ideas from theschool curriculum and ask teachers to analyse thoseideas from the learners’ perspective; others may usepupils’ mathematical thinking as a springboard tomotivate the teachers’ learning of mathematics; stillothers might begin with elements of teaching practiceor curricula and move towards a consideration of theirpotential influence on progressing mathematicalthinking.

It is essential that teachers have sufficient subjectknowledge to challenge and develop the full range ofpupils whom they teach, otherwise pupils will not gainthe full benefits of their education. Broadening anddeepening mathematical knowledge andunderstanding means teachers can become increasinglyaware of key ideas, new ways to promote mathematicalreasoning as appropriate to diverse pupils, differentrepresentations and links within mathematics, as well aslinks to other subjects where mathematics plays a role. Italso encourages a positive attitude to mathematicsamong teachers, which is crucial to their continuedenthusiasm for the subject.

But for teachers of mathematics an important part ofbroadening their knowledge is appreciating how pupilslearn mathematics and the potential obstacles tolearning that they are likely to face. Improvingawareness of the different methods of teachingmathematics allows teachers to become ever better atteaching through a process of reflection and self-critique. Finally, teachers should have the opportunity toreflect upon different approaches to the mathematicscurriculum: how it is structured in terms of progressionin any one topic area, the links made between topicsand the way the topics are introduced and revisited indifferent contexts.

We recommend that all CPD for teachers ofmathematics should contain an element ofbroadening and deepening of mathematical

knowledge. This should complement anappreciation of how pupils learn, and acomparison of varied methods of teaching,mathematics. The weighting of each of thesecomponents will vary from course to courseaccording to teachers’ and schools’ needs andgoals. A survey of teachers of mathematics to elicittheir views on CPD would help to determine theseneeds fully.

2.2 Starting from needs: a coherentprogramme for a diverse community

Professional development should be differentiatedaccording to the diverse needs of teachers ofmathematics. Teachers have different pedagogical skills,mathematical knowledge and experience of teachingand aspirations. CPD should be sufficiently flexible toallow teachers to recognise and work on their differentneeds, and should provide a structure within whichteachers can identify their needs and how they might bemet. Thus a range of provision must be availablenationally and locally at different stages of teachers’professional careers or different points in theirmathematical development.

We highlight some distinct categories of teachers ofmathematics with potentially differing CPD needs (seeAnnex 3 for a series of fictional case studies to illustratesuch provision):

1. Primary school mathematics co-ordinators; 2. Primary schoolteachers generally; 3. Secondary school heads of mathematics or aspiring

heads of mathematics;4. Secondary school specialist mathematics teachers;5. Secondary school non-specialist mathematics

teachers (defined as those teaching mathematicswhose main subject specialism is not mathematics ora closely aligned discipline); and

6. Further Education lecturers in mathematics andnumeracy.

In addition, there will be other groups of teachers withan involvement in mathematics teaching, e.g. thoseworking with pupils with special needs. We recognisethat within each of these categories there remainsenormous variation in teachers’ backgrounds, goals andneeds. We would envisage, for example, the followingprovision, some or all of which might include award-bearing courses: courses for NQTs; courses for those intheir first year of holding a co-ordinating/ leading post;courses for each group in their second or third year ofteaching or holding a co-ordinating/leading post; amore diverse range of focused courses for teachers with


2 A CPD programme for teachers of mathematics

more than 5 years’ experience in their current role.Additionally, there is a need for provision concentratingon particular areas of mathematics (for example thepresent need for statistics and data handling), giftedpupils or those with special needs, new initiatives incurricula or in resources, and integration of Informationand Communications Technology (ICT).

All of the evidence suggests that short courses(half/one/two day) are optimally effective when there istime for teachers to reflect on what has been learnt, toseek the best ways of implementing the ideas andmethods in the classroom and to reflect on thesepractices in an informed way. Short-term training isfuelled by short-term issues, such as how to cope withnew assessment demands. It does not necessarily buildup into general professional expertise (to include, forexample, understanding of the complexity of andinterconnections between mathematical ideas and theirrepresentations, how these ideas might be taught andwhat the implications for learning are). Time forreflection and for trialling in the classroom anddiscussion of follow-up actions and furtherdevelopments are essential for sustained professionaldevelopment of teaching skills. We would recommendthat within CPD there should be opportunities forteachers to meet with peers and those with appropriateexpertise to discuss theory and practice as a basis forreflection and a starting point to trial ideas in theirclassrooms. Additionally, teachers need opportunities toreflect on and critique curricular materials and methods.This enables development of practice rather thanreinforcement of current methods. For this to beachieved, support is needed from those with a view,either of mathematics or of the teaching and learning ofmathematics, which is wider than delivery of immediatecurriculum goals. Reflection opportunities that involvediscussion or writing about iterative changes to activitiesor lessons can be valuable.

Thus we envisage that part of a CPD programme shouldbe personalised, to address teachers’ needs and supportthem in developing their own versions of theories orunderstanding of mathematics and mathematicsteaching, and part should be generalised, so thatteachers can place their theories and actions within awider perspective, but also see how they might

influence their own practice in the classroom or school.It is through this interchange of new ideas with practicethat teachers’ development can be sustained over time.

We recommend that part of any CPD programmeshould be structured so as to allow opportunitiesto relate theory to practice in the classroom, and toprovide time for informed and collaborativereflection with peers and with those withappropriate expertise.

2.3 Entitlement, accountability and rewards

We believe that teachers of mathematics should havean expectation and a responsibility to engage in CPD,which will support them throughout their workingcareers. This must involve a requirement to participate inCPD, an entitlement to time and funds alongside asystem of accountability and rewards. However, in orderthat CPD becomes an integral part of the culture ofteaching, a coherent infrastructure needs to be set upwith adequate funding and support. Our proposals areset out in section 3 of this report.

We envisage it may be necessary to encourage teachersof mathematics to engage in CPD, and to reward insome way those who do so (for example by salaryincrement). Heads of departments and mathematics co-ordinators will need to take the responsibility, with thesupport of the senior management of the school, toensure that their team, and individuals within it, keepup to date and enhance skills and keep abreast of newdevelopments. Performance management may helpsupport and encourage CPD, with teachers being settargets for their own development. Equally, the buildingup of a CPD Portfolio may be an important part ofprogression, and the key to higher salaries andpromotion. CPD should also include an obligation toshare good practice and disseminate ideas withindepartments, schools and local areas.

We recommend that teachers of mathematicsshould be expected to engage in CPD throughouttheir working careers. This implies an entitlementto time and funds alongside a system ofaccountability and rewards.


In this section we set out our proposals for putting inplace an infrastructure to support CPD for teachers ofmathematics.

3.1 Within the school or college

Schools and classrooms can be places for teachers aswell as pupils to learn. Professional developmentprogrammes that engage teachers in reflective practicein their own classrooms should provide the basis forteachers’ learning to become generative so that theirknowledge and practice continue to grow and evolve.We envisage that this process can be encouraged inthree ways.

Firstly, teachers have a great deal to learn from observingother colleagues and from good practitioners in otherschools, provided observation is undertaken from aninformed standpoint. A system of ‘Peer Mentoring’would be beneficial, provided there is appropriate timeand support. Peer Mentoring generally should be bothsupportive and developmental, enabling lessonobservation and discussion of teaching practice tobecome more commonplace in schools and acceptable toteachers. To further discussion and reflection on practice,teachers might also be encouraged to join a nationalprofessional subject association. Furthermore, some ofthese organisations might well be encouraged to developcareer structure grades for mathematics teachers as partof their membership.

Secondly, professional development requires themarshalling of substantial resources. One of the criticalresources is time. Teachers need frequent and regularopportunities to try out ideas and approaches with theirpupils and to discuss their experiences with specialists inmathematics and in the teaching and learning ofmathematics, as well as with other mathematicsteachers. These opportunities should not be limited to aperiod of a few weeks or months, but be part of theongoing culture of professional practice. There is verylittle non-contact time in schools. Heads of departmentand mathematics co-ordinators, who are key to thedelivery of improvement, often teach a full programme,and so have little in-school time to plan, organise andlead their team. They must be given time to spendworking alongside teachers in their team to developgood practice, as well as to manage their departmentseffectively. Additionally, timetabling constraints oftenmean that there is little time for team meetings aboutmathematics. Colleagues need the opportunity to meettogether to discuss issues and to share commonexperiences and good practice. Thus we suggest theremust be timetabled time for teams to meet regularly todiscuss the teaching of mathematics.

Thirdly, within schools, there is a shortage of money forprofessional development generally and, in practice,short-term issues take priority. Funding for CPD forteachers of mathematics has to compete with otherrequests and generally is inadequate to begin to resolvethe current concerns for the subject. Generally, outsideof the national initiatives, teachers of mathematicsreceive little CPD and they have access only to trainingor short professional development courses. Clearly, themathematics teaching profession will not be able todevelop a culture of CPD unless sustained and improvedfunding is made available. We consider that there is aneed for direct funding to each school for this purposeand that some of this should be specifically allocated toheads of department or mathematics co-ordinators toallow them to plan for the CPD of staff within theirdepartment.

We recommend that teachers of mathematicsmust be given an allocation of time and resourcesto enable coherent planning and development totake place at an institutional level. There iscurrently a crisis in mathematics teaching, andsome funding tied to CPD for teachers ofmathematics must be provided directly to schoolsand colleges. The Government should commissiona study to quantify both teacher in- and out-of-school training entitlement and the resourceimplications for schools of making such anallocation.

3.2 Setting up a local and a nationalinfrastructure for CPD

Learning in ways that continue to be generative overtime is best done in a community of fellow practitionersand learners, and professional development is mosteffective when it extends beyond the individual teacher.When teachers have opportunities to continue toparticipate in communities of practice that support theirCPD, the effects of CPD can be sustained more easily.Some of this will occur in school communities, but oftenit is effectively developed in wider communities based inLocal Education Authorities (LEAs), around theEducation and Mathematics departments in HigherEducation Institutes (HEIs) or around professionalsubject association groups. Creating synergies across allthese parts of the mathematics community has theadded advantage of engaging as many as possible infacing up to the challenge of providing quality CPD.

We note, however, that there is a shortage of individualswith broad experience and expertise to offer training,support and guidance to teachers of mathematics, andit is a matter of concern that the pool of people with


3 A support network for CPD provision

expertise to provide CPD and offer advice is shrinking.There is scarcity in capacity throughout the system withadvisors in LEAs, National Numeracy Advisors, andteachers in HEIs all fully stretched. We therefore foreseea need for a national campaign to encourage thedevelopment of this expertise, which could itself formpart of a CPD programme. What may be needed, forexample, to build on the efforts already in place in someareas, is to set up a cadre of ‘expert teachers’, similar to‘leading mathematics teachers (LMTs)’, who may remainclassroom based (alongside traditional ‘trainers’), butwho could also form a part of a network of localresource centres for teachers of mathematics. Theselocal centres should be cross-phase (primary, secondary,Further Education, and Higher Education) to encouragethe development of a community of mathematicsteachers in a locality, as well as providing resources andinformation for schools and teachers.

We recommend that a network of LocalMathematics Centres (LMCs) should be developedto encourage the growth of a community ofteachers of mathematics across all phases and toprovide a source of expert advice, resources andinformation. The Government should commissiona feasibility study of how LMCs might functionand then set up a pilot centre involving teachers,LEA staff and academics from mathematics andeducation departments.

Given the fragmentation, lack of coherence and gapsin CPD provision reported to us and noted above,together with the need to support teachers inengaging with future curricular initiatives, aninfrastructure for mathematics CPD must be set up toco-ordinate provision across the country and organiseit at a strategic level. We have been impressed by themodels of CPD in operation in France through theIREMs (Instituts de Recherche sur l’Enseignement desMathematiques – literally translated as ‘ResearchInstitutes for Mathematics Teaching’), and in Israel

through the Weizmann Institute. In particular, we havenoted the impressive ways that teachers, mathematicseducators, and mathematicians work together indesigning and implementing CPD. We suggest theestablishment of an ‘academy’ for mathematicsteaching, a centre of excellence to provide a uniquepoint of reference for all teachers of mathematicsregardless of phase or experience, as well as to set outstrategic objectives for CPD and champion theirimplementation. We note that some of theseproposals follow similar lines to those for theenhanced teaching of science in schools through theproposed National Centre for Excellence in ScienceTeaching.

We recommend that a National Academy forTeachers of Mathematics (NATM) should beestablished to have a strategic overview of CPD ata national level and to co-ordinate its operationlocally. The Government should commission afeasibility study to set out a range of options withcostings and then seek private sponsors forfunding.

Finally, while recognising that the Government isalready spending heavily on its centrally controlledinitiatives at KS3 and on the NNS, we believe it isnecessary for the Government to establish and fundsome teachers directly (possibly co-ordinated throughthe NATM) to foster their individual development.Teachers who seek particular expertise should beencouraged and supported in furthering their ownprofessional and academic development in the teachingof mathematics by attending longer courses supportedby national bursaries.

We recommend that some CPD funding should bemade available directly to teachers ofmathematics to enable them to undertakesubstantial professional development accordingto their individual needs and goals.


ACME believes that the CPD infrastructurerecommended in this report will begin the process ofensuring that professional development is seen as acontinuous and integral part of the experience ofteachers of mathematics, to which teachers should beentitled at different points in their careers, and for

which they are responsible. Through the network ofnational, local and school provision proposed, weenvisage that the profession of teaching mathematicswill grow in stature with benefits for the profession,pupils and society as a whole.


4 Conclusion

ACME has consulted the mathematics, teaching andeducation communities throughout this project, forwhich it would like to thank the following organisationsand individuals.

Evidence was given to the Committee by:

- Department for Education and Skills (Ellen Crehan,Janet Dallas and Diane Mankelow)

- General Teaching Council for England (MaureenBurns, Head of Policy and Communications andSarah Stephens, Policy Advisor)

- Key Stage 3 Strategy (Sarah Sharkey)- National Association of Mathematics Advisors

(Gillian Thumpston, Honorary Secretary)- National Numeracy Strategy (Carole Macintyre)

Communications were received from:

- Sian Acreman, Blue Gate Fields Junior School, TowerHamlets

- Mundher Adhami, Cognitive Acceleration inMathematics Education Project

- Lucy Allen, Institute of Mathematics and itsApplications

- Robert Barbour- Alan Bloomfield, University of Gloucestershire- Professor Margaret Brown, King’s College London- Dr Colin Campbell, Edinburgh Mathematical Society- Lynn Churchman, HMI

- Caroline Dawes- Dr Ruhama Even, Weizmann Institute of Science,

Israel - Geoffrey Faux, Peter Lacey and Barbara Ball,

Association of Teachers of Mathematics- Dr Tony Gardiner, University of Birmingham- Professor Harvey Goldstein and Mr Gerald Goodall,

Royal Statistical Society - Professor John Howson, Education Data Surveys- Rosalyn Hyde, Professional Development Officer, and

members of The Mathematical Association- Dr Barbara Jaworski and Dr Anne Watson, University

of Oxford- Dr Sue Johnston-Wilder, The Open University- Sir Alistair MacFarlane, Chair Royal Society Education

Committee- Roger Porkess, Mathematics in Education and

Industry- Irene Robinson, Manchester Metropolitan University- Mary Russell, Universities Council for Education of

Teachers- Professor Peter Saunders, London Mathematical

Society - Paul Scruton, Schools Mathematics Project- Professor Alan Smithers, University of Liverpool - Dot Sutherland, Senior Mathematics Advisor for

North Yorkshire - Professor David Stirling, Heads of Departments of

Mathematics- Professor Alison Wolf, Institute of Education- Professor Derek Woodrow, Manchester Metropolitan

University


Annex 1: List of contributors

The range of types of professional development now onoffer to teachers of mathematics includes:

1. Award-bearing courses run by HEIs;2. In-school development run by teachers themselves;3. Courses run by the NNS at primary level;4. Courses run by the KS3 Strategy for mathematics;5. In-school development by numeracy or

mathematics consultants employed to implementthe two government strategies;

6. Demonstration lessons by LMTs or work withAdvanced Skills Teachers (ASTs);

7. Courses run by examination boards to update onsyllabi or moderate coursework;

8. Conferences and working groups and day coursesrun by professional subject professionalassociations;

9. Day or longer courses run by other organisationse.g. Stands for Education, BEAM Education; and

10. Development as part of government initiatives suchas Excellence in Cities (EiC) and Education ActionZones.

1. Award-bearing courses run by HEIs: these maylead to diplomas, MAs or PhDs and may involveprofessional associations. The focus varies but is likelyto include mathematics, statistics, teaching andlearning and associated research. They are oftenfunded by the individual teachers participating andinvolve part- or full-time study. Long courses havelargely disappeared into modular provision, of whichusually between one-sixth and one-twelfth ismathematics related. These courses are also in decline.The uptake might be small but they have a high impacton those involved.

2. In-school development: each school will have apolicy on CPD and a person responsible for co-ordinating and managing mathematics education.There is likely to be a plan for development inmathematics, which includes use of external courseand in-school shared development: for example, theremay be plans for reciprocal lesson observations byteachers in the school, or scheduled use of meetingtime for discussion of key areas of the curriculum. Thisis available to all teachers but may not always be usedproductively and is rarely mathematics related. The useof time in schools may be supported by theprofessional development materials provided by theNNS and KS3 Strategy. Uptake will reach all teachersbut impact is variable, depending on the school.

3. Courses run by the NNS at primary level:consultants in each LEA run nationally prescribed andlocally developed courses. A key course is the five-daycourse, which includes content and pedagogy.Information from the NNS suggests that every primaryteacher would be entitled to attend this course at sometime. Within each LEA certain courses are for ‘intensive’schools (selected by the LEA as being those who wouldmost benefit from support) while some are for allschools. There are short courses run specifically formathematics co-ordinators.

4. Courses run by the KS3 strategy: consultants ineach LEA run nationally prescribed and locallydeveloped courses. These have included courses forheads of department and KS3 co-ordinators, whichinclude developing skills in leading departments. A four-day course has been run for less experienced teachers ofKS3 mathematics which includes content andpedagogy. Forthcoming courses include how to usematerials in departmental meetings to ensure discussionof content and pedagogy. Within each LEA certaincourses are for ‘intensive’ schools while some are for allschools. Uptake: some courses have been attended bydelegates from almost every maintained school; othershave been available to intensive schools only.

5. In-school development for numeracy: LEAconsultants work in ‘intensive’ schools to help embedideas from the courses and to develop skills in teachingand planning. They may work with individual teachers,pairs of teachers or provide training sessions for allteachers of mathematics. This work generally embracescontent and pedagogy and action planning. Thisresource is available to intensive schools (approximatelyone-third at any one time).

6. Demonstration lessons by LMTs: in primaryschools, LMTs are identified within each LEA who willdemonstrate lessons in their own schools to teachersfrom other schools. Advanced skills teachers in bothphases will demonstrate lessons and work with teachersin the ‘learning’ teachers’ classrooms.

7. Courses run by examination boards: these are keysources of information and training at KS4 and 16-19levels. Examination boards run courses usually focusedon changes to syllabi or assessment methods. There is asmall percentage uptake of these courses but theyinfluence an opinion forming sector.


Annex 2: Professional development currently available for teachers of mathematics

8. Conferences/working seminars run byprofessional subject associations: these are usuallyat weekends or in school holidays. There are also regularlocal meetings of professional subject associations aswell as annual conferences.

9. Other organisations (including private sector):these run courses for mathematics teachers, often onaspects of managing the curriculum; assessment;teaching more able or less able pupils; managingbehaviour, etc. Few of these are focused onmathematics and pedagogy.

10. Government initiatives: there are often cross-subject developments as part of Government initiativessuch as the Gifted and Talented strand of the EiCinitiative and the transition work as part of EducationAction Zones. This may well lead to professionaldevelopment for those involved.


The following vignettes reflect the opportunities thatwould become available with the implementation ofACME’s CPD recommendations. The individual profilesof types of teacher illustrate different possible scenarios.

Parveti is mathematics co-ordinator in aprimary school.

Parveti did a BA (QTS) with a mathematics specialismand has an MA(Ed) which included some mathematics-focused modules.

She is part of a group working at the Local MathematicsCentre working with Special Educational Needs Co-ordinators on an intervention programme for pupilsexperiencing difficulties with mathematics in year 2.This is funded as a local initiative and her school receivessupply cover costs.

She has attended a short course run by the LocalMathematics Centre on ‘Working with parents’. As thisis a school priority it was funded by the ring-fencedmathematics CPD budget. Now she is leading a wholeschool initiative on ‘Working with parents onmathematics’.

Jackson is a newly qualified primaryschoolteacher.

Jackson has a degree in history, which he followed witha Primary PGCE course. He has a Grade ‘C’ GCSE inmathematics and describes his own mathematics as‘shaky’. However, he appears very confident with thepupils. He is in his first year of teaching and his CareerEntry Profile has highlighted consolidation of personalsubject knowledge and integration of Information andCommunications Technology (ICT) as needingdevelopment.

Jackson is attending a five-day course at a LocalMathematics Centre jointly run by the local Universityand the Local Education Authority (LEA). This is part ofhis CPD entitlement as a Newly Qualified Teacher (NQT).The course uses ICT to broaden and developmathematical ideas as well as demonstrating soundpedagogy. It began with two days in the LocalMathematics Centre followed by a four-week gapduring which he tried out ideas in his own classroomwith support from the mathematics co-ordinator. Therewas then one day at the Centre to share experiencesand receive expert advice on how to progress. After

another three weeks in school there was another day inthe Centre for more guided reflection. There will beanother Centre-based day towards the end of nextterm.

The Centre has also set up an email chat room for NQTsand each member of the course can access expertadvice by telephone or email.

Jackson’s school is also freeing him up for 1 hour perweek to observe and work collaboratively with a teacherof the parallel year group who is very good atintegrating ICT into her teaching.

Lynn is Head of a mathematics department ina comprehensive school.

Lynn has a good first mathematics degree and an MSc.After a couple of years in industry she did a PGCE andhas been a head of department for 5 years.

She is using a teacher bursary to research ways in whichother schools manage their programmes for gifted andtalented mathematicians of all ages. She is consideringregistering for a doctoral programme, which is run byher local university in association with the NationalAcademy for Teachers of Mathematics.

She is an active member of a professional subjectassociation and is making a presentation on enhancingthe teaching of geometry at the Annual Conference.

Khalid is a mathematics teacher in asecondary school.

Khalid came into teaching through the GraduateTeacher Programme, after 5 years in accountancy. Nowin his third year of teaching he wishes to extend hissubject knowledge.

He is already teaching an A2 statistics class and has thesupport of his head of department for one lesson aweek. During the weekly departmental meetings he isable to discuss his successes and to ask for advice frommore experienced members of staff.

Khalid attends a 10-week part-time (one evening aweek) masters module on statistics, which is deliveredby the mathematics department of his local university.He is considering adding some education modules infuture years.


Annex 3: Case studies of CPD opportunities that would become available

Nadia is a PE teacher in a secondary school –she also teaches some mathematics.

Nadia has a BA in Sports Psychology and is currently inthe first year of a new masters degree scheme, whichfocuses on both mathematics and education. As well aslecturers from the local university and LEA advisers,there are weekend schools at the National Academy forTeachers of Mathematics, which include input frominternational experts.

Her head of department is working alongside her forone lesson a week as part of a whole school initiative onimproving participation by African-Caribbean boys. Thisis part of a research and development project jointlymanaged by the Local Mathematics Centre, LEA and thelocal university, and funded by a charitable trust. Nadiawill use this work towards part of her masters degree.

Mike works in a College of Further Educationwhere he is responsible for Key Skills(Numeracy).

Mike has found himself teaching mathematics toyoung people on a number of programmes includingthe GNVQ manufacturing strand, even though he wasoriginally employed as a science tutor. He feelscompetent with the skills element of his teaching but isnot sure that he can motivate the students as much ashe would be able to in his own field. Sometimes hestruggles to find real life examples of the mathematicshe is teaching and to make the connections with otheraspects of mathematics, which he knows is important.

Mike’s Local Mathematics Centre arranges for him tospend time in the classroom of an ’expert teacher‘ in alocal school with its own sixth form. The ’expert teacher‘also hosts an email discussion group, providing a forumin which non-mathematicians can get advice onplanning from mathematicians in universitymathematics and education departments, and fromexperienced teachers. Mike is attending a course at hislocal HEI which is aimed at teaching mathematics toyoung adults, and in particular he is considering theapplication of mathematics.


The Committee was also informed by the followingpublications:-

Askew M., Brown M., Rhodes V., Johnson D. andWilliam D. (1997) The contribution of professionaldevelopment to effectiveness in the teaching ofnumeracy. Teacher Development 1, No. 3,

pp. 335-355.

Davis J. (undated) In-service secondary mathematics re-training: an evaluation. Occasional Paper No. 3.Cumbria: Charlotte Mason College.

Even R. (1999) The development of teacher-leaders andin-service teacher educators. Journal for MathematicsTeacher Education 2, 3-24.

Even R. (1999) Integrating academic and practicalknowledge in a teacher leader’s development program.Educational Studies in Mathematics 38, 235-252.

Hershkowitz R., Dreyfus T., Ben-Zevi D., Friedlander A.,Hadas N., Resnick T. and Tabach M. 2003 Mathematicscurriculum development for computerizedenvironments: a designer-researcher-teacher-learneractivity in English L.D. (ed) Handbook of InternationalResearch in Mathematics Education. Hillsdale, NJ:Lawrence Erlbaum Associates. (In the press.)

Ingvarson L. (2002) Building a learning profession.Australian Council for Educational Research.

Kilpatrick J., Swafford J. & Findell B. (eds) (2001) Addingit up: helping children learn mathematics. MathematicsLearning Study Committee, National Research Council.Washington, DC: National Academy Press.

McNamara O., Jaworski B., Rowland T., Hodgen J. andPrestage S. (2002) Developing mathematics teachingand teachers. (See http://mathsteachdev.maths-ed.org.uk.)

Melrose J. (1982) A report of an investigation to monitorthe progress and assess the effectiveness of TheMathematical Association’s Diploma in MathematicsEducation. University of Durham.

Millett A., Askew M. and Simon S. (2002) Responses ofteachers to a course of intensive training. King’s CollegeLondon: The Leverhulme Numeracy Research Project.

Roberts, G. (2002) SET for success. The supply of peoplewith science, technology, engineering and mathematicsskills. The Report of Sir Gareth Roberts’s Review.London: HM Treasury.


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