6th European Summer University Epistemology and History in Mathematical Education.
Vienne (Autriche), 1923 juillet 2010
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The initiative of organizing a Summer University (SU) on the History and Epistemology in Mathematics Education belongs to the French Mathematics Education community, in the early 1980’s. From those meetings emerged the organization of a SU on a European scale, as the European Summer University (ESU) on the History and Epistemology in Mathematics Education, starting in 1993. Since then, ESU was successfully organized in 1996, 1999, 2004 and 2007 in different places in Europe1. By now, it has been established into one of the main international activities of the HPM Group, which  from 2010 onwards  will be organized every four years, so that every two years there will take place at least one major international meeting of the Group; namely, ESU and the HPM Satellite Meeting of ICME.
Aim and focus of the ESU
The ESU mainly aims

to provide a forum for presenting research in mathematics education and innovative teaching methods based on a historical, epistemological and cultural approach to mathematics and their teaching, with emphasis on actual implementation,

to give the opportunity to mathematics teachers, educators and researchers to share their teaching ideas and classroom experience related to this perspective,

in this way, to motivate further collaboration along these lines, among members of the mathematics education community in Europe and beyond, attempting to reveal the following aspects of mathematics:

Mathematics should be conceived as a human intellectual enterprise with a long history, a vivid present and an as yet unforeseen future;

Although its “polished” products form that part of mathematical knowledge that can be communicated, criticized (in order to be finally accepted or rejected) and serve as the basis for new work, the process of “doing mathematics” is equally important, especially from a didactical point of view;

Hence, the meaning of mathematical knowledge is determined, not only by the circumstances in which it becomes a deductively structured theory, but also by the procedure that originally led, or may lead to it and which is indispensable for its understanding. Therefore, learning mathematics includes the understanding of implicit motivations, the sensemaking actions and the reflective processes, which are aimed at the construction of meaning; hence, teaching mathematics should include the opportunity given to students to “do mathematics”;

This conception of mathematics should be, not only the core of the teaching of mathematics, but also the image of mathematics spread to the outside world.

In this connection, putting emphasis on historical and epistemological issues constitutes a possible natural way for exposing mathematics in the making that may lead to a better understanding of specific parts of mathematics and to a deeper awareness of what mathematics as a whole really is. This is important for mathematics education, helping to realize that:

Mathematics is the result of contributions from many different cultures;

Mathematics has been in constant dialogue with other sciences, arts and technics;

Mathematics has been a constant force of scientific, technical, artistic and social development;

The philosophy of mathematics has evolved through the centuries;

The teaching of mathematics has developed through the ages; and in this way, to improve the learning of mathematics and stimulate students’ interest to it;
This helps to improve mathematics education at all levels, at the same time, however, realizing that although mathematics is central to our modern society and a mathematically literate citizenry is essential to a country’s vitality, it is not the sole subject worth studying. It is the harmony of mathematics with other intellectual and cultural pursuits that makes the subject interesting, meaningful and worthwhile. In this wider context, history and epistemology of mathematics have a yet more important role to play in providing a fuller education of the community. This is most important, especially today that many countries are concerned about the level of mathematics their students learn and about their decreasing interest in mathematics at a time when the need for both technical skills and a wider education is rising.