The fundamental idea of the ICMI Study 13 is outlined as follows: Education in any social environment is influenced in many ways by the traditions of these environments. As a consequence the results of such education will naturally differ with different traditions in different environments. Indeed, this is necessary since one of the intentions of education is to support the traditional continuity of structure and function of a special environment.

On the other hand, today we are observing a growing interdependence between environments like regions, states, countries, and different cultural areas of the world. In many respects they have to rely on corresponding or equivalent standards of education, and differences can cause irritations.

In mathematics education also, taking an international and intercultural point of view, we face this split phenomenon of difference and correspondence, linked with the perpetual challenge to improve the quality of mathematics education. A study attempting a comparison between mathematics education in different traditions will be helpful to understand this phenomenon in detail and exploit it for the sake of mathematics education.

The Study Volume will reflect the structure of the conference in four sections of revised papers, integrating insights, results and implications from the comparative discussions. To achieve this revision and integration, section editors have initiated vivid interaction with and between authors of the four working groups. The editors (Leung, Lopez, Graf) expect the Volume to be published in the series of ICMI studies by Springer in spring 2005.