Discussion Meeting

Where will the next generation of UK mathematicians come from?

18-19 March 2005, Manchester

Supported by Manchester Institute for Mathematical Sciences, by the London Mathematical Society, by the Institute of Mathematics and Applications and by the UK Mathematics Foundation.

Preliminary Report  *  Media Coverage * Responses to the Report * Other Documents

Participants  *  Meeting Subthemes * Programme




A meeting with this theme took place on 18-19 March 2005 in Manchester.  Participants represented many different constituencies - including government agencies, the mathematics research community, university admissions, mathematics education, mathematics competitions, teachers, and young mathematicians who have themselves been through the system.  


As a result of the meeting, we produced a Preliminary Report  for wide circulation, as part of a process leading to a more substantial investigation of the issues and possibilities. A more detailed Discussion Document is in process of preparation. Your comments on the Preliminary Report are especially welcome, please send them to Alexandre Borovik,


and Tony Gardiner,



Media coverage:


  • From Letters and Opinion, THES, July 8 2005, p.17:


“On the one hand, the UK mathematics community falls short of reproducing itself. On the other, mathematicians have the highest earnings expecta­tions of all graduates ("Home PhDs trumped by overseas maths experts", July 1).


This is hardly the efficient market that the Higher Edu­cation Funding Council for England believes it is operat­ing. But the Hefce analysis of the market is flawed. The key change has been the boom in jobs in information technology and finance. As a result, few maths graduates or PhDs become teachers or lecturers, with the result that demand outstrips supply even further.


In an efficient market, career prospects alone would motivate teenagers to study maths, but this is surely nei­ther realistic nor desirable. If the nation wishes to supply its jobs market, schools maths teaching must be improved and better funding and bursaries provided in universities. Hefce already sets the finan­cial parameters for the student market: why does it fear inter­vening further?”


Niall MacKay, York University




  • The Times Higher Education Supplement: Leader: Mixed messages on key subjects (01 July 2005)

“One day senior mathematicians say there is a crisis in the subject that is the bedrock of the sciences, the next day the Higher Education Funding Council for England tells us not to panic and to leave it to the market. In both cases, perhaps they would say that, wouldn't they? Mathematicians are frustrated by the lack of progress since Adrian Smith's critical report on the subject last year, while the funding council sensibly does not want to be called in to offer aid every time a department is in trouble. But if the UK Mathematics Foundation is right about the scale of decline in secondary and higher education, the Hefce response risks looking dangerously complacent.”


 "Changes brought in in England in 2000, which divided A-levels into two separate parts - divided into modules - had been the "most recent and most public nail in the coffin" of decline.

They had made it "impossible to teach and to assess mathematics in an integrated way", making the subject "less appetising".

The report also described a need to "revive" teaching of the subject to able pupils aged 11 to 16.
The current system of "acceleration", where more gifted children move ahead of their classmates, had "made the problem worse".

It had meant less focus on the "elementary" aspects of maths, which were important to know when moving on to A-level."


"Lost count of gloomy reports about the state of maths in schools and universities? For more than a decade mathematicians have been moaning and the government has responded with inquiries, changes in the curriculum, numeracy hours in primary schools, golden hellos for maths teachers and a plethora of other initiatives in England.

Yet today the angriest report yet is published by a group of mathematicians, calling for drastic action to save the subject. Where will the next generation of UK mathematicians come from, asks the group, drawn from university maths departments around the country, learned societies and the government's curriculum watchdog.

At the moment the answer seems to be "from Russia and Hungary". In many university maths departments nine out of 10 of appointments go to candidates from abroad, while the shortage of maths teachers in schools has got so bad that the Department for Education and Skills has stopped collecting the figures."


  • The Daily Telegraph: Teaching of maths in spiral of decline, say dons. (28 June 2005)
    "Maths teaching in schools and universities has entered "a spiral of decline" and the Government has failed to grasp the nature of the crisis, leading mathematicians said in a report yesterday. They said the performance of more able pupils had collapsed; the numbers taking A-level maths were falling dramatically; those with top grades were "increasingly innumerate and even ineducable"; the shortage of qualified maths teachers had reached "dangerous" levels; national test results were grossly inflated; and postgraduates with a PhD in maths from a British university were now "largely unemployable" in British universities."


Some documents prepared for the Meeting:

·        P. Andrews, The future of mathematics: insights from comparative education. [pdf]

·        P. Andrews, Quality control of school textbooks. [pdf]

·        A. V. Borovik, What is it that makes a mathematician? [pdf]

·        A. V. Borovik and T. Gardiner, A dozen problems. [pdf]

·        D. French, Subject knowledge and pedagogical knowledge. [pdf]

·        D. French, Further thoughts on routes to improvement. [pdf]

·        Mathematical Education on Merseyside. [pdf]

·        P. Thomas, A view from a mathematics teacher in a sixth-form college. [pdf]



Some relevant official documents:

·        London Mathematical Society. Submission to the Select Committee on Science and Technology's Inquiry into Strategic Science Provision. [pdf]

·        Ofsted subject reports 2003/04: Mathematics in secondary schools. [pdf]



Participants of the Meeting act in their private capacity and do not necessarily represent position and views of their institutions and organisations. The list includes


Stephen Abbott HMI (Ofsted)

Dr Paul Andrews (Cambridge University; Chair, Association of Teachers of Mathematics ATM); web

Professor Margaret Brown (Department of Education, Kings College London; Advisory Committee on Mathematics Education ACME); web  

Richard Browne (Qualifications and Curriculum Authority QCA)

Doug French  (Centre for Educational Studies, Hull University; President

Designate, Mathematical Association MA); web

Gwyneth Gardiner (King Edward's School, Birmingham)

Professor Celia Hoyles (Institute of Education; Government Chief Advisor for Mathematics, DfES); web

Jenny Ingram (Sidney Stringer Community Technology College, Coventry)

Dr Andrew Jobbings (United Kingdom Mathematics Trust UKMT; Arbelos)

Dr Gerry Leversha (St Paul’s School, London;  Mathematical Association MA; Editor, The Mathematical Gazette)

Dr Hovik Khudaverdyan (University of Manchester); web

Dr Richard Lissaman (Mathematics Institute, Warwick University; Mathematics in Education and Industry MEI); web

Dr Mario Micallef (Mathematics Institute, Warwick University; Admissions Tutor in the School of Mathematics); web

Dr Graham Niblo (University of Southampton and National Cipher Challenge); web

Dr Karen Page (Department of Computer Science, University College London); web

Jenny Piggott (Faculty of Education, Cambridge University; Millenium Mathematics Project MMP)

Dr Ian Porteous (Department ofMathematics, University of Liverpool; Mathematical Education on Merseyside MEM); web

Professor Chris Robson (School of Mathematics, University of Leeds; Advisory Committee on Mathematical Education ACME); web

Dr Alice Rogers (King's College London; Heads of Departments of Mathematical Sciences HoDoMS); web

Dr Chris Sangwin (School of Mathematics, University of Birmingham; Mathematics, Statistics and OR Network, Higher Education Academy HEA); web

Dr Brian Stewart (Exeter College, Oxford; London Mathematical Society LMS, Education Secretary); web

Peter Thomas (Hills Road Sixth Form College, Cambridge; Chair, Post-16 Subcommittee, Schools and Further Education Committee, Institute of

Mathematics and its Applications IMA)

Professor Alexander Veselov (Department of Mathematical Sciences, Loughborough University); web

Dr George Wilmers (School of Mathematics, University of Manchester; Director of Postgraduate Studies); web



Dr Helen Carter  (Mathematics Programme, Engineering and Physical Sciences Research Council EPSRC)



Professor Alexandre Borovik (School of Mathematics, University of Manchester); web

Dr Tony Gardiner (School of Mathematics, Birmingham University); web



Meeting Subthemes:


·      What kind of early educational environments foster students who have the potential to become research mathematicians and which environments tend to have the opposite effect?

·      Where will the next generation of mathematicians come from within the UK? Are we content to become dependent on other countries?

·      And what might we do to increase the local flow?


In the mathematical community, there is a growing concern that the supply of bright and motivated undergraduate and postgraduate students of UK origin is insufficient. A healthy economy cannot depend on plundering talent from poorer countries, but needs policies and structures which ensure a regular and adequate supply of talent from its own sources. The attention of current policymakers is mainly concentrated on “numeracy” and the lower end of the spectrum of mathematical education. Thus it is left to mathematicians to highlight the growing problem of nurturing the future generation of highly able graduates and research mathematicians and computer scientists. However, there is at present no agreed “common position” (even among mathematicians) on these controversial issues. Therefore the meeting would necessarily be breaking new ground.  However, it is important, before formulating the proposed direction more firmly, to draw on the insights of colleagues with experience from a number of different domains.



Discussion Document.


The meeting will produce a discussion document, prepared and agreed among the participants within a month of the date of the meeting, and delivered to interested organizations (DfES, EPSRC, LMS, IMA, RS, MA, ATM etc.).  We expect that the Discussion Document will contain


¨        A first attempt to specify the relevant target group and to outline a collection of “profiles”, which indicate the variety of “mathematically able” school students, formulated in psychological and cognitive (and, therefore, curriculum-independent) terms rather than in terms of curriculum attainment.

¨        Pertinent observations on the relevant sections (e.g. Recommendations 4.5 and 4.10) of the Smith Report “Making Mathematics Count”.

¨        An initial attempt to formulate some generic advice to (interested) schoolteachers of how mathematical cognitive traits can be developed and supported in students in the course of routine school work.

¨        Possibly, some advice to universities’ admission tutors.

¨        Discussion of possible “outreach” policies towards schools and teachers of mathematics aimed at raising awareness of the special nature of mathematical abilities.

¨        Discussion of possible “outreach” policies towards mathematically able children.

¨        Address policy issues affecting undergraduate and postgraduate recruitment and career paths for young mathematicians. Discussion of more general policies and structures in the area of education which would create a learning and teaching environment more conducive to nurturing mathematical talent.







FRIDAY 18th March


Session            1: 5.30-7pm.                 Tony Gardiner

                                                            Background: a survey

                                                            General discussion


Dinner:             7.30pm


Session 2:         8.30-9.30pm.                 Experiences and examples 1 (including both promising and sobering experiences).


                                                            Ian Porteous

                                                            The Experience of Merseyside Mathematics Roadshows


                                                            Richard Lissaman

                                                            Further Mathematics centres and distance learning


                                                            Andrew Jobbings

                                                            Issues arising from UKMT provision of the national mathematics competitions


SATURDAY 19th March


Session 3:         9-10.30am.                   Experiences and examples 2 (followed by coffee break).


                                                            Doug French (with input from Paul Andrews)

                                                            Issues emerging from current provision and needs of pre-service and in-service teacher training


                                                            Peter Thomas

                                                            Issues emerging from a committed Sixth Form College


                                                            Mario Micallef

                                                            Issues emerging from attempts to use university

                                                            admissions procedures to encourage schools/colleges to address the

                                                            needs of able students (STEP, AEA, FM and all that)


                                                            Margaret Brown

                                                            Personal perspective


Session 4:         11-1pm.                        Small groups each with a precise brief to generate ideas.


Lunch                 1-2pm.


Session 5:         2-4pm.                          Towards workable policies (practical, professional and political; small-scale and large-scale).


                                                            Issues to be covered:

1.     recognising the importance of a (large) "critical mass" of able students;

2.     curriculum and assessment (including "Functional mathematics" and the "Extension curriculum and assessment framework");

3.     teacher recruitment and training;

4.     extra-curricular provision;

5.     undergraduate  provision;

6.     postgraduate provision and post-doctoral career structure.


Tea, Departure: 4-5pm.



Venue and Time: Chancellors Conference Centre in Manchester, http://www.conference.manchester.ac.uk/chancellorshotelconferencecentre/

from 17:00 pm on Friday 18 March to 17:00 pm on Saturday 19 March 2005.


 Last update 4 August 2005