Mathematics education in contrast has a variable and culturally based character, and this is certainly true of educational organization and practice. Educational research is both an applied social science and a multidisciplinary domain of theoretical scholarship.

Among organizations devoted to mathematics education, The International Commission on Mathematical Instruction (ICMI) is distinctive because of its close ties to the mathematics community. The great challenges now facing mathematics education around the world demand a deeper and more sensitive involvement of disciplinary mathematicians than we now have, both in the work of educational improvements and in research on the nature of teaching and learning.

This book constitutes the Proceedings of the Ninth International Conference on Mathematical Education (ICME9), which was held in Tokyo/Makuhari Japan, in July and August 2000. ICME9 brought together experts from 70 countries, working to understand the challenges of mathematics education including boundary crossing and collaboration, such as the need to reconcile language, epistemology, norms of evidence and, in general, all of the intellectual and attitudinal challenges that face multidisciplinary research and development.

The program for ICME9 reflects a truly international character and includes four distinguished regular lectures, 52 lectures, four national presentations and reports from current ICMI Studies and ICMI Affiliated Study Groups. The goal of the meeting was to offer presentations and learning on various aspects of mathematics educations; its research, experiences, materials, and information with special emphasis on achievements and trends thatarose in mathematics education during the period of 1996-2000, and that would make important contributions to mathematics education in the new century.