Does history of mathematics have a role in mathematics education?  The tenth ICMI Study was conceived in the early 1990s in order to tease out the different aspects of this question, as the endeavours of ICMI's affiliated study group HPM (International Study Group on the Relations between History and Pedagogy of Mathematics) encouraged and reflected a climate of greater international interest in the value of history of mathematics for mathematics educators, teachers and learners.  Concerns throughout the international mathematics education community began to focus on such issues as the many different ways in which history of mathematics might be useful, on scientific studies of its effectiveness as a classroom resource, and on the political process of spreading awareness of these benefits through curriculum objectives and design.  It was judged that an ICMI Study would be a good way of bringing discussions of these issues together and broadcasting the results, with benefits, it is to be hoped, to mathematics instruction worldwide.

ICMI Studies typically fall into three parts: a widely distributed Discussion Document to identify the key issues and themes of the study; a Study Conference where the issues are discussed in greater depth; and a Study Volume bringing together the work of the Study so as to make a permanent contribution to the field.  ICMI Study 10 has followed this pattern.

The Discussion Document was drawn up by the two people invited by ICMI to co-chair the Study, John Fauvel (Open University, UK; HPM chair 1992-1996) and Jan van Maanen (University of Groningen, Netherlands; HPM chair 1996-2000), with the assistance of the leading scholars who formed the International Programme Committee: Abraham Arcavi (Israel), Evelyne Barbin (France), Jean-Luc Dorier (France), Florence Fasanelli (US), Alejandro Garciadiego (Mexico), Ewa Lakoma (Poland), Mogens Niss (Denmark) and Man-Keung Siu (Hong Kong).  The Discussion Document was widely published, in for example the ICMI Bulletin 42 (June 1997), 9-16, and was translated into several other languages including French, Greek and Italian.  From the responses and from other contacts, some eighty scholars were invited to a Study Conference in the spring of 1998, an invitation which in the event between sixty and seventy were able to accept.

The Study Conference took place in the south of France, at the splendid country retreat of the French Mathematical Society, CIRM Luminy (near Marseille), from 20 to 25 April 1998.  Local organisation was in the hands of Jean-Luc Dorier (University of Grenoble).  The scholars attending were from a variety of backgrounds: mathematics educators, teachers, mathematicians, historians of mathematics, educational administrators and others. This rich mix of skills and experiences enabled many fruitful dialogues and contributions to the developing study.

The means by which the Study was advanced, through the mechanism of the Conference, is worth description and comment.  Most participants in the Conference had submitted papers, either freshly written or recent position papers, for the others to read and discuss, and several studies were made available by scholars not able to attend the meeting.  These, together with whatever personal qualities and experiences each participant was bringing to the Conference, formed the basis for the work.  Apart from a number of plenary and special sessions, the bulk of the Conference's work was done through eleven working groups, corresponding, in the event, to the eleven chapters of the Study Volume.  Each participant belonged to two groups, one meeting in the mornings and one in the afternoons.  Each group was led by a Convenor, responsible for co-ordinating the group?s activities and playing a major part in the editorial activity leading to the eventual chapters of the book.  Each group's work continued for several months after the Conference, with almost everyone participating fully in writing, critical reading, bibliographical and other editorial activities.

This way of group working for a sustained period towards the production of a book chapter was a fresh experience to many participants, since the pattern of individual responsibility for separate papers is a more common feature of such meetings and book productions.  In this instance the participants proved remarkably adept at using the new structures to come up with valuable contributions to the development of the field, all the more valuable for their being the results of consensual discussions and hard-written contributions, which are presently being edited and designed into the Study Book.

The Study Volume which is presently taking shape, and will be handed over to Kluwer shortly for publication at ICME-9 in August, has several functions, namely to

• survey and assess the present state of the whole field;
• provide a resource for teachers and researchers, and for those involved with curriculum development;
• indicate lines of future research activity;
• give guidance and information to policy-makers about issues relating to the use of history in pedagogy.

Part 1   Social and Cultural Framework
Chapter 1 The political context
Convenor: Florence Fasanelli; with Abraham Arcavi, Otto Bekken, Circe Mary Silva da Silva Dynnikov, Fulvia Furinghetti, Lucia Grugnetti, Jean-Pierre Kahane, Manfred Kronfellner, Lesley Jones, Anne Michel-Pajus, Mogens Niss, João Pitombeira de Carvalho, Yannis Thomaidis, Constantinos Tzanakis

Chapter 2  Philosophical, multicultural and interdisciplinary issues
Convenor: Lucia Grugnetti; with Jaime Carvalho e Silva, Coralie Daniel, Miguel de Guzmán, Hélène Gispert, Abdulcarimo Ismael, Marta Menghini, George Philippou. Luis Radford, Leo Rogers, Ernesto Rottoli, Daina Taimina, Wendy Troy, Carlos Vasco

Chapter 3  Integrating history: some perspectives
Convenor: Evelyne Barbin; with Giorgio Bagni, Lucia Grugnetti, Manfred Kronfellner, Ewa Lakoma and Marta Menghini

Part 2   Student Framework
Chapter 4  History of mathematics for trainee teachers
Convenor: Gert Schubring; with Éliane Cousquer, Chun-Ip Fung, Abdellah El Idrissi, Hélène Gispert, Torkil Heiede, Abdulcarimo Ismael, Niels H. Jahnke, David Lingard, Sergio Nobre, George Philippou, Chris Weeks

Chapter 5  The historical formation of mathematical thinking and the contemporary student understanding of mathematics
Convenor: Luis Radford; with Maria Bartolini Bussi, Otto Bekken, Paolo Boero, Jean-Luc Dorier, Victor Katz, Leo Rogers, Anna Sierpinska, Carlos Vasco

Chapter 6  Use of history in support of diverse educational requirements-opportunities for change
Convenor: Karen Dee Michalowicz; with Coralie Daniel, Gail FitzSimons, Maria Victoria Ponza, Wendy Troy

Part 3   Classroom Framework
Chapter 7  Analytical survey of ways of integrating history of mathematics in the classroom
Convenors: Constantinos Tzanakis and Abraham Arcavi; with Carlos Correia de Sa, Masimo Isoda, Chi-Kai Lit, Mogens Niss, João Pitombeira de Carvalho, Man-Keung Siu

Chapter 8  Analysis and consideration of using original sources
Convenor: Niels Jahnke; with Abraham Arcavi, Evelyne Barbin, Otto Bekken, Circe Dynikov, Fulvia Furinghetti, Abdellah El Idrissi, Chris Weeks

Chapter 9  Historical support for particular subjects
Convenor: Man-Keung Siu; with Georgio Bagni, Carlos Correia de Sa, Gail FitzSimons, Chun Ip Fung, Torkil Heiede, Wann-Sheng Horng, Victor Katz, Manfred Kronfellner, Marysa Krysinska, Ewa Lakoma, David Lingard, João Pitombeira de Carvalho, Michel Rodriguez, Maggy Schneider, Constantinos Tzanakis, Dian Zhou Zhang

Part 4  Resource Framework
Chapter 10  Multimedia and other resources
Convenor: Ryo Nagaoka; with Maria Bartolini Bussi, Glen Van Brummelen, Masami Isoda, Jan van Maanen, Karen Dee Michalowicz, Maria Victoria Ponza

Chapter 11  Bibliographic resources
Convenor: John Fauvel; with Éliane Cousquer, Abdellah El Idrissi, Lit Chi Kai, Anne Michel-Pajus, Sergio Nobre, Gert Schubring, Harm Jan Smid.
 

John Fauvel, Co-chair of the Study
Faculty of Mathematics, Open University
Milton Keynes M7 6AA, UK
j.g.fauvel@open.ac.uk

Jan van Maanen, Co-chair of the Study
University of Groningen, Departmnent of Mathematics
PO Box 800, 9700 AV Groningen, Netherlands
j.a.maanen@math.rug.nl

Participants to the ICMI Study on History in Mathematics Education
Picture taken at the International Center for Mathematical Meetings
(Centre international de rencontres mathématiques - CIRM)
located on the Luminy university campus, in a wonderful "Provençale" surroundings