The International Commission on Mathematical Instruction
Bulletin No. 48
Report by HPM
The International Study Group on the Relations between the
History and Pedagogy of Mathematics
HPM Activities 1996-2000
The period since the last General Assembly of ICMI in Seville has seen further developments in the increasingly widespread interest in the relation between history and pedagogy of mathematics. Articles in books, journals and conference proceedings have reported upon a number of efforts resulting in enlivening mathematics lessons through the history of mathematics, through anecdotes and old problems, through original sources and theatre, through sums and differences. The main focus of the kernel of HPM was the ICMI Study, chaired by John Fauvel and Jan van Maanen. The current state of the art about the relations between history and pedagogy of mathematics world wide is documented in the report of this Study, which will appear June 2000.
Structure of HPM
For the period 1996-2000, the HPM Advisory Board has consisted of
George Booker (Australia)
Jacques Borowczyk (France)
Gerard Buskes (USA), editor 1996-1999
Ubiratan D'Ambrosio (Brazil), former chair
Florence Fasanelli (USA), former chair
John Fauvel (UK), former chair
Gail FitzSimons (Australia)
Lucia Grugnetti (Italy)
Abdulcarimo Ismael (Mozambique)
Hans Niels Jahnke (Germany)
Charles V. Jones (USA)
Victor J. Katz (USA), Americas Section chair
Maasouma Kazim (Egypt)
Israel Kleiner (Canada)
Osamu Kota (Japan)
Jan van Maanen (Netherlands), chair
Mohini Mohamed (Malaysia)
Eduardo Veloso (Portugal)
Greisy Winicki Landman (Israel)
The 2000-2004 HPM chair will be elected in August 2000, during ICME-9.
In the last four years a number of major international conferences have been held to explore, communicate and share experiences in the integration of history in mathematics education.
1996: Braga, Portugal 24 - 30 July
ICME-8 satellite meeting of HPM, joint with the second European Summer University on history and epistemology in mathematical education. In this conference, which was held in the exquisite premises of the University of Minho at Braga, Eduardo Veloso, Maria Fernanda Estrada, Evelyne Barbin, John Fauvel and the local team brought together over 400 teachers and academics in a open and enthousiastic atmosphere.
1998: Luminy, France 20 - 25 April
ICMI Study conference on The role of the history of mathematics in the teaching and learning of mathematics. Invitational conference for 75 participants, organised by Jean-Luc Dorier, John Fauvel and Jan van Maanen. More about the ICMI Study below.
1998: Lorena, Brazil 26 -27 July
Conference organised by Sergio Nobre for the Brazilian Committee for the History of Mathematics, linking a national meeting for mathematics educators and the 5th Latin-American Congress of History of Science and Technology.
1999: Louvain-la-Neuve and Louvain, Belgium 15 - 21 July
Third European Summer University on history and epistemology in mathematical education, organised by Patrica Radelet, Dirk Janssens and Michel Roelens, with the support of HPM in the International Program Committee.
2000: Taipei, Taiwan 9 - 14 August
The ICME-9 satellite meeting of HPM will be welcomed by the Department of Mathematics of National Taiwan Normal University, Taipei. This conference, chaired by Wann-Sheng Horng and Jan van Maanen, will focus particularly on history and pedagogy east and west.
In addition there have been a number of other conferences across the world in the area of history and pedagogy of mathematics, notably in the tradition of the French IREMs (Institutes for Research of Mathematical Education), whose conference in Nantes, France (12 - 17 July 1997) resulted in a firm volume of proceedings (Contribution à une approche historique de l'enseignement des mathématiques), and in the long line started in 1990 by the British Society for the History of Mathematics, which organised another international HIMED (History in Mathematics EDucation) conference in Exeter, UK (18 - 20 April 2000). Conferences in the USA are discussed below.
The only formal sub-section of the Study Group is the Americas Section, whose chairs over the period have been V. Frederick Rickey, Charles V. Jones and presently Victor Katz. It holds various meetings, notably in connection with the annual meeting of the National Council of Teachers of Mathematics (Minneapolis 1997, in the form of a 'Conference Within a Conference' at Washington 1998 and in Chicago 2000). Important historical input was also given at the joint meetings of the American Mathematical Society and the Mathematical Association of America. Another development was the Institute in the History of Mathematics and its use in Teaching, co-directed by Victor Katz and Fred Rickey, and taught with the help of a team of colleagues on the campus of American University in Washington. In three successive years (June of 1995, 1996 and 1997) 80 faculty members in U.S. colleges and universities improved their knowledge and skills in the history of mathematics. This project, funded by the National Science Foundation, gathered high plaudits for its quality and success, and it has been continued since to great acclaim. An important feature of its success is that participants are encouraged to go away, apply the lessons, techniques, resources and skills they have learned, and report back to the following major MAA meeting.
The ICMI Study
Concerns throughout the international mathematics education community have over a period of years focused 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 by ICMI Executive Committee 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 world-wide. As with earlier ICMI Studies the Study about The role of the history of mathematics in the teaching and learning of mathematics fell into three parts:
The current Study 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, HPM Chair 1998-1992), 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 report of the Study, with contributions by 65 authors edited by John Fauvel and Jan van Maanen, History and Mathematics Education. The ICMI Study, will appear June 2000 with Kluwer Academic Publishers (Dordrecht, NL), ISBN 0-7923-6399-X, 456 pp.
- 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.
A refereed selection of the talks given at the 1996 Quadrennial Meeting of HPM, in Braga, will be published by the Mathematical Association of America in: Victor Katz (editor), Using History to Teach Mathematics: An International Perspective, Washington DC: Mathematical Association of America, announced for 2000.
The reports of the IREM conference in Nantes (1997) and the ICMI Study have already been discussed above.
Moreover some issues of journals appeared that were especially devoted to the theme of history in mathematics education, notably Mathematics in school vol. 26 no. 3 (1997) and 27 no. 4 (1998), and Mathematik lehren vol. 91 (December 1998)
A number of other research papers have appeared, many of which are abstracted in chapter 11 of the ICMI Study Volume.
After 22 issues (Nos. 17-38) of the HPM Newsletter edited by Victor Katz, Gerard Buskes took over in the summer of 1996, and edited six issues, the last one being No. 44 (August 1998). Various problems urged Gerard to step down as the editor in 1999; since that time the editorship is vacant. This is a serious drawback for HPM, since the Newsletter has always been the main uniting force in this informal group, which can work without money since - except for the U.S. - the regional distributors have support from their institutions in order to print and distribute the issues. Active steps are under way in order to restore the Newsletter as a mirror and focus of HPM's activities; a number of possibilities are currently being investigated.
As the report of the ICMI Study shows, through its articles and through its extensive bibliography, research into the history of mathematics in relation to mathematics education matures. A research methodology is taking shape, and it is tested and further developed in many smaller and larger studies. The results give rise to optimism and critical thinking; optimism since in specific situations history seems to improve the quality of mathematical education; critical thinking since many problems are still unsolved. But that seems to be the spirit of any living science, that there are positive results and many unsolved problems. HPM will go on to flourish in the next quadrennium.
Jan van Maanen, Chair
University of Groningen, Department of Mathematics
P.O. Box 800, 9700 AV Groningen, The Netherlands