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					                                                 The Consultation
                                          GIVE PEACE A VOICE
                                           St George's House, Windsor
                                             28th-29th January 2009

      Appendix A (last revised 7th December 2008)

      Participants, or their representatives, room allocations, and visitors:

1.    Dr. Sheikha Bint Jabor Al-Thani, Vice President, Qatar University (AA AA);
2.    Professor Dr E. Vásárhelyi, Eötvös Lorand University, Hungary (AA);
3.    Professor Nancy Nagel, Lewis and Clark College, USA (A);
4.    Dr Ayman Bassil, Senior Research Analyst, Qatar Foundation (A);
5.    Dr. Bruno Behr, Director, Qatar Leadership Academy (A);
6.    Dr. Mahmoud Boutefnouchet, Head, Department of Mathematics and Physics, Qatar University (A);
7.    Dr Chee Wen Chong, Head, Research Partnerships, Qatar Foundation (A);
8.    Emeritus Professor Dr Duane Davis, Mercer University, USA (AA);
9.    Emeritus Professor Dr Paul Ernest, Exeter University, UK (A);
10.   Professor Johan Galtung, Rector, Transcend Peace University (AA);
11.   Professor Dr Humam Ghassib, Jordan University, for HRH Prince El Hassan (A);
12.   Mr Colin Hannaford, IDM, Oxford, UK (AA);
13.   Dr. Gregory Hedger, Director, Qatar Academy (A);
14.   Mr. Michael Hitchman, Head of Senior School, Qatar Academy (A);
15.   Professor Dr Hani Khoury, Mercer University, USA (video presentation);
16.   Herr Wolfgang Ringkowski, representing Dr Hartmut Köhler, Stuttgart Landesinstitut für Schulentwicklung,
      Germany (A);
17.   M. Didier Nordon, Bordeaux University, France (AA);
18.   Dr Jerome Ravetz, James Martin Institute, Oxford University, UK (A);
19.   Professor Michael Savage, University of Leeds, UK (A);
20.   Mr. Adel Al Sayed, Director of Evaluation Institute for the Supreme Education Council (A);
21.   Mr Roger Sutcliffe, founding President of SAPERE ( Society for the Advancement of Philosophical Enquiry
      and Reflection in Education), UK (A);
22.   Mr Stuart Tester, for TRH the Prince of Wales and Duchess of Cornwall (A);
23.   Mr and Mrs Jimmy Kilpatrick, Education News, USA (AA);
24.   Ms Katalin Fried, assistant to Professor Vásárhelyi (sharing, see above);
25.   Mrs Jackie Fairchild, Assistant Head, Gosford School, Oxford, UK (A).

      NB       AA means a twin bed room; A is a single bed room.
      Currently single rooms for participants 3, 4, 5, 6,7,12, 13, 14, 21 are assigned to Qatar) and there are no more
      spare rooms.

      Visitors (confirmed):

1.    H.E. Mr Yigit Alpogan, Ambassador of the Republic of Turkey.
2.    H.E. Ms. Borbála Czakó, Ambassador of the Republic of Hungary.
3.    H.E. M. Maurice Gourdault-Montagne, Ambassador of the Republic of France will be represented by Dr Serge
      Plattard, Conseiller pour la Science et la Technologie.
4.    H.E. Mrs Barbara Tuge-Erecinska. Ambassador of the Republic of Poland, will be represented by Mr Emil
      Pietras, First Secretary (Science and Education).
5.    H.E. Mr Georg Boomgaarden, Ambassador of the Federal Republic of Germany will be represented by Mrs
      Margit Hosseini, Education Attachée.
6.    Ms Julia Strong, Deputy-Director, National Literacy Trust, UK.
7.    Ms Delia Stafford, President, Haberman Educational Foundation, USA.
Appendix B

       A unique opportunity to participate in a groundbreaking debate at Windsor Castle, January 2009
                           on using mathematics education in schools to
                                   GIVE PEACE A VOICE

The Socratic Methodology for teaching mathematics will be explained at a conference in St George's House,
Windsor Castle, England in January 2009. Since this historic setting offers very limited space, only selected
international representatives can be invited. They will be shown how mathematics can be taught to form
models of peaceful interaction and positive cultural exchange.
No expensive training is required for this approach. Although actually extremely simple, the Socratic
Methodology offers a fully developed approach to progressive mathematics education with consistent
empirical and moral aims. Qualitative and quantitative skills are developed in the early years. Literacy and
numeracy are later combined, allowing pupils to learn an honest understanding of mathematics from collective
discussion of expert texts, rather than pretended understanding of imperfectly given or received instruction.
This practice also makes easier the usually difficult transition from primary to secondary education. The
ultimate aim, openly shared with pupils, is the attainment of their intellectual and moral maturity,
strengthening their preference for critical, constructive, receptive discourse rather than anger and violence.
The philosophy of this approach has already resulted in government-funded development in Germany. It is
also being taught in an important student teacher programme in the United States as the basis of democratic
citizenship education.

                                           The Consultation
                      St George's House, Windsor Castle, 28th-29th January 2009
     Adopting the Socrates Method for teaching mathematics: encouraging a culture of democratic
            behaviour to foster inter-cultural and inter-faith understanding and tolerance

Day 1 (28th afternoon) Supported by the Qatar Foundation (Its Chair, H.H. Sheikha Mozah, consort of the
Emir of Qatar, is UNESCO Special Envoy for Basic and Higher Education and winner of the 2007 Chatham
House prize). The Foundation will share in inviting international specialists in education to this opening forum.
HRH Prince Charles, The Prince of Wales, will be represented, as will HRH Prince El Hassan of Jordan, Chair
of the Global Commons.

Conference.Day 2 (29th) Participants will learn about the development of this new approach through the
original two-year study directed in Germany for the EU Education Commission; through university research in
Hungary; government sponsored development and the production of new textbooks in Germany; and its
application in student teacher courses in the United States. Papers by participants will be distributed and
further global academic collaboration will be invited.
Appendix C

                                              Printed Introduction

Distinguished Guests,

In this short meeting, in this historic setting of St George's House, my colleagues and I intend to explain how a
very simple change in mathematics education can achieve what mathematics education was originally
supposed to achieve: competence in critical, constructive, receptive discourse, the basis of democratic
citizenship and national unity.
We hope you will question everything we have to say. We believe we can convince you that there exists today
no better, simpler, or more inexpensive solution for resolving civic, national - and even international - discord.
We believe that in this short meeting we can begin to show how all the cultures of the world are actually
united, and how they can become more aware of this essential fact.

In 1992 the American scientists Carl Sagan and Ann Druyan wrote a book that they called 'Shadows of
Forgotten Ancestors'.
On its first page they pointed out that by the early 1980s the United States and the Soviet Union - for such
reasons, they suggest, as 'deterrence, coercion, pride, and fear' - had together created arsenals totalling at least
60,000 nuclear weapons.
Both countries and their proxies engaged simultaneously in a furious propaganda war: praising their own
people for representing 'humanity', whilst declaring that the people of the other nation represented a danger to
The Sagans reckoned that the United States spent ten trillion dollars assembling its own arsenal. Mathematics
had been vital in constructing them. The consequences of using them were also calculated using mathematics.
As a young man I spent several intervals of my life on the North German plain, waiting to defend democracy
as part of the 'trip-wire' strategy: the planned 'success' of which would have left all of Central Europe - at the
very least - a radioactive desert for hundreds, possibly thousands, of years. This made the prospect of war so
frightening that no major power dared begin it.
But today we have to reckon on the possibility that some much more minor power would begin a nuclear war
if only they were able. One of the reasons for our being here is therefore to Give Peace a Voice: to think of a
way of showing the billions of young people in the world whose lives wars would destroy how to resolve
difficult problems peacefully. All of this: without having trillions of dollars to spend.
Dr Sagan and his wife, like many others, seemed to believe that a major obstacle to peace is the belief of many
people that God has a plan for them to follow. If only, they thought, such people might be persuaded to
abandon these beliefs, the light of pure human intelligence, no longer confused and no longer distracted, would
show them the right path to take.
Well, maybe. But it may be remembered that pure human intelligence created those 60,000 nuclear weapons -
about 30,000 of which, incidentally, still exist in the United States and the previous Soviet Union, and other
countries are eager to have or add to their own.
The Chapel of St George, next to this house, is dedicated to a soldier saint. The history of St George is actually
rather obscure; but the English, who rather like their heroes rather obscure, decided that he was - and is - a
fitting symbol of themselves. It was also dedicated to the Blessed Virgin Mary, and to a much earlier English
King Edward - who is, incidentally, the patron saint of all kings: and difficult marriages! It was Edward - this
earlier Edward - who also built what is now called Westminster Abbey.
The Chapel was built to the glory of God, the Virgin, saint of all mothers, and to strengthen the loyalty of the
English nobles - and people - to their King.
So Christianity has more than just some resonance here: it is the reason that this place exists at all. The ground
around us - within these walls of Windsor Castle - is arguably one of the most important Christian centres in
Europe. It was also, in effect, a military headquarters. The soldiers you see on duty here are not here only for
So how can we escape - in this place, above all - from the shadows of centuries of vicious conflict between
Christian nations, between Christian and Muslim, between all the different factions of the human race, which
disgrace us all as the human race?
Two thousand three hundred and forty two years ago - that is in three hundred and thirty three BC - we are told
that Alexander the Great of Macedonia was invited to attempt to untie the famous Gordian Knot in a place
called Telmissus, the ancient capital of Phrygia, now in Central Turkey.
I am sure you all know the story. This was a Knot so complex that no-one had ever been able to undo it. But it
had been prophesied that whoever would separate the two ends of the rope would go on to conquer the world.
Alexander did not try to undo the Knot. He took his sword and cut it in two.
The Oxford Dictionary has a nice way of explaining the modern use of 'cutting a Gordian Knot'. It suggests
that this means solving impossible problems by 'eliminating the conditions which create the problem.'
I enjoyed the Sagans' book. There is much to learn in it. (i) But what if our pure intelligence has been
attempting to show us precisely how to 'eliminate the conditions which create our problems' - for thousands of
What if we have still not recognised that path?
What if those who believe in God's inspiration of humankind are not as naïve as the Sagans appeared to
believe, and as many others seem to believe today?
What if many are so fascinated by the complexity of what separates one end of the rope from the other, that
they do not see what joins them!
Mathematics joins all the cultures on earth.
To cut through our Gordian Knot, of conflicts and divisions which now threaten the survival of us all, we need
to explain to those who have not yet noticed that mathematics has not become the universal language of
humankind because it is an easy language to learn. It never was an easy language. It never will be. It is not
composed of obvious facts, as many like to think. It is composed almost entirely of arguments. That one plus
one equals two - for example - is not actually a fact; it is first of all an argument, and quite a difficult argument
at that.
We do not need to confuse little children with these details. They already know that mummy and daddy made
three - at least: not always two!
The far more important fact that needs to be known, however - and I will state it in the words of Dr Hani
Khoury's 2006 paper for the Qatar Foundation's Second Innovation in Education Symposium - is: 'mathematics
is a universal moral system.' (ii)
This is the crux, the heart, of the matter. Humankind has always sought certainties. Far too often their
certainties drive people apart rather than unite them. Very often they also serve to release man's inexhaustible
capacity for cruelty and evil.
Today we know that the dream that mathematics might be made a perfect system of certainty is impossible.
There will always be truths we cannot prove; inconsistencies we cannot resolve; (iii) statements beyond the
reach of theory. (iv)
But if we are aware that mathematics must remain an incomplete and imperfect language, we have also
become aware that its creation has always been driven by an older, deeper, and actually far stronger impulse
than reason. This impulse suggests that, if the perception of any one mind is adequately expressed, all other
minds, in varying degrees, should be capable of sharing its perception.
This is an astonishing idea. In principle - and morality, after all, consists of principles - there are no exceptions.
All our understanding can be, will be, and must be, shared. This is the real basis of humanity. In mathematics -
in particular - all people are morally equal.
This is the morality that our societies need to teach young people: that in their mathematics lessons they can
learn the skills of critical, constructive, but - above all - receptive discourse, which allow such individual
perceptions to be shared.
We may have more hope for their future if this ability is sufficiently well understood. Without it, their future,
and ours, is to be feared. Our world is about to teach us that we were given an Eden, and we have desecrated it
- and the world is now ready to take its revenge.
We cannot stop this revenge. But we can provide our children - and then, we may hope, they can provide their
children - with a better understanding of the only universal language that no one can misunderstand or corrupt
for very long.
Whatever may befall our civilisations, it is just possible that with this knowledge of the real importance of
mathematics as a universal language and as a universal moral system - our survivors may be able to build a
civilisation that does not carry within itself the seeds of its own destruction.
The Socratic Methodology is not a new idea. Its deliberate introduction into school education is a new idea: but
it is not a revolution. All that we have discovered is that children learn best through discussion and that they
learn least well from instruction.
Through directed discussion, especially in mathematics - which, it must always be remembered, actually began
as forms of discussion to encourage democratic debate - they can learn to listen to one another more
respectfully, to accept criticism and correction, even gratefully, and to understand that learning is more useful
for society as a whole when it is a co-operative, and not a competitive, endeavour.
Whether we want to believe that this is because of evolution, or whether it is because of God's inspiration, I am
personally sure: God will not mind.
Thank you! Please prepare your questions!

                                                                                    Colin Hannaford, Oxford, UK;
                                                                               Ed. Dr Duane Davis, Georgia, USA.
Appendix D

                                      St George's House, Windsor,
                                         28th-29th January 2009

Proposed Programme

28th Jan

16.00   Registration and Tea

17.30   Welcome: Colin Hannaford: Reasons and Aims.

        Dr Vásárhelyi: Pedagogical Research, Hungary.

        Comments and questions noted.

19.00   Supper

20.45   Talk: Dr Davis.

29th Jan

09.00   Colin Hannaford: the EU Education Commission study, Stuttgart 1996-98

09.15   Dr Nordon: the French perspective

09.45   Dr Ravetz: Toxic maths.

10.15   Discussion: (Chaired by Dr Davis.)

10.45   Coffee

11.15   Dr Köhler: the German experience.

11.45   Dr Khoury (represented): the United States experience.

12.15   Discussion: Chaired by Dr Ernest.

12.45   Lunch

14.15   Global perspectives: Dr Galtung.

14.45   Discussion: Chaired by Dr Nordon.

15.15   The Way Forward: Qatar

15.45   Ends.
Appendix E

               Biographical Summaries of Contributing Participants (on 3rd October 2008)

Professor Dr. Éva Vásárhelyi:
I was born in the small village of Biharuga in Hungary in 1951, and went first to my village school and then to
Eötvös József Gymnasium in Budapest. After achieving my diploma at Eötvös Loránd University, I was
appointed to teach mathematics in the Gymnasium and the University. I have held simultaneous appointments
ever since, and at once became a member of the Institute of Mathematics and later, in 1991, of the
Mathematics Teaching and Education Centre (integrated in the Institute of Mathematics). In 2008 I became the
director of this Centre.
I was one of the founders of the doctoral studies of the didactics of mathematics in Hungary. Since 1991 I have
been holding scientific co-operations (research and lectures) with several other European universities,
especially with the University of Salzburg, in which I also did teaching experiments in schools and at that
Throughout Eastern Europe there is concern for the many multi-cultural minorities in schools. These children
must be taught to read, write and speak a national language, and to integrate socially. Most important is to
teach all the children independent competence in learning.
We have found that this is best achieved through dialogues (directed class discussions): the first activity with
help of paper and pencil models (enactive level); later on of pictures and films (iconic level); and eventually of
mathematic symbols (symbolic level). The quality of discussion is found to improve successively of the
difficulty of the problems being discussed.
My colleagues and I engage in continuous interdisciplinary research with the emphasis on competence in
learning (Lernkompetenz).
I met Mr. Hannaford in 1999, and thereby learnt of the 1996-98 study he had inspired for the European Union.
I informed him of my Department's research, and I was subsequently invited to participate with him and Dr.
Khoury in the Qatar Foundation's 2006 Symposium.
As the Director of Mathematics Teaching and Education Centre, I am convinced that teaching mathematics
through discussion is essential in achieving competence in learning, in promoting social responsibility, and in
reducing potentials for violence everywhere. I fully endorse the aims of this event.

Professor Nancy Nagel, Lewis and Clark College, Oregon, USA.
My background in mathematics is in teaching graduate level courses to future and current teachers, primarily at
the elementary school level. My work has also focused on mathematics as problem solving (which, of course,
connects well with the theme of the conference). I am not a mathematician, but a teacher educator who has
taught courses in teaching elementary school mathematics for over 10 years. I have had in all thirty years'
experience as a teacher educator, elementary school teacher, researcher, and author. .My career has fostered
scholarship in real-world problem-solving, teacher education, the process of equitable and democratic
education, and mathematical education. Since arriving at Lewis & Clark in 1992, I have coordinated an
elementary cohort, coordinated the early childhood/elementary program, served as chair of teacher education
and as Associate Dean of the Graduate School. I am in the process of writing a book on "integrating
curriculum through service-learning," which focuses on community connections and "real" use of curriculum
and learning. I am editor of the journal 'Democracy and Education'.

Professor Dr Humam Bishara Ghassib
Born in Amman, Jordan on 27 April 1948. Educated at University of Manchester, UK, 1968-74: BSc Hons in
Physics, 1971; PhD, Theoretical Physics, 1974.
Deputy Secretary General (formerly, Director of Studies & Programs), Arab Thought Forum, and Advisor to
HRH Prince El Hassan bin Talal, 1999 to date. Professor of Physics, University of Jordan, 1986 to date.
Fulbright Senior Research Fellow, Cornell University, 1983-84. Chairman, Department of Physics, University
of Jordan, 1986-88. Dean of Research, 1990-94. Associate, [Abdul Salam] International Centre for Theoretical
Physics, Trieste, 1977-90; Editor-in-Chief: The Cultural Journal (Arabic), 1989-99; Dirasat (refereed research
journal, Arabic and English), 1990-94; Al Muntada (Journal of Arab Thought Forum, Arabic and English
editions), 1999 to date.
Awarded: Abdul Hameed Shoman Prize for Young Arab Scientists in Fundamental Sciences, Amman, 1986.
Al-Hussein Order of Merit for Distinguished Contribution, Amman: 2nd order, 1998; 1st order, 2000.
Member, New York Academy of Sciences, 1981; Jordan Academy of Arabic, 1984 - . Fellow, Third World
Academy of Sciences (TWAS), 1988 - .
Research Areas: low and ultralow temperature physics (theory); many-body theory; liquid 3He and 4He; 3He-
4He mixtures; other quantum fluids; thin films and low-dimensional systems; superfluidity; physics education;
history and philosophy of science; Arabic language; culture.
Mr Colin Hannaford:
I began to teach mathematics when I was thirty. I was never a mathematician. I became a soldier in the British
Army when aged seventeen. The basis of my training was in engineering, and this was so outstanding that I
may claim some skill in virtually every mechanical skill - beginning with blacksmithing! The Army paid to
send me to university, but it required only basic degrees. Soldiers do not usually need PhDs.
Given this rather unusual background, my good fortune as a teacher has been remarkable. Within three years of
receiving my certificate to teach, the most basic requirement, I was appointed a head of mathematics in one of
the official European Schools of the European Union.
This meant that I now worked with the best qualified, most experienced teachers of the European Union. I was
teaching generally intelligent multi-national pupils for the European Baccalaureate, a final examination of
many subjects, all at university entrance level.
This is an extremely difficult exam. As their teacher, I was virtually autonomous. I could choose to teach them
as I wished. After seven years I had made two important observations. My pupils were passing their
Baccalaureate with amongst the highest grades of all the twelve European Schools. This was what I aimed for.
Far more important was that I knew that very few really understood what they were doing. I also realised that
some in the middle years hated me intensely.
To learn why all three of these facts could be simultaneously true - and were true for other mathematics
teachers - took me on a ten year odyssey through Europe and America. I believe we can now explain why it is
our schools are not making all our children healthy - as we expect that they should - but make many of them
very sick indeed: some fatally - to themselves or to others. Mathematics should teach that differences of
opinion are natural, not threatening. It does not do this and the result is serious social fracture and dysfunction.

Dr. Gregory A. Hedger.
Dr. Hedger is in his second year as the Director of Qatar Academy. He began his education career as a teacher
in Minnesota, USA, which was followed by 18 years abroad in Romania, Indonesia, Pakistan, and the Cayman
Islands before coming to Qatar. Dr. Hedger completed an Ed.D. in Educational Policy and Administration
from the University of Minnesota in 2005. His family, which includes his wife Kirstin, and three daughters, are
with him in Qatar.

Michael Hitchman.
Born and schooled in London, Michael worked for nine years, as a Physical Education and Science teacher, in
a large comprehensive school in the UK. In 1989 he accepted a position at the prestigious Dubai College
(UAE) and so began his overseas educational career, which has spanned almost 20 years. Following spells in
China and Turkey Michael returned to the Gulf in 2006, as Head of Senior School at Qatar Academy. Married
with two children, he completed his MA in Education at Bath University in 2002.

Dr. Hani Q. Khoury
Professor of Mathematics and Chair of the Mathematics, Science, and Information Systems Department at
Mercer University's College of Continuing and Professional Studies, Georgia, USA. The grandson of a Greek
Orthodox Priest, Dr. Khoury was born in Nablus, Palestine, and came to the United States in 1983 at the age of
18. He earned a Bachelor of Arts degree in Mathematics and a Bachelor of Science degree in Systems and
Information Science in 1987, a Master of Science degree in Computer Science in 1989, and a Doctor of
Philosophy degree in Mathematics Education in 1995, all from Syracuse University, New York.
In 1993, Dr. Khoury was selected as a Chancellor's Advisor at Syracuse University. He served on the
American Friends Service Committee as a Third World Coalition committee member and a Disability Issues
subcommittee member (1988-1994). He also served as President of the Georgia Chapter of the American-Arab
Anti Discrimination Committee (2000-2001). Dr. Khoury received the Excellence in Teaching Award for the
year 2000 at Mercer University's School of Education and the Professor of the Year Award for the year 2008 at
Mercer's College of Continuing and Professional Studies. He has written several articles and has given
numerous presentations on the quest for justice and peace in the Middle East and on empowering people with
Dr. Khoury is a member of the task force sponsored by the Qatar Foundation in Doha, Qatar, and by UNESCO
charged with providing a forum for international scholars to explore the implications of their research for
practical educational endeavors. The series began in 2004 with a forum dedicated to the Art and Science
Partnership, and in 2006 the series explored Technology, Empowerment and Education. On March 12, 2007,
Dr. Khoury participated in a third conference addressing the Literacy Challenge in the Arab States. Currently
he is serving as a Governor's Teaching Fellow for the academic year 2008/2009 at the Institute of Higher
Education, University of Georgia in Athens, Georgia, USA.
Dr. Jerome R. Ravetz:
Born in Philadelphia, United States in 1929. He came to England as a Fulbright Scholar, and did his Ph.D. in
mathematics at Cambridge. Dr Ravetz is a leading authority on the social and methodological problems of
contemporary science. With Silvio Funtowicz, he created the NUSAP notational system for assessing the
uncertainty and quality of scientific information, and also the concept of Post-Normal Science, relevant when
'facts are uncertain, values in dispute, stakes high and decisions urgent'.
For many years he taught the History and Philosophy of Science at the University of Leeds. He has held
positions at Utrecht (Netherlands), Harvard, The Institute for Advanced Study (Princeton), California (Santa
Cruz), FuDan (Shanghai), EC. Joint Research Centre (Ispra, Italy), Texas (Dallas), and Carnegie Mellon. He is
currently an Associate Fellow at the James Martin Institute for Science and Civilization at the Saïd Business
School in the University of Oxford.
His earlier seminal work Scientific Knowledge and its Social Problems (Oxford U.P. 1971, Transaction 1996)
now has a smaller sequel, The No-Nonsense Guide to Science (New Internationalist 2006). His other
publications include a collection of essays, The Merger of Knowledge with Power (Mansell 1990), and
collaborations with Zia Sardar (Cyberfutures, Introducing Mathematics).
Selections from his recent work are found on the website and on his personal website Recent essays include 'Maturing contradictions of European Science', 'Global systems
failures', and 'Towards a non-violent discourse in science'.
Appendix F