ICMI

Bulletin No. 49

December 2000

President Yoshikawa,

President Sugiyama,

Chairman Fujita,

Secretary Sawada,

Guests and Participants of the Ninth International Congress on Mathematical Education,

As the incoming President of the International Commission on Mathematical Instruction, it is my honor and privilege to welcome you to this important Congress, and to express the appreciation of all participants for the generous efforts of our Japanese hosts. Particular thanks are due to the International Program Committee, chaired by Professor Fujita, and the National Organizing Committee, chaired by Professor Sugiyama together with its Secretary, Professor Sawada, for their major organizational work, and to the Science Council of Japan, led by Rector Yoshikawa, for its generous support of the Congress.

This Congress represents two important and underdeveloped kinds of linkage. They are symbolized in the very name of the Congress. One is the strong connection between mathematics education on the one hand, and mathematics as a discipline on the other. The other is the international character of the Congress, which creates opportunities for building cross-cultural linkages among people concerned with educational practice and scholarship.

Mathematics as a discipline has a long history, emerging from many cultures. It is truly international, even universal, in character. Mathematicians throughout the world have a fundamentally common understanding of the nature of mathematics and of its central problems and methods. Research mathematicians working on a mathematical problem, be they in Africa, Asia, Australia, Europe, or the Americas, are part of a cohesive intellectual community that communicates fluently. Though mathematics is an enabling discipline for the other sciences, it has a theoretical core whose interest does not reside solely in these applications.

Mathematics education, in contrast, has a variable and culturally based character. This is certainly true of educational organization and practice. Education is conditioned by social goals and educational organization that vary widely in different countries. Educational research is both an applied social science and a multidisciplinary domain of theoretical scholarship. And it too is culturally influenced. So the international assemblage of educational practitioners and researchers at this congress is much more extraordinary and significant than the corresponding gatherings of mathematicians at the International Congresses of Mathematics.

Among organizations devoted to mathematics education, the International Commission on Mathematical Instruction (ICMI), the sponsoring organization of this Congress, is distinctive because of its close organizational and structural ties to the mathematics research community. One expression of this is that ICMI has historically been presided over by research mathematicians, including such figures as Felix Klein, Hans Freudenthal, and Marshall Stone. As strong and fruitful as this tie has been, it does not imply an automatically healthy and symbiotic relationship between the mathematics and mathematics education professional communities. Indeed, the great challenges now facing mathematics education around the world demand a much deeper and more sensitive involvement of disciplinary mathematicians than we now have, both in the work of educational improvement and in research on the nature of teaching and learning. There are many things that have impeded such 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. ICME-9 brings together people who know and understand different things, to learn from each other, and hopefully to foster collaboration.

Let me conclude with some observations about the central place of mathematics in the school curriculum. Along with language, mathematics has always been at the core of education in all civilized societies. Today the study of mathematics occupies many students for the entire twelve years or more of their public schooling. This preeminent place of mathematical study is being seriously questioned in some quarters. It places hard and exacting demands on students. Other subjects, in the social as well as natural sciences are making claims for a larger share of the curricular territory. Much of the skill traditionally conveyed by the study of mathematics is now considered by some people to be made obsolete because of the presence of modern computational technology.

Most people I know in mathematics and in mathematics education, myself included, feel deeply that this is a misguided and retrograde tendency. Yet we are challenged to articulate a compelling case for maintaining, and even strengthening, the study of mathematics in the schools. The traditional rationale has been a mixture of pragmatic, economic, social, intellectual, and cultural reasons. Pragmatic to learn the basic skills of arithmetic and of measurement, and the rudimentary geometric concepts and figures. Economic because of the quantitative literacy demanded by the rapidly evolving technological workplace. Social to provide the resources for responsible citizenship in a modern democracy. Intellectual since mathematics is the enabling discipline for all of science, and it offers fundamental tools of analysis, quantitative expression, and disciplined reasoning. Cultural because mathematics exposes students to some of the most subtle and sublime achievements of the human spirit.

Yet people can still question whether these arguments suffice to justify so many years of mathematical study. Who today will be doing significant arithmetic without a calculator? How many people will ever have occasion as adults to solve a quadratic equation? Even engineers have no need to prove that their mathematical methods work. Why are our cultural arguments for the study of mathematics so different from those advocating the study of ancient languages and history?

I believe that these questions have compelling answers. But the answers must be framed in new ways, and grounded in new conceptions of what a contemporary mathematics curriculum and learning goals must look like. Articulating that new rationale for, and conceptualization of the study of mathematics in the schools is an important challenge to all of us. Perhaps the participants at this congress can give some thought to this question.

With that, it is now my privilege, on behalf of the International Commission on Mathematical Instruction, to join with Secretary Sawada in declaring open this Ninth International Congress on Mathematics Education.

Hyman BassPresident of ICMI