Over the last four years, since the last General Assembly of ICMI in Quebec, the HPM Study Group has continued to build on its earlier work and to develop its role of exploring, researching and promoting the relations between history and pedagogy of mathematics. Much has been achieved. A number of major international conferences have been held, twelve newsletters have been published and distributed to an ever-wider list of people around the world, books have appeared arising out of conferences and related activities, and continued progress has been made in working towards the research programme that will result in an ICMI study.
For the period 1992-1996, the HPM Advisory Board has consisted of
The concerns of the Study Group have been pursued through a major international HPM conference in each year of the quadrennium as follows:
The Montpellier conference, organised by Evelyne Barbin, Franioise Lalande and Yves Nouaze on behalf of IREM (the French Institutes of Research into Mathematics Education) was the first European Summer University on history and epistemology in mathematics education. Reports appeared in HPM Newsletter 30 (pp. 3-7). The Blumenau HPM conference, organised by Ubiratan D'Ambrosio, is reported in HPM Newsletter 33 (pp. 2-6). The Cairns HPM conference, organised by George Booker, is reported in HPM Newsletter 36 and (with photograph) in BSHM Newsletter 30 (pp.20-21). The Braga conference, organised by Eduardo Veloso,Maria Fernanda Estrada, Evelyne Barbin and John Fauvel, is the final conference of the quadrennium, (even though for reasons of the Spanish climate and European school year it is actually taking place after ICME Seville and thus after the next ICMI General Assembly), at which the HPM Chair for the forthcoming quadrennium will be elected.
In addition there have been a number of other conferences across the world in the area of history and pedagogy of mathematics, as the reports in each issue of the HPM Newsletter demonstrate. In particular, two international conferences on History in Mathematics Education (HIMED) have been organised by the British Society for the History of Mathematics: 1994: Winchester, UK, 28-31 March; 1996: Lancaster, UK, 12-14 April. Reports of these, and many other conferences of one day or more, appear both in the HPM Newsletter and the BSHM Newsletter.
The only formal sub-section of the Study Group is the Americas Section, whose chairs over the period have been V. Frederick Rickey and Charles V. Jones. It holds various meetings, notably in connection with the annual meeting of the National Council of Teachers of Mathematics (Seattle 1993, Indianapolis 1994, Boston 1995, San Diego 1996).
As is clear from the range of conferences held over the period in Europe, South America and elsewhere, the Study Group has been deeply involved in permeating and working with other organisations such as IREM and BSHM to further its overall aims.
A refereed selection of thirty of the talks given at the 1992 Quadrennial Meeting of HPM, in Toronto, together with HPM talks given at ICME-Quebec, have been published by the Mathematical Association of America in a volume edited by Ronald Calinger:
Ron Calinger (editor), Vita mathematica: historical research and integration with teaching, Washington DC: Mathematical Association of America, 1996. xii + 359 pp. ISBN 0-88385-097-4 The text on the back cover of this lavishly-designed book gives a fair summary of the content: 'This volume demonstrates that the history of mathematics is no longer tangential to the mathematics curriculum, but deserves a central role.'
Publications from the subsequent HPM meetings are under way also. The proceedings of the Blumenau meeting have already appeared, edited by Sergio Nobre, under the title Meeting of the International Study Group on the Relations between History and Pedagogy of Mathematics, HPM-Blumenau/Brazil 25-27 July 1994. This contains the full text of four of the plenary addresses, thirteen talks from the parallel sessions and six further communicati ons. The proceedings of the Cairns HMP conference are presently being edited for publication by George Booker.
Throughout this period the Newsletter has been edited by Profesor Victor J. Katz, University of the District of Columbia, USA. This has appeared regularly, three times a year, so twelve issues in all, nos. 27-38, have appeared between November 1992 and July 1996.
The HPM Newsletter fulfils a crucial role of informing and keeping in touch people throughout the world. For very many readers, the Newsletter is the main source of information about the activities of others in this field. To a considerable extent, HPM is its newsletter, and the role of its editor is therefore pivotal. We have been exceedingly fortunate to have had in Victor Katz an editor of superlative efficiency and powerful editorial skills who brought out the Newsletter with unfailing regularity, unperturbed by bringing out his highly acclaimed History of mathematics: an introduction (Harper-Collins, 1993) at the same time. Not the least of Victor's achievements over his period as editor is to have built up the panel of distributors so that there is now a very strong distribution network which serves also as a local focus for HPM activities and promotion. Having been appointed at the beginning of the previous quadrennium in 1988, that is, having now served an eight-year, 24 issue stint, Victor is giving up the editorship at Braga and applying his energies to fresh challenges. He is not abandoning HPM, but becoming chair of the Americas section. We are all very greatly in his debt.
Distribution of the HPM Newsletter throughout the world is through the kind services of 23 distributors, as follows:
The Study Group is greatly indebted to these distributors, and to their supporting institutions, who generally take responsibility for copying the newsletter, from masters supplied by the Editor, and distributing it by post and at meetings to interested people in their areas, as well as promoting the Study Group throughout their distribution areas.
For much of this period, the central production and distribution costs were generously met by the University of the District of Columbia. Financial pressures in 1995 meant this support could no longer be provided, so the 1500 people on the US mailing list are now asked to contribute some $10 per year towards the production and distribution costs. The rest of the world is currently unaffected by this, though it is not clear for how long local distributors will be able to continue various ad hoc distribution arrangements through the generosity of their organisations and institutions.
Further technological solutions are being pursued, and the BSHM Newsletter is now available on the World Wide Web.
Several individuals within HPM have been formulating and conducting research in different countries on the use of history of mathematics in mathematics education. Some of the results of this research have been communicated at HPM meetings, at meetings of other organisations, and through papers in the usual journals. One of the benefits of the considerable consolidation and growth of interest in HPM over the past four years is that a research programme is beginning to emerge, with contributions from many places over the globe, which is now about ready to be put into operation. This will involve a consolidated critical bibliography of work that has been done hitherto (over the last century, and increasingly since HPM became established in recent years), and a programme for developing a deeper understanding of the factors involved in the relations between history and pedagogy of mathematics, in different areas of mathematics, and with pupils and students at different stages and with different environments and backgrounds. One of the main challenges for HPM in the next quadrennium, besides the further wide promotion of interest in its area of concern, will be to work on the long-promised ICMI study, and report back by the end of the millennium.
John Fauvel, Chair
The Open University, Milton Keynes, UK