Towards better Regional Collaboration in Mathematics Education Alan J. Bishop, Professor of Education Faculty of Education, Monash University Clayton, Victoria 3168. ABSTRACT The idea of international collaboration in mathematics education has a long history and the International Commission for Mathematics Instruction (ICMI) carried out its first survey in 1912. Since then international collaboration has progressed largely at the level of information exchange via conferences, journal articles and occasional comparative research studies. ICMI held its large and latest four-year Congress in 1992, but increasingly it is holding other conferences of a regional nature. In April 1995 one such regional conference will be held at Monash University. This structure now makes regional collaboration much more feasible, and with the help of telecommunications technology, systematic collaboration between centres in neighbouring countries on a regular basis becomes a reality. The questions now are not so much to do with how can collaboration take place, but why, for what reasons, for what benefits, and to whom? What is the role of research in supporting these developments? This paper will present the background to, and explore some of these issues. The paper is also supporting a symposium entitled "Developing the Educational Collaboratory" proposed by Liddy Neville, Alan Bishop and Andrew Treloar. 1.Mathematics education - an international discipline Mathematics is known to be one of the most important subjects in the modern world. Linking as it does with every conceivable aspect of modern life - from computers to check-outs, from ergonomics to economics, from government forecasts to gambling, from weights and measures to weather prediction - the quality of mathematics teaching is of crucial concern to every country. This quality depends on many factors - on the teachers, and the other human resources available; on the books, learning materials, and test and assessment facilities; on the teaching and learning environment; and inevitably now, on the provision of calculator and computer resources. Mathematics education is a burgeoning field with challenges for all who work in it or with it. For those who work in it the main challenges concern how to develop the mathematical competence and understanding of all students within the given institutional and organisational constraints, and how to change those constraints to enable teaching to use the latest ideas from research. An international perspective on these issues enables a far wider range of strategies to be used. Mathematics education has had an international perspective for many years. The International Commission on Mathematical Instruction was first proposed in 1905 by the American mathematician David Eugene Smith. A formal proposal was approved by the fourth International Congress of Mathematics held in Rome in 1908, and ICMI's first president was Felix Klein the famous German mathematician. ICMI is still a very active body, is a sub-commission of IMU, which itself is a body of the International Council of Scientific Unions. At its first meetings, Australia was only deemed to be an 'associated country' but it is now a full member. One of ICMI's earliest efforts was the preparation of a report documenting the teaching practices in member countries. As Howson (1984) reports: Each participating country appointed a sub-commission to prepare national reports, often in many volumes, and the result was outstanding both in terms of quantity and quality. Thus, for example, the French report ran to five volumes and that of the U.S.A. to eleven. The British contributed only two volumes, but the first of these had over 600 pages! Certainly, nothing on the same scale had been attempted before, or has been attempted since. Moreover, not only did countries comment on their own systems, but, for example, as part of the German contribution G. Wolff (who attended ICME2 at Exeter in 1972 and ICME3 at Karlsruhe in 1976) wrote a fascinating account of secondary education in England, Der Mathematische Unterricht der Hoheren Knabenschulen Englands (Wolff, 1915), which still remains a model of a successful comparative case study. That its delayed publication should have taken place in 1915 when the two countries were locked in battle is just one further bewildering and poignant fact to be recorded from those years. (p77,78) Not only was there sharing of information, and a desire to find out more about practices in other countries, but there was also a strong motive concerned with trying to deal with the problems of mathematics education through international collaboration. Also interesting was the start of comparative research into mathematics education, an aspect which has grown recently through the work of the International Association for the Evaluation of Educational Achievement (IEA) which was established in 1960. This body has been responsible for two surveys of mathematical achievement, and the Third International Mathematics & Science Study (TIMSS) is well under way, involving more than 50 countries. These studies are enormous and expensive, but have strong support from both Governments and those research bodies which receive the funding to perform the testing and statistical analysis. These studies however have many critics - one of the most vocal being Hans Freudenthal (1975), a distinguished and widely respected mathematician and educator. The criticisms relate to every conceivable aspect of the research - the objectives, the test items, the language, the administration, the inadequacy of the surrounding contextual data etc. indeed to whether this kind of activity is research at all. Despite these criticisms, and the expressed wish of the 'leader' of the IEA movement, Torsten Husen, that these comparative studies should not develop into a horse-race, with tables of winners and losers, it is hard to avoid the thought that Governments continue to fund the studies precisely because they want to see where their country stands in the league tables. There is the inevitable flurry of media interest when any tables are revealed, and usually the lowly standing of some countries seems to gain prominence over the high standing of others! Generally Asian countries perform very well on these comparisons, but it is only recently that other research has tried to understand more about possible reasons (see for example Stigler et al 1990). The recent Handbook of Research on Mathematics Teaching and Learning (Grouws, 1992) has a whole chapter devoted to 'International studies of achievement in mathematics' and it is clear that these studies are now a significant part of the international scene in mathematics education. Whether they are a force for the encouragement of collaboration rather than just competition is however a moot point - although of course in order to compete, there must be a certain level of collaboration, even if only to agree on the rules. 2.International collaboration in research in mathematics education There are two different but related levels at which international collaboration is now taking place. The first is at the level of institutions and organisations like ICMI. This body now organises four-yearly International Congresses on Mathematics Education (ICME) around the world, with very detailed programmes and with many strands associated with research. ICMI itself has several sub-groups which also have a strong research focus - the International Group for the Psychology of Mathematics Education (PME), the International Study Group for the Relations between the History and Pedagogy of Mathematics, the International Organisation of Women and Mathematics Education, and the World Federation of National Mathematical Competitions. All these organisations have regular meetings and conferences, and research of various kinds is reported and discussed. At another level, there are international journals such as Educational Studies in Mathematics and the Journal of Research in Mathematics Education which although being a journal of the National Council of Teachers of Mathematics in USA has a strong international profile. The book market is also an important one for encouraging collaboration in research. These books and journals are increasingly referring to research topics and issues which transcend national boundaries by focussing directly on aspects of social, cultural and political context which take seriously into account the many differences between the educational experience of different learners. The social dimension generally has become an important focus for research in mathematics education (see Bishop, 1992), and recognises the important influence which many people and institutions, have on the mathematical education of the students. 3.Relationships between the researchers and the system In particular, this new focus for research is putting into the spotlight the relationship between the researcher and the education system. We can clearly see that as education becomes an increasingly significant political arena, so researchers cannot refrain from positioning themselves in that political arena. Research is increasingly being driven by political agendas - even in a subject like mathematics education, which many might erroneously consider to be a politically neutral subject. Documentation of recent national curriculum developments in mathematics such as those by Dowling & Noss (1990) and by Ellerton and Clements (1994) demonstrate vividly the involvement of many kinds of researchers in the political agendas of our times. It is no accident that a recent UNESCO publication produced by members of the PME group is entitled 'Significant Influences on Children's Learning of Mathematics' (Bishop et al, 1993) and over half of the book focuses on influences from society and from culture. Nor is it a mere coincidence that in 1990 a new research focus group began with the title 'Political Dimensions of Mathematics Education' (PDME, 1993). The researcher/system relationship is most obviously at stake in mathematics education over aspects such as mathematics curriculum and the assessment of students. However, other high profile aspects are teacher numbers and quality of training, in-service professional development, calculators and computers. Researchers in all those areas are acutely aware of the sensitivity of their relationship with the system over aspects such as whether the research can be funded, controls on the research findings, access by researchers to information and sources of data, and even the way the research process itself can be seen as an overt criticism of government or system policy, irrespective of its findings. Governments are notorious for offering funding and support for research into what they consider to be the important problems. They are less pleased about, and less keen to support, research which might be seen to raise problems that they would rather not know about. Research contracts in the UK concerning the National Curriculum contained clauses prohibiting publication before government approved screening, and also allowed government authorities full access to and inspection of, every piece of data obtained - even permitting total scrutiny of the researchers' offices if necessary. Thus we can see a growing interest in mathematics education at a social system level, which is being fostered by, and which is itself encouraging, collaboration between researchers and educators across national boundaries. We are learning much more about how languages, culture, societal values, economic situations, family values, etc are influencing the kind and the quality of mathematics learning. We are recognising the important similarities and differences between societies which affect mathematics education in those societies. 4.Regional collaboration in mathematics education From the perspective of 'regional collaboration', there are many important similarities and differences between the countries of our region, which we shall take to include South-East Asia, the Pacific region and Australasia. There are general issues of teaching styles, assessment procedures, exceptional learners, resource provision, languages, etc. which exist in every country. There are also more specific issues to do with, for example, rural disadvantaged learners, cultural and moral values, shortages of qualified teachers. Mathematics educators at all levels are trying to collaborate more and more in order to learn from each others' experiences and to share ideas about solutions to common problems. Groups such as the South East Asian Mathematics Society and the Mathematics Education Research Group of Australasia hold regular conferences. Individual countries hold many conferences and courses for mathematics teachers and educators, and the International Commission on Mathematics Instruction (ICMI) has held regional conferences in Japan and China. As a reflection of this growing interest in regional collaboration, April 1995 will see a significant conference take place at Monash University, with the title 'Regional Collaboration in Mathematics Education'. This first ICMI Regional Conference to be held in Australia, will have several unique features, the most important of which is that, reflecting the issues already referred to above, it will bring together people from three rather different communities - from mathematics and mathematics education, from governmental and non-governmental education agencies, and from business and industry. The aims of the conference are: * to address the issues, problems and mechanisms concerning regional collaboration in mathematics education, which exist in all regions of the world, * to demonstrate by actions before and during, the conference, processes by which such collaboration can be enhanced, * to produce recommendations for policy regarding regional developments in mathematics education. Thus far in the paper, the discussion has concerned those who work in the field of mathematics and their relationship with the education system. What of the other communities who will be involved in the conference? 5.Business and industry perspectives Enlarging the researcher/system issues referred to earlier, it is very clear that business and industry is having an increasingly significant influence on mathematics education in different countries in the region. As employees of school and university leavers, they have a keen interest in the mathematical preparation of students, as shown by their strong support for mathematical competencies in the debate over national curricula. This interest is particularly strong in the computer, engineering and telecommunications industries, which rely heavily on the mathematical expertise of their employees. In more general terms, industry continues to be involved with issues surrounding the mathematical literacy of the populace, and companies in the oil industry, for example, have funded significant projects, activities and indeed, internationally recognised Centres of Mathematics Education, to encourage the mathematical education of all students, and in all countries. Industry also develops material resources for mathematics education. Publishers have been in the forefront of this activity of course, and the learning materials industry has expanded considerably in the last thirty years, from a situation where one textbook sufficed, to today where everything from mathematics dictionaries to puzzles and games books are available to entice the learners, to arouse their interests, to challenge them, and of course to educate them. Calculators and computers now play a significant role in schools, colleges, and universities in many countries although there are still issues surrounding their most effective use in mathematics education. Moreover there are wide differences around the region particularly over the cost of resourcing schools and universities. However it is certain that educational computer use will grow across the region as the quality of programs improves and as teachers develop their skills in using calculators and computers. One issue for the ICMI conference is how to collaborate effectively in terms of that expertise. This will involve the computer business community and mathematics educators alike. Business interests also concern distance education, and as this sector grows in its ideas, and in its range of developments, so the whole telecommunications industry is becoming aware of the dramatic possibilities opening up for education in different regions of the world. Mathematics education at all levels is now being exported and imported through various products, and is a potential leader for educational innovation through distance activities. When allied to the increasing use of computers in mathematics education around the region the possibilities opening up are overwhelming. How educators react and respond to these possibilities will determine whether education will drive the developments or will be driven by them. 6Governmental and non-governmental education agencies. At the heart of many of the issues surrounding regional education collaboration lies the problem of resources, and the roles of governmental and non-governmental agencies in controlling and distributing their resources. This is a crucial area of focus for this conference and particularly offers the opportunity for those who shape resource provision, policy, and procedures, to meet with the mathematics education and business communities over issues concerning regional collaboration. Government agencies control the majority of educational funding in their countries, but in all countries in the region private education at all levels, is expanding, particularly in high demand subjects like mathematics. After-school programs are increasing, for example, and the private education 'industry' is beginning to develop regional and international links in ways which are important to know about, and to debate. Government is however not just in control of much educational funding, it also structures relationships with other countries, and inter-Government relationships are crucial determinants of much international educational development. From the perspective of mathematics education, there is little point in trying to pursue cooperative ventures if the necessary support is not present or is not forthcoming. Business developments in education are also likely to founder if governmental agencies are not involved in discussions of policy and planning. Non-government agencies, both national and international, are increasing their role in education, and we have seen a growing presence of such agencies as UNESCO, World Bank, Asian Development Bank etc., in the field of education. Increasingly, as the importance of mathematics education is realised in all countries, we find large development projects being funded in mathematics education specifically. Representatives from these agencies are being invited to the ICMI conference in order to engage them in relevant mathematics education issues. 8.Research consequences As mathematics educators grow in their confidence to look seriously at what happens in other countries, they are realising that there are important avenues for research to explore. Mathematics may be a unique subject because it is a subject taught in every country in the world. It is therefore an interesting vehicle to analyse systemic differences. Moreover the mathematics taught is recognisable everywhere. Whether, or why, this should be the case has been explored elsewhere (Bishop 1991) and is a continuing issue. However it is more important for this paper to recognise that * mathematics education researchers do not operate in a political or societal vacuum, * business, industry and governmental influences are significant in mathematics education, and need to be better understood, * comparative mathematics education research is primitive, still in its infancy, and needs structural development * regional collaboration between researchers will not only generate more knowledge about educational influences, but will also enhance international understanding, a crucial goal at the present time. References Bishop, A. J., Hart, K., Lerman S., and Nunes, T. (1993) Significant influences on children's learning of mathematics. Paris, France: UNESCO Bishop, A. J. (1992) 'International perspectives on research in mathematics education' in D. A. Grouws (Ed) Handbook of research on mathematics teaching and learning (pp 710- 723) New York: MacMillan Bishop, A. J. (1991) Mathematical enculturation: a cultural perspective on mathematics education. Dordrecht, Holland: Kluwer. Freudenthal, H. (1975) Pupils achievements internationally compared Education Studies in Mathematics, 6, 127-186. Grouws, D. A. (ed) (1991) Handbook of research on mathematics teaching and learning. New York: MacMillan. Howson, A. G. (1984) Seventy five years of the International Commission on Mathematical Instruction. Educational Studies in Mathematics 15, 75-93. Julie, C., Angelis, D., and Davis, Z (Eds) (1993) Political dimension of mathematics education 2: Curriculum reconstruction for society in transition. Cape Town: Maskew Miller Longman. Stigler, J. W., Lee S. Y. and Stevenson, H. W. (1990) Mathematical knowledge of Japanese, Chinese and American elementary school children. Reston, V.A.: National Council of Teachers of Mathematics.