ICME8

8th International Congress on
Mathematical Education

SCIENTIFIC PROGRAM

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Index

Plenary Lectures

DE GUZMAN, Miguel (Spain)

"On the role of the mathematician in Mathematics Education"

Mathematical education is a rather complex task. The different groups which constitute the mathematical community have to assume a joint responsibility and to collaborate together in order to face its many difficult problems with efficiency. In this contribution we shall examine in particular those problems an those tasks in which the intervention of the sub community of mathematicians would be most welcome, since they are the ones who, by their type of preparation and by their experience, can afford the right light and perspective. We shall try to detect the obstacles in today's structure of the mathematical community which counteract an adequate collaboration with other groups within the mathematical community.

FREIRE, Paolo (Brazil)

"Social-philosophical aspects of mathematics education"

SIERPINSKA, Anna (Canada)

"Whither mathematics education?"

The title of this talk is meant to evoke Morris Kline's deliberations on the foundations of mathematics expounded in his book "Mathematics, the loss of certainty", in which one of the chapters bears a similar name. Kline's book discusses the mathematicians' concerns about the consistency of their theories, the sources of their convictions, the respective roles of intuition and logic. But mathematicians seem to nurture these concerns only on week-ends. On week-days they proceed with confidence and faith with their research, and most of their papers do not reflect their doubts about the certainty of the foundations upon which they have laid their results. How different is the situation for researchers in mathematics education? Why is it so that each research reporting mathematics education must start with an exposition of the theoretical framework underlying it? What are the mathematics educators' concerns about the foundations of their discipline? Is there such a discipline? If there is, in what sense can one speak about its foundations?

TALL, David (UK)

"Information Technology and Mathematics Education: Enthusiasms, Possibilities and Realities"

This talk addresses critical issues in the use of information technology in Mathematics Education. It will consider developments of enthusiastic researchers using technology to teach mathematics at various ages, the possible gains shown by this research and the realities of what might be achieved on a wider scale.

International Roundtable

"Mathematics Teachers as decision makers: changes and challenges"

Moderator: Alan Bishop (Australia)
Participants: Gail Burrill (USA), Ruhama Even (Israel), Francisco Hernan (Spain), Maria Salett (Brazil), Thang Ruifen (China)

Regular Lectures

ABRANTES, Paulo (Portugal)

"Project work as a component of the mathematics curriculum"

Current concerns about competencies that school mathematics should develop and belifs about relations between learning and motivation support the idea that project work can play a unique role in the students' mathematical education. Curricular innovations also give contributions to discuss ways to integrate project workin the mathematics curriculum.

ARBOLEDA, Luis Carlos (Colombia)

"The conceptions of Maurice Frechet on mathematics and experience"

We will analyze the philosophical and educational ideas of one of the founders of the theory of abstract spaces, general topology and functional analysis, etc. and we will show relations with certain social epistemology of mathematics and with the social-constructivist approach of mathematics education.

ARTIGUE, Michele (France)

"Teaching and learning processes in elemental analysis"

Didactical research developed around the conceptual field of elementary analysis provides us with efficient means for understanding both students' difficulties and the failure of traditional teaching strategies. In the first part of the lecture we present its main results in a synthetic way. Then, we address the fudamental issue of action on educational systems. We show the limits of the epistemological and cognitive approaches mainly used in didactical research in this area, for this purpose and stress the risks of rough transposition of research experimental tools to the educational world.

BALBUENA, Luis (Spain)

"Innovation in Mathematics Education"

We will analyze the existing ideas about the concept of innovation. The classroom is one of the places where any teacher, who wants to do a better qualitative job, may carry out new experimentations. But it seems necessary to clarify many concepts and to give teachers some guides so they know (and become concious) about the criteria of quality concerning their innovative work. Several concrete experiences will be presented.

BARTOLINI-BUSSI, Maria G. (Italy)

"Drawing instruments: historical and didactical issues"

A drawing instrument is a plane articulated system, whose degree of freedom is one (during the motion, the points of the links draws algebraic curves). Drawing instruments have a long history both inside and outside geometry. They constitute a field of experience for geometrical activity in the research project Mathematical Machines for secondary school.

BENDER, Peter (Germany)

"Basic Images and Ways of Understanding of Mathematical Concepts for all Grades"

To primary students, as well as to working mathematicians, mathematical concepts are not mere definitions, but they consist of individual intuitions. These intuitions are formed in processes of imagination and comprehension, closely depending on each other. The conception of basic images and ways of understanding can help the teacher to create, together with the students, commonly shared kernels of mathematical concepts.

BORWEIN, Jonathan (Canada)

"Virtual Research: The Changing Face of Mathematics"

I aim to illustrate the radical impact that the computer -with the Internet- is having on mathematics and the way mathematicians do mathematics now and in the near future.

BROUSSEAU, Guy (France)

"The unbalanced conditions of the didactical system"

CAMPBELL, Patricia F. (USA)

"Transforming mathematics instruction in every elementary classroom: Using research as a basis for effective school practice"

Research on mathematics teaching and learning may support school-based professional development. This session describes how a constructivist perspective was used to improve the quality of mathematics content and pedagogy in every classroom of schools enrolling children of diverse enthnicities and languages. Growth in student achievement and teacher change will be characterized.

COOB, Paul (USA)

"Supporting young children's development of mathematical power"

This presentation focuses on exemplary teacher's proactive role in supporting her six-year-old students' mathematical growth. Particular attention is given to how the teacher communicated to her students what she valued mathematically, and schemes used to symbolize students' explanations and solutions. Excerpts from the classroom will be used as illustrations.

COONEY, Thomas J. (USA)

"Conceptualizing the professional development of teachers"

A rationale and theoretical perspectives for conceptualizing teachers' professional development will be presented. Research from longitudinal studies involving secondary teachers as they progress through their preservice program and into their first year of teaching will be discussed along with specific activities intended to enhance their development.

DALMASSO, Juan Carlos (Argentina)

"Olimpiada Matem tica Argentina: past, present and future"

DOUADY, Adrien (France)

"Seeing and reasonning in parameter spaces"

Often a problem boils down to geometry in the space where the solutions are to be found. We will show how this works in the two following problems:
1)Given u, v, w real numbers with u<v, w<v, can one find a monic quartic polynomial f with critical values u, v, w?. Is f unique up to a change of variable x--> x+p?
2)Given an arc of curve A, tangent at both ends to a line L, can one move a straight line D in the plane and bring it back to its position with orientation reversed without having D tangent to A at any time?
This problem leads to topology in a Moebius strip. The answer depends on A.

D'AMBROSIO, Ubiratan (Brazil)

"Ethnomathematics: where does it come from and where does it go?"

The history and geography of human behavior allows for us to have a new look into the emergence of mathematical ideas in different cultural environments. With this background, we can develop a conceptual framework for ethnomathematics. Scenarios of the future can lead to considerations about the next steps of the ethnomathematics movement.

DOERFLER, Willibald (Austria)

"Means for Meaning"

Three potential sources from which students could derive meaning and understanding are presented: (i) Mathematical structures viewed as protocols of processes and actions; (ii) Thinking by prototypes for mathematical concepts. (iii) Re-interpreting the mathematical discourse: we speak (and think) as if there were specific objects with the ascribed properties and relations though we only can access so-called representations and verbal descriptions (metaphoric use of the word "object").

ERNEST, Paul (UK)

"Social Constructivism as a Philosophy of Mathematics"

Social constructivism as a philosophy of mathematics is concerned with the genesis and warranting of mathematical knowledge. These processes take place both in the contexts of research mathematics and in the contexts of schooling, where they concern learning and assessment. A theoretical account of these processes situated in human practices will be given, based on the work of Lakatos and Wittgenstein. The resulting theory might be termed a post-modernist philosophy of mathematics, since it dethrones logic as the foundation of mathematical knowledge in favour of decentred human practices and context-bound warranting conversations. Attention will also be devoted to the relations between the philosophy of mathematics and mathematics education. The fact that developments in the philosophy of mathematics and corresponding informal conceptions have important outcomes for mathematics education is widely noted. What is less remarked is that issues of learning and assessment have significant implications, for the discipline of mathematics and for its philosophy, at least from social constructivist and fallibilist perspectives. This will be discussed, together with other relevant issues.

FORTUNY, Josep M. (Spain)

"Range of Abilities. Learning and Assessing Geometrical Knowledge in Environmental Context"

We tackle the complex problem of skill's processes in L & A and present a brief historic perspective about research approaches (factorial, conceptual, structural, hierarchical, degrees of acquisition, and cognitive range of abilities). We focus on the design of the learning environment which enhances the development of high order abilities, and on the continuous improvement and adaptation to diversity.

FUJITA, Hiroshi (Japan)

"High lights and shadows of recent Japanese curriculum for secondary schools"

The current Japanese national curricula have been put in force in 1961 for the senior high schools. Its part for SHS mathematics is characterized by double-focused targets (mathematical literacy and mathematical thinking), the Core-Options structure, and introduction of computers. Various difficulties in implementation have come up, while recently we are concerned with "Crisis of mathematics education", of which a main symptom is students' disinclination for mathematics and science.

GALBRAITH, Peter (Australia)

"Issues in Assessment: a never ending story"

This talk does not concern itself with aspects such as instrument design, or with how to make techniques or systems work better. Rather it identifies and elaborates points of debate at technical, practical and political levels that make assessment in mathematics at once an important, a stimulating, and a controversial subject.

GARFUNKEL, Sol (USA)

"Applications reform: a brief history in time.

This presentation will give an historical perspective of the current reform movement in mathematics education from an international perspective. The focus will be on the inclusion of applications of mathematics, the introduction of mathematical modeling, and of contextual approaches to curriculum development at both the secondary and tertiary levels.

GAULIN, Claude (Canada)

"Difficulties and challenges in the implementation of "problem solving" in school mathematics curricula"

Since fifteen years, there has been an increasing international trend to emphasize "problem solving" in school mathematics curricula. What major difficulties have been observed in its implementation? What are the new challenges for research on problem solving? These questions will be discussed in the light of an international survey conducted recently.

GERDES, Paulus (Mozambique)

"Culture and mathematics education in (southern) Africa"

GJONE, Gunnar (Norway)

"A new role for curriculum documents - from inspiration to production plans?"

In many countries new educational thoughts have emerged. Education and research have been increasingly influenced by economic considerations. Education clearly has implications for economic growth, but only in recent years have the models of management i production been adopted for education. We will discuss how curriculum documents reflect this development.

GU, Lingyuan (China)

"An experiment in Qingpu - A report on Math Education Reform of the Contemporary Standard in China"

From the year 1977 to 1992, we developed an experiment on a large scale in education reform in Qingpu county (regarded as an epitome of then China) and made the qualified rate in maths by all county middle school students go up from 16% to 85% and more. The State Education Commission has defined it as the important achievements in basic education reform and decide to spread it out all over the country. The report briefly introduces the unique system of experiment methods suitable for teachers in group and the experiment results of teaching principles and strategy etc. to let all students study efficiently.

HART, Kath (UK)

"What responsability do researchers have to mathematics teachers and children?"

In many countries there is little "Mathematics Education Research". Repeatedly we are told that it has little influence on what happens in the classroom. Perhaps this is because it is insufficiently relevant to the classroom non-generalisable and liable to concerned with theory building.

HOWSON, Geoffrey (UK)

"Mathematics and Commonsense"

What are the relations between mathematics and commonsense? To what extent is it possible to teach mathematics as commonsense and what are the dangers inherent in such an approach?

KEITEL, Christine (Germany)

"Teaching maths anxiety - A circulus of aversion to mathematics with teachers and students"

The way mathematics is taught in study courses for teachers at university level negatively determine perceptions of mathematics and mathematics education and the kind of "transmission" still typical for high school mathematics. Based on research about the social view of mathematics held by teacher students for all school types which were gained by questionnaires at the beginning of university studies, i.e. perceptions mainly determined by school experiences, and later compared with views developed during university at the end of their undergraduate studies, it will be discussed how teachers transform their negative experiences with teaching methods at high school and university explicitly and implicitly into conceptions of aversion or avoidance of mathematics with students which reversely "bequeath" maths anxiety.

KIERAN, Carolyn (Canada)

"The changing face of school algebra"

In the past, school algebra has been viewed chiefly as generalized arithmetic. However, recent attempts to enrich its content by including, for example, problem solving, functional concepts, modeling, and pattern generalization, as well as the use of the computer to encourage algebraic thinking, have all played a role in redefining what we are coming to mean by school algebra.

KIRCHGRABER, Urs (Switzerland)

"On some aspects in the teaching of mathematics at secondary schools in Switzerland"

We briefly describe some specific features of the Swiss secondary school system (upper gymnasium) and we discuss a number of recently developed new tools for teaching under-graduate mathematics.

KRAINER, Konrad (Austria)

"Some considerations on problem and perspectives of mathematics teacher inservice education"

The increasing complexity of discussion in mathematics education changes our view on teacher education and on professional teaching. There are more and more international reports about involving (practicing and prospective) mathematics teachers into research projects and integrating research components into teacher education courses. The self-critical investigation of a teacher into his own teaching will be illustrated.

LANGE, Jan de (Netherlands)

"Real Problems with Real World Mathematics"

We do need real problems, and not whimsical ones or artificial or dressed up problems for real world math education. But makes a problem a good problem? that depends largely on the purpose of the problem, the age of the students, and the goals of the curriculum. We don't need real problems, but get them anyway, when teaching real world mathematics. There are many obstacles. Teachers feel insecure, need more mathematical background. Assessment designers feel not very confident. Mathematicians don't recognise the mathematics, let alone some structure. Parents feel unable to help their children. Both kind of problems will be addressed from experiences in different countries.

LEDER, Gilah (Australia)

"Mathematics Education and Gender Issues"

Critical developments in research on mathematics and gender are traced in this session: from early work on recording differences between males and females in performance and participation in mathematics to more recent feminist perspectives which argue that equity for females requires a reevaluation of current social structures, popular values and norms.

LUELMO, M. Jesus (Spain)

"Gender and Mathematics: an spanish point of view"

MOORE, David S. (USA)

"New Pedagogy and New Content: The Case of Statistics"

Teachers of mathematics at all levels are being urged to adopt a new pedagogy that emphasizes active learning and places more emphasis on group work and communication of results. The call for reform often includes a call to revise our learning objectives to, for example, emphasize flexible problem-solving skills. In statistics, changes in the field itself, driven by technology and professional practice, have moved the content of beginning instruction somewhat away from mathematics toward experience with data. The interaction between these trends has led to rapid change in statistics instruction. This talk will review current trends in statistics teaching and attempt to describe the lessons learned.

NESHER, Pearla (Israel)

"School stereotype word problems and the open nature of applications"

A dilemma is presented to math educators: is problem solving teachable? In most cases, the student learns how to solve problems by working on a variety of examples. Is there a way to teach this proficiency explicitly and in a more articulate way? Findings from cognitive psychology suggest that one should uncover the scheme underlying the problem and that the basic general schemes could be directly taught. Empirical findings will also be presented.

OSTA, Iman (Lebanon)

"3D Geometry learning with computers"

Progress in the graphic capabilities of computer during the last decade makes it a potential useful tool for many educators, especially in teaching geometry. Already, many "Computer-Based Interactive Environments" for learning geometry were developed during the last few years, most of which aiming at teaching plane geometry. Relatively, very few are those dedicated to teaching 3D geometry, despite the valuable possibilities offered by computers for the manipulation of 3D objects. Based on a didactical situation designed for learning 3D geometry concepts using a computer software, we attempt in this lecture to analyse the peculiarities of 3D vs. 2D geometry learning, using Computer as a medium of knowledge representation.

OTEIZA, Fidel (Chile)

"Mathematics in context: an integrated approach for the development of the curriculum"

PAPASTAVRIDIS, Stavros G. (Greece)

"Assessing the effectiveness of teaching applications of mathematics"

PEREZ FERNANDEZ, Javier (Spain)

"Symbol manipulators in Mathematical Instruction"

Symbol manipulators can and must play an important role in mathematics teaching. With adequate planning they can assist in bettering understanding, studying in depth numerous concepts, be a valuable educational instrument in problem solving and influence curriculum planning in terms of content, selection and order. Their use must be placed within what is known as "experiental mathematics teaching" and must not be hidden in activities aimed at learning as a set of fixed "symbol manipulators" to resolve determined routine exercises. The software in question has been selected on a basis of characteristics accumulated from studies, from students and from other available sources. Alongside an overview of its advantages and inconveniences in relation to its educative tasks, the presentation will incorporate activities directed towards secondary school and university students.

PUIG, Luis (Spain)

"What I have learnt about problem solving from history and research"

There is a wealth of possible worlds of problem solving. Heuristics is the study of one of such worlds. The method of analysis and synthesis, from Pappus through Ibn al-Haytham to Lakatos, has been endowed with the power of leading both the search of solutions and the generation of new problems.

QIU, Zonghu (China)

"Mathematics competitions in China - success and deficiency"

In this talk the activities generated by mathematics competitions in China will be detailed. The influence of mathematics competitions into mathematical education will be examined... and the problems arising when paying too much attention to the mathematics competitions will be discussed.

RICO, Luis (Spain)

"Doctoral and Academic Research programs in Mathematics Education at the Spanish University"

The general content of this lecture will be related to the current development research in Mathematics Education at the Spanish University from 1984 on, with the new universitary estructure derived from the University Reform Law (LRU), the arising of the Knowledge Field of Didactics of Mathematics and the Doctoral Programs in this discipline. In each one of the current programs, a number of Doctoral Thesis have been defended, which state a core of specialized knowledge, academically validated, which conform a well stablished theoretical and practical scientific corpus. In the Spanish Mathematics Educators community, a serious and rigorous scientific field has been settled, with its own entity and inquiry practices. The lecture is aimed to present the backgrounds of the academic research in Didactics of Mathematics, the state of art, with the achievements reached to the present and the major research lines for the next years.

SCHMIDT, S. (Germany)

"Semantic Structures of Word Problems - Mediators Between Mathematical Structures and Cognitive Structures of the Students?"

The existing body of research on semantic structures of word problems concerning addition, subtraction, multiplication, and division on the primary level shall be discussed focussing these problems: - What epistemological status of such semantic structures does appear to be appropriate? - What kind of help can such structures provide for the teacher?

SCHUPP, Hans (Germany)

"Regeometrization of school geometry - through computers?"

The decline of geometry at the secondary and its death at the post-secondary level (s. ICME-4) is caused -among others- by the comfortable transition from Euclidean to Cartesian representations and methods. This talk will analyse how the facilities of computer graphics can be used to arouse and to foster genuine geometric intuition and reasoning.

SFARD, Anna (Israel)

"On metaphors and models for conceptual change in mathematics"

Among the many streams that combine into a steadily growing flow of research in mathematics education, one of the most prominent is the study of the development of mathematical concepts. This talk will be devoted to reflections on the past, present, and future of this line of research. More specifically, a critical thought will be given to different metaphors that have been inspiring the study of conceptual change over time. The main focus will be on the ways in which the evolving idea of biological growth have been shaping researchers' approach to the subject since the works of Piaget and Vygotsky.

SKOVSMOSE, Ole (Denmark)

"Critical Mathematics Education - Some Philosophical Remarks"

Mathematics education must serve also as an invitation for participating in democratic life in a highly technological society, in which conditions for democracy may be hampered by exactly the technological development for which mathematics education also serves as a preparation. This challenge signifies the importance of critical mathematics education. However, what then is the nature of critical mathematics education?

STRAESSER, Rudolf (Germany)

"Mathematics for Work - a Didactical Perspective"

The world of work is full of Mathematics. Abstract Mathematics is the most powerful mathematics for work. Computer use implies sophisticated mathematics at work. The average employee / worker must learn (no) mathematics for her / his work. The lecture will comment on these and other slogans on mathematics for / at work.

STREEFLAND, Leen (Netherlands)

"Historical learning for future teaching, or turning a sphere inside out. No kinks"

Stephen Smale made considerable progress in the theory of dynamical systems. His learning process, indeed, is a revealing paradigm. It will be analysed as such. Could its outcomes be exploited for teaching and learning mathematics at different levels, or not? The affirmative answer will be supported by a wealth of examples.

SZENDREI, Julianna (Hungary)

"The role of mother tongue in mathematics learning"

THOMPSON, Alba (USA)

"Conceptual and Calculational Orientations in Teaching Mathematics"

We will contrast two orientations to mathematics teaching, calculational and conceptual, focusing on what instructional patterns characterize the two and the knowledge base that teachers need to draw from in order to teach mathematics conceptually.

TRI, Nguyen Dinh (Vietnam)

"Some aspects of the University Mathematics curriculum for engineers"

My talk is based on my experience of mathematics teaching in Hanoi University of Technology for many years. I will address some factors that need to be considered when we design the curriculum of Mathematics for our students of engineering. I would like to insist on this point: one of the main purposes of the undergraduate training for engineers in Mathematics is the encouragement of independence, creativity of students, particularly the abilities in problem posing and problem solving, in modeling and model solving (by mathematics tools). The curriculum of Applied Mathematics for mathematics engineers of our university will be described.

VASCO, Carlos (Colombia)

"A general theory of processes and systems in research in mathematics and in mathematics education"

The task of doing mathematics is viewed as the detection of patterns and regularities in real processes, and the production of systems composed of elements, transformations, relations, in order to explore their behavior. An interpretation of the concepts of structure and dynamics of a mathematical system is proposed, as well as the implications of this general process/systems theory in research in mathematics and in mathematics education.

VERGNAUD, Gérard (France)

"Important cognitive changes in the learning of mathematics. A developmental perspective"

VICENTE, Jose Luis (Spain)

"Geometry and Simbolic Calculus"

In the last years we have seen a large quantity of research on the applications of simbolic calculus, and its systems, to Geometry. There are several reasons behind this: the growing implementation of the systems of simbolic calculus in research and educational centers and the pure scientific reasons (e.g., invention of new and fast algorithms to do repetitive tasks, computer graphics, data basis...). We will review recent developments in this field, and applications to teaching at various levels. We will dedicate special attention to topics like authomatic proofs in plane geometry, non-euclidean geometries, algebraic curves and surfaces and computer graphics.

VIGGIANI-BICUDO, Maria Aparecida (Brazil)

"Philosophy of Mathematical Education: An Phenomenological Approach."

This lecture will focus the meaning of philosophy of mathematical Education comparing it with that of Philosophy of Education and of Philosophy of Mathematics. Then, it will focus the natural attitude and the phenomological attitude pointing out the ways in which reality and knowledge can be worked out both in the Mathematical Education context.

WANG, Changpei (China)

"Mathematics Education - An Oriental point of view"

The modern reform of Chinese mathematics education has been drived by the two main forces: development of it's own society and the western movement of mathematics education. The report will try to explain how Chinese mathematic education is now moving up to a new paradigm (it is a systematic and profound change towards the 21st century) and how the changing process has to be carefully planed and controled.
Other regular lectures may be delivered by Janvier, Bernadette (Canada) Lesh, Richard (USA) Meyer, Ives (France) Volmink, John (South Africa)

Working Groups

WG1. Communication in the classroom.

CO: Hermann Maier (Germany)
AP: Susan Pirie (Canada), Heinz Steinbring (Germany)
LO: M. Victoria Sanchez (Spain)
The work group offers an opportunity of exchanging ideas and results, and discussing problems, in:
- empirical research into every day classroom communication by quantitative or qualitative methods, emphasizing a psychological, a sociological or a linguistic perspective;
- theoretical analysis into every day classroom communication, looking at it as a social event (a culture), as an environment for learning, as a language game, or with respect to distrubances or obstacles;
- interventions into classroom communication for reasons of research, investigation or improvement (change in teaching style, introduction of learning aids, different forms of social organization, etc.);
- empirical research into small group work or into individual work of pupils by means of overservation or (clinical) interview, with interest for, e.g., processes of problem solving, pupils cognitions or concepts.

WG2. Forms of mathematical knowledge.

CO: Dina Tirosh (Israel)
AP: Tom Kieren (Canada), Lena Lindenskov (Denmark)
LO: Javier Brihuega (Spain)
Various types of knowledge are used in mathematical activities, including algorithmic, formal, visual, and intuitive knowledge. In the working group we shall define, discuss and contrast these forms of mathematical knowledge. We shall also provide examples of instruction that attempt to integrate the various, sometimes insufficiently integrated, forms of knowledge.
Some of the issues to be discussed in this working group are:
1. The role of intuitive, algorithmic and formal knowledge in various mathematical activities.
2. The role of various forms of knowledge in specific mathematical domains (e.g., arithmetic, algebra, geometry, calculus, probability).
3. Similarities and differences between elementary and advanced mathematical thinking.
4. Philosophical aspects related to various forms of mathematical knowledge.
5. Forms of mathematical knowledge: The case of the mathematics teacher.

WG3. Students' attitudes and motivation.

CO: Fong Ho Kheong (Singapore)
AP: Douglas McLeod (USA)
LO: Manuel Torralbo (Spain)
The working group will focus the discussions on the students' attitudes and motivation in front of the learning of mathematics and how to improve the situation in the future.

WG4. Students' difficulties in learning mathematics.

CO: Ivan Jezik (Austria)
AP: Luciano Meira (Brazil), Jose M. Alvarez Falcon (Spain)
LO Jose A. Ruperez (Spain)
The aim of the working group is to identify the main students' difficulties in learning mathematics and how teachers can face and solve these problems.

WG5. Teaching mixed-ability classes.

CO: Liora Linchevski (Israel)
AP: Margaret Cozzens (USA), Zmira Mevarech (Israel) Nada Stehlikova (Czech Rep.)
LO: Francisco Esteban (Spain)
Every session will be devoted to a different topic related to the Learning of Mathematics in Mixed-Ability classes as follows:
(a) ability grouping vs. mixed ability classrooms: a look from a theoretical and empirical perspectives;
(b) innovative methods designed for mixed ability classrooms;
(c) alternative assessments emerge from the mixed ability classes needs;
(d) teacher training for mixed ability classes.

WG6. Gender and mathematics.

CO: Barbro Grevholm (Sweden)
AP Jeff Evans (UK), Roberta Mura (Canada), Fidela Velazquez (Spain)
LO: M& Eugenia Jimenez (Spain)
Gender and mathematics encompasses a broad range of themes. Many aspects have been explored at conferences and in recent publications. In spite of this solid foundation, research perspectives and goals, educational practices and intervention may need to be re-examined and reshaped. Five topics relevant to gender and mathematics will be examined: different research perspectives; manifestations of gender inequities; ethnic, cultural and social conditions associated with equity issues; international, regional and local cooperation in research; focus on directions for change in educational contexts. In each case, short presentations from different perspectives will be followed by discussions and work in smaller and/or larger groups.

WG7. Mathematics for gifted students.

CO: Vladimir Burjan (Slovak Republic)
AP: Fou Lai Lin (China-Taiwan), John Webb (South Africa)
LO: Diego Alonso Canovas (Spain)
WG7 will focus on: the notion (phenomenon) of "giftedness" (who are mathematically gifted students? which are the characteristics? which types? how can we recognize?...); approaches to identification and fostering of mathematical giftedness within the educational systems; what mathematics should be the gifted taught and how?, which out-of-class and out-of-school activities must be organized for the mathematically gifted?

WG8. Mathematics for students with special needs.

CO: Jens Holger Lorenz (Germany)
AP: Marie-Jeanne Perrin-Glorian (France), Nuria Rosich (Spain), Olof Magne (Sweden)
LO: Luis M. Casas Garcia (Spain)
The working group will try to identify which are the main problems, and possible solutions, in the teaching and learning of mathematics for students with special needs.

WG9. Innovation in assessment.

CO: Antoine Bodin (France)
AP: Kenneth Travers (USA), Bengt Johansson (Sweden), Nitsa Movshovitz-Hadar (Israel), Vicente Riviere (Spain), Gill Close (UK)
LO: Adela Jaime (Spain)
This working group concerns recent innovation in assessment of mathematics learning from the individual classroom up to national level. It will focus on assessment innovation which have improved assessment or learning for students, including why and how these happened. Small discussion groups will be based on specific assessment questions or methods actually used in school, which illustrate innovations in: written, oral and practical assessment; assessment of mental processes; self-assessment and peer assessment; adaptive / interactive testing; recording progress of large classes; methods for designing questions and tests; style of internal and external assessment; teachers' use of question data banks; use of learning theories to design assessments; scaling of tests results. Discussions will be summarised in plenary sessions.

Boundaries and aims of the group

The WG will be a forum for sharing an recording up-to-date information on innovations in assessment. It also aims to identify factors contributing to successful innovations and to disseminate these. It plans to build up a network of participants, indicating their interests, to facilitate sharing of information and collaboration. Our work will not overlap that of WG20 or TG26. It will not deal with international comparative studies or any administrative, social or political aspects of large scale assessment. It will not deal with any evaluation of systems, schools, curricula, etc. It will focus on assessment of students' learning from individual classroom level up to national level using both internal and external assessment. It will include only innovations in assessment which the contributors judge to have improved assessment or learning in their classrooms or countries. This subjective judgement will vary across countries as will the date when the innovation was introduced.

We specially want to include examples from countries and from schools which few people already know about. The innovation might be very small, but we would still like to know about it. We would be grateful for examples from you. Please e-mail this message to anyonewho you think might be able to help.

WG10. Languages and mathematics.

CO: Jose F. Quesada (Spain)
AP: Ferdinando Arzarello (Italy), Joop van Dormolen (Israel)
LO: Alicia Bruno (Spain)
The working group will focus the attention on activities which facilitate the transition from properties and relations dicovered in "everyday" language and real situations to verbal an written presentations, and from these to graphical languages (drawings, diagrams, graphs,...) and towards symbolization.

WG11. A curriculum from scratch (zero-based).

CO: Anthony Ralston (USA)
AP: Hugh Burkhardt (UK), Nerida Ellerton (Australia), Susan Groves (Australia), Rolf Hedren (Sweden)
LO: Salvador Guerrero (Spain)
Suppose mathematics education did not exist and you needed to invent in 1996. What would the curriculum look like? The Working Group will address this question with the aim of assessing how far from the current K- 12 curriculum an ideal curriculum would be and, also, how the political, social and economic constraints on curriculum change might be overcome in order to get from where we are to where we would like to be. Some presentatios at ICME-8 will consider this question from the perspective of subject matter (what portions of current school mathematics should be in any curriculum? what subject matter not now commonly taught in school mathematics should be in the curriculum?). Other presentations will discuss the impact of the zero-based idea on pedagogy, teacher education and testing and, as well, will consider what research in mathematics education can tell us about a zero-based curriculum. It is intended to publish a proceedings consisting of the papers presented and the discussions at ICME-8.

WG12. Curriculum changes in the primary school.

CO: Mary Lindquist (USA)
AP: Maria Canals (Spain), Michala Kaslova (Czech Rep.), Hans Nygaard Jensen (Denmark)
LO: Carmen Burgues (Spain)
Curriculum Changes in Primary Mathematics focus on CHANGE---new expectations of students, change in the mathematics content, change in the sequencing, research that supports change, recommendations for further change. Participants should bring curriculum documents of their country, region, or school and a brief description of the major thrusts and recent changes.

WG13. Curriculum changes in the secondary school.

CO: Martin Kindt (Netherlands)
AP: Abraham Arcavi (Israel), Margaret Brown (UK), Eizo Nagasaki (Japan), F. Villarroya (Spain).
LO: Francisco Garcia (Spain)
In this group we will focus the discussions on the topics: algebra/calculus; Geometry; Discrete Mathematics (graph theory, combinatorics, probability, statistics, cryptography. There will be two simultaneous sessions in the first three meetings (12-16; 16-19) and the last session will be a plenary discussions on trends in currciulum changes all over the worl. In all sessions there will attention to what are the influences on new curricula of changing view on learning; changing societ, changing mathematics, changing technology.

WG14. Linking mathematics with other school subjects.

CO: Fred Goffree (Netherlands)
AP: Rolf Biehler (Germany), Mario Carretero (Spain), Kurt Kreith (USA), Howard Tanner (UK).
LO: Mariano Dominguez (Spain)
In this working group different points of view will be taken on four schoollevels: Kindergarten (almost all mathematical activites are linked to overall tasks), primary education (mathematics and other subjects are taught by the same teacher), lower secondary and upper secondary (different teachers for maths and other subject areas). Some points of views to consider: parts of the rich history of attempts, arguments and philosophies, the study of designing integrated maths teaching, reports from development and research on this topic, presentations of paradigms of integrated math lessons, concerning low and high achievers when maths is linked with other school subjects, reflecting related theories of learning and teaching, experiencing the need of using a didactical phenomenology according to H. Freudenthal, practising how to present mathematics in the context of other subjects and the problems of culture, language and media. A core question: "integrating maths and other school subjects needs a balance between maths learning in contexts and maths learning in isolation".

WG15. The impact of technology on the mathematics Curriculum.

CO: Michal Yerushalmy (Israel)
AP: David Chazan (USA), Al Cuoco (USA), Koeno Gravemeyer (Netherland), John Monaghan (UK)
LO: Jacinto Quevedo (Spain)
Technology is currently central in many of the attempts to reform the mathematics curriculum and is intimately connected with the goals of creating meaningful mathematics for diverse groups of students. In ways that would otherwise be unrealistic, technology can be used to support learners in communicating about mathematics, in constructing and manipulating mathematical objects, and in carrying out mathematical reasoning. The development of many new technology-intense mathematics curricula around the world suggests a serious discussion of the opportunities and problems raised by widespread use of technology in school mathematics. The group will concentrate on three major characterizations of current technology-intense curriculum reform:
1. Modeling based curricula: curriculum which is organized around "real life" applications that create opportunities to learn mathematics.
2. Curricula organized around big mathematical ideas: developments that re-think the organization and the emphases of the current traditional content of the curriculum.
3. Curricula organized around new themes and topics: developments that suggest that the content of the curriculum should be changed to better represent modern mathematics.

WG16. The role of technology in the mathematics classroom.

CO: Marcello Borba (Brazil)
AP: Manuel Armas (Spain), Jim Fey (USA), Maria Mas- charello (Italy)
LO: Miguel de la Fuente (Spain)
The aim of this working group is to discuss both from a theoretical and practical point of view the changes in the mathematics classroom as computers and graphing calculators are introduced in the classroom.

WG17. Mathematics as a service subject at the tertiary level.

CO: Eric Muller (Canada)
AP: Jairo Alvarez (Colombia), Fred Simons (Netherlands)
LO: Ceferino Ruiz (Spain)
This group aims to provide participants with opportunities to discuss and share experiences relating to their teaching of mathematics as a service subject. The group will consider, but will not be limited by, the following questions:
1. What kind of mathematical preparation is needed for the technical workforce of the twenty-first century?
2. What is the impact of modern technology on the content and to the didactic of the service courses?
3. What service course experiences assist the students' development of mathematical reasoning as it pertains to their area of specialization? The overall aim is to suggest methods by which mathematics can become more effective in its service to other disciplines, and to point to possible new areas of service courses.

WG18. Adults returning to mathematics education.

CO: Gail Fizsimons (Australia)
AP: Diana Cohen (UK)
LO: Antonio Renguiano (Spain)
The goal of this WG is to propose a set of recomendations related to mathematics education for the different populations of adults returning to the educational system. There will be discussions on how to reach adults who may benefit from mathematics education, what mathematical content should be considered, what achievements levels should be aimed at, what teaching, strategies can be used, etc.

WG19. Preparation and enhancement of teachers.

CO: Marjorie Carss (Australia)
AP: Barbara Jaworski (UK), Milan Koman (Czech Rep.)
LO: Jose Ramon Pascual (Spain)
The mathematics curriculum in all countries faces the challenge of social change, developments in information technology, and changes in mathematics itself. How do we prepare teachers to be reflective practitioners and lifelong learners who can make decisions about what mathematics is to be taught, how it is to be learned and why? How should we help people to undertsand and identify the mathematics and methodology in initiatives that emphasise active learning; problem solving; real life applications? Professional development (enhancement) in both content and pedogical knowledge is needed even for those with experience if they are to continue as effective teachers and as teachers who can reliably describe classroom interactions and evaluate and record student achievement.

WG20. Evaluation of teaching, centers, and systems.

CO: David Robitaille (Canada)
AP: Fernando Hernandez-Guarch (Spain), Norman L. Webb (USA)
LO: Antonio Molano (Spain)
One focus of the Working Group will be on prominent cases of reform activity in mathematics education around the world which emphasize the role of teachers and teacher education in mathematics education, how the role of teachers is changing. A second focus will be on innovative approaches to evaluation including the use of portfolios, perfomance assessment, and others. A panel discussion will be a featur of the first session of the WG, and subsequent sessions will include both paper presentations and group discussions.

WG21. The teaching of mathematics in different cultures.

CO: Jerry Becker (USA)
AP: Sunday A. Ajose (USA), Andy Begg (New Zealand), T. Fujii (Japan), Martha Villavicencio (Peru)
LO: Andres Marcos (Spain)
The program will provide for presentation, discussion and dissemination of current research on culture and mathematics teaching and learning; exchanging perspectives (e.g., the role of language in mathematics learning, relationships between teachers and students); consideration of students' prior experiences as a basis for constructing knowledge; cultural contributions to the development of specific mathematics (e.g., counting systems, arithmetic, problem solving); development of new ideas for research and cross-cultural research of critical aspects of mathematical understanding and problem solving inside and outside school; and theoretical considerations.

WG22. Mathematics, education, society, and culture.

CO: Richard Noss (UK)
AP: Cyril Julie (South Africa), Jean M. Kantor (France), Catherine Vistro-Yu (Philippines)
LO: Jose L. Alvarez (Spain)
The group will focus on the social and cultural dimensions of mathematics education. Key themes will include the relationship between the socio-economic structures of society and mathematical education; the political determinants of curricula; the social shaping of technology and mathematics education; work school, and mathematics; the notion of ideology and its relevance for mathematical education; and the politics of assessment.

WG23. Cooperation among countries and regions in mathema- tics education.

CO: Bienvenido Nebres (Philippines)
AP: Emma Garcia Mora (Spain), John Egsgard (Canada), Murak Jurdak (Lebanon), Aderemi Kuku (Nigeria), Bernardo Montero (Costa Rica)
LO: Mercedes Garcia (Spain)
WG23 will focus on the possible cooperation among countries and regions in order to improve mathematics education at the international level.

WG24. Criteria for quality and relevance in mathematics education research.

CO: Kenneth Ruthven (UK)
AP: Robert Davis (USA), Angel Gutierrez (Spain)
LO: Salvador Llinares (Spain)
The quality and relevance of research in mathematics education is assessed in different ways for differing purposes. The aim of the working group will be to explore the criteria that are appropriate in assessing research for purposes such as:
- the award of a doctoral degree in mathematics education;
- publication in a refereed journal in mathematics education;
- inclusion in a course aimed at the professional preparation or development of mathematics teachers;
- to inform policy formation in mathematics teaching and the development of professional guidelines;
- to design resources for mathematics teaching, such as textbooks and other classroom materials.

WG25. Didactics of mathematics as a scientific discipline.

CO: Nicollina Malara (Italy)
AP: Carmen Azcarate (Spain), Hans-Georg Steiner (Germany), Stephen Lerman (UK)
LO: Maria del Carmen Batanero (Spain)
The working group will face the following questions:
1. Which paths have we followed in order to arrive at the conception of Didactis of Mathematics as a scientific discipline? Is the vision agreed on internationally? To what extent?
2. Is the difference between "Didactics of Mathematics" and "Mathematics Education" only a linguistic problem due to different cultures?
3. What are the characteristic features which define the scientific status of the discipline according to the various paradigms?
4. Didactics of Mathematics is linked, as well as to Mathematics, to different disciplines such as epistemology, pedagogy, psychology, sociology, anthropology, etc. In what way is it related to each of these?
There will be work-sessions organized in subgroups, according to the number of participants and their contributions. There will be some general presentations and a roundtable.

WG26. Connections between research and practice in mathematics education.

CO: Beatriz D'Ambrosio (USA)
AP: Luciana Bazzini (Italy), Morten Blomhoj (Denmark), Sandy Dawson (Canada)
LO: Lorenzo Blanco (Spain)
Throughout the sessions of this working group we hope to generate discussions in which participants share their experiences in bridging the gap between research and practice. We will explore the relationships between research and practice by looking at ways in which practice serves as a source for research questions and ways in which research results are used in practice. Other dimensions of this relationship will emerge throughout our discussions. Examples of questions that may arise include the following:
What practices seem effective in bridging the gap between research and practice? What counts as research? What counts as evidence? Can practitioner research be considered a form of scholarship? Does practitioner research help bridge the gaps between theory and practice? What are the means through which scholarly work impacts the work of practitioners? These are but a few of the questions that we anticipate will emerge during the working group discussions.

Topic Groups

TG1. Primary school mathematics.

CO: Regine Douady (France)
AP: J. Klep (Netherlands), Helen Mansfield (USA)
LO: Francisco T. Sanchez-Cobo (Spain)
In present-day society, every citizen needs to have at his/her disposal a certain mathematical knowledge. Work starts at elementary school and has to be established on the long run. Rather, starting at elementary school if you admit that long term learning is necessary, mathematics play an essential role in the forming of scientific thought and thus of critical mind. Which mathematics at elementary school? How to put them on stage?; How to organize the relationship between the teacher and the pupils concerning mathematics? What does the teacher take charge of and what does he/she leaves to the responsibility of the pupils? How does he/she organize the shifting of responsibilities? What is the impact on the pupils' knowledge, on their ability to make hypotheses, choices, arguments, to reconsider misdirected choices and make new ones, in order to deal with unfamiliar context? Can one detect regularities beyond the diversity of pupils teachers,...? The group TG1 will be devoted to debating on the pertinency, when elementary school is concerned, of such questions and other ones arising from the points mentionned above. Pieces of work will be presented, which are related to the above problematic - possibly opposed to it with arguments, and which have been produced since ICME 7.

TG2. Secondary school mathematics.

CO: Glenda Lappan (USA)
AP: Dirk Janssens (Belgium), Hans C. Reichel (Austria)
LO: Juan Gallardo (Spain)
This group will focus on research and development issues in the areas of curriculum, instruction, assessment and the alignment of these aspects of secondary mathematics education. The presentations and discussions will focus on work that helps illuminate questions such as the following: What is the interaction between new curriculua, new instructional strategies, new assessment strategies and the professional development of teachers? What are the "big" ideas in mathematics at the secondary level and what are compelling contexts that give stduents access to these ideas? What are the most important research questions that need to be answered to guide change in curriculum teaching, and learning over the next decade? What are the issues of articulation between secondary school and primary school? Between secondary school and higher education? Between secondary school and the world of work?

TG3. University mathematics.

CO: Joel Hillel (Canada)
AP: Francine Gransard (Belgium), Habiba El Bouaz- zaoui (Marocco), Lee Peng Yee (Singapur)
LO: Jose Carmona Alvarez (Spain)
This group will examine how the traditional university mathematics curriculum is being influenced by general phenomena such as: changes in the student clientele in terms of their mathematical preparation, attitudes and aspirations; results of research in mathematics education related to undergraduates' learning of specific topics; computer technology and specific mathematical software; new emphases within the discipline of mathematics; changes in employment prospects for students in the mathematical sciences.

TG4. Distance learning of mathematics.

CO: Haruo Murakami (Japan)
AP: David Crowe (UK), Nerida Ellerton (Australia)

LO: Jose M. Gairin (Spain)
The group will examine the latest innovations on the distance learning of mathematics with special reference to the use of technological and audiovisual tools.

TG5. Education for mathematics in the working place.

CO: Annie Bessot (France)
AP: Marilyn Mays (USA), Jim Ridgway (UK)
LO: M. Dolores Eraso (Spain)
This topic group is the extension of the topic group "Mathematics for work: vocational education" (ICME-7). This is why, we propose to organise the work around the following questions: what is the vocational use of mathematics? how does mathematical knwoledge integrate into vocational situations? what are the appropriate research methods for the exploration of the vocational use of mathematics? what changes in the teaching of mathematics will be brought about by technologica progress (including the growing use of computers) in vocational education?

TG6. Mathematics teaching from a constructivist point of view.

CO: Ole Bjoerkqvist (Finland)
AP: Jere Confrey (USA), Tadao Nakahara (Japan)
LO: M.V. Garcia-Armendariz (Spain)
The topic group is concerned with the impact of constructivist theories of learning on the teaching of mathematics in various countries. It includes reports from classrooms inspired by constructivism as well as changes in assessment practice and effects on national curricula or educational policy. Another focus is on the reverse process, the impact of current practice and educational policy on theories of learning mathematics and the nature of mathematical knowledge.

TG7. The fostering of mathematical creativity.

CO: Erkki Pehkonen (Finland)
AP: J.G. Greeno (USA), Yoshihiko Hashimoto (Japan)
LO: Lluis Segarra (Spain)
Creativity is a topic which is often neglected within mathematics teaching. Usually teachers think that mathematics need in the first place logic, and that creativity has not much to do with learning mathematics. On the other hand, if we consider a mathematician who develops new results in mathematics, we cannot oversee his/her use of the creative potential. Thus, the main questions within TG7 are: What is the meaning of creativity within school mathematics? Whcih methods could be used to foster mathematical creativity within school situations? What scientific knowledge, i.e. research results, do we have on mathematical creativity?

TG8. Proofs and proving: Why, when and how.

CO: Michael de Villiers (South Africa)
AP: Fulvia Furinghetti (Italy), David Pimm (UK)
LO: Encarnacion Castro (Spain)
We will be having 2 sessions of 90 minutes each with the first session a panel discussion followed by the second session where we may split up in smaller interest groups if necessary. Some of the questions to be addressed will be: How are computers and the development of so-called "experimental" mathematics affecting our notions of proof? How can we make proof a meaningful activity for students? What balance should we strike between informal and formal proofs, and how can we assist the transition from the former to the latter? What proof representations do students spontaneously produce themselves? What are students' needs for conviction and explanation? How can we demystify the construction of auxiliary lines in geometry proofs? What contexts can be utilized to present proof as meaningful activity?

TG9. Statistics and probability at the secondary school.

CO: Brian Phillips (Australia)
AP: Ruma Falk (Israel), Juan A. Garcia-Cruz (Spain), Tibor Nemetz (Hungary)
LO: Eliseo Borras (Spain)
This topic group aims to highlight the issues involved in, and to provide directions for the future of, the teaching of statistics and probability at the secondary level. The programme will include an overview of the state of the art of these topics, discussions on children's understanding of the basic concepts of probability and statistics, general issues such as the curriculum, assessment, teacher training, the use of technology and how research may affect how these topics are taught in the future. The format of the sessions are planned to enable participants to focus on either probability, or data analysis issues and a special session will be provided for Spanish speakers. There will be a forum discussion which will focus on the question: How statistics and probability can best be incorporated in the overall school program?

TG10. Problem solving throughout the curriculum.

CO: Kaye Stacey (Australia)
AP: Maria L. Callejo (Spain), Mary Falk (Colombia), Diana Lambdin (USA)
LO: Jose Carrillo (Spain)
Increasingly the success of mathematical education is being judged by the power which it imparts to students to deal with aspects of their lives at work, at home and as informed citizens. This topic group is concerned with theories and practices which give students the power to use mathematical ideas to solve problems arising from outside mathematics or which take an inter-disciplinary approach to developing mathematical skills, processes and concepts. Contributions will discuss curriculum materials, school organisation and structures, and empirical and philosophical research studies into thinking, learning and teaching.

TG11. The future of calculus.

CO: Ricardo Cantoral (Mexico)
AP: Peter Bero (Slovaquia), Paul Zorn (USA)
LO: Jordi Deulofeu (Spain)
The aim of the group is to support the improvement of the teaching Calculus taking into account the differences due cultural context. This group will focus on how the traditional Calculus curriculum is being influenced by phenomenas such as: results of research in mathematics education, new approaches in mathematics and several reform's movement in teaching Calculus. We want to organize the interaction (reflection and discussion), and possibly confrontation, among participants whose views of the discipline are different. We will organize both, short talks on a specific domain of research and a sharing of ideas about the teaching-learning interface of Calculus. Some particular questions will be focused: What are the objectives of a Calculus courses? What are the connections of Calculus courses with courses in Precalculus, Mathematical Analysis, Discrete Mathematics and Differential Equations? Which conceptions of the content of the Calculus and of its teaching are at the base of teaching experiments? How has the new technology affected the teaching Calculus? What does mean "understand" in the Calculus domain?

TG12. The future of geometry.

CO: Joe Malkevitch (USA)
AP: Maria A. Mariotti (Italy), Richard Pallascio (Canada)
LO: Francisco Castro (Spain)
Geometry has grown rapidly beyond its traditional boundary of attempting to give a mathematical description of various aspects of physical space. It now includes such subdisciplines as convexity, graph theory, knots, tilings, and computational geometry, to name but a few. This rapid growth has been accompanied with broadening applicability to robotics, image processing and computer graphics, knotting of DNA, etc. These dramatic developments create challenges for mathematics educators to integrate emerging with traditional geometry. One important consideration is the use of software systems to help with visualization and geometric explorations.

TG13. The future of algebra and arithmetic.

CO: Joaquin Gimenez (Spain)
AP: Teresa Rojano (Mexico), Barbara Wittington (USA)
LO: Bernardo Gomez-Alfonso (Spain)
In this topic group there will be selected presentations on innovative aspects, projects and proposals for the new ways of treating algebra and airthmetic throughout the curriculum.

TG14. Infinite processes throughout the curriculum.

CO: Bruno D'Amore (Italy)
AP: Raymond Duval (France), Vera W. de Spinadel (Argentina)
LO: M. Carmen Penalva (Spain)
Numbers, sequences, functions, iterative methods, geometrical foundations, fractals,... infinite processes play a role throughout the curriculum. The topic group will treat the various aspects of this processes.

TG15. Art and mathematics.

CO: Dietmar Guderian (Germany)
AP: Nat Friedman (USA), Doris Schattschneider (USA)
LO: Rafael Perez-Gomez (Spain)
The group will focus on the following topics: mathematics in modern art; mathematics in the precolumbian art in America; mathematics in the historical arabian art; mathematics in the historical asiatic art; mathematics in european classic art (greece, roman); mathematics in the european medieval art,...

TG16. History of mathematics and the teaching of mathematics.

CO: Louis Charbonneau (Canada)
AP: Evelyne Barbin (France), Man Kenng Siu (Hong Kong)
LO: Santiago Fernandez (Spain)
The two poles of interest on the subjet of the use of history in mathematics education shall be discussed successively in two sessions. The principal aim is to get some perspective on how history has been applied in the classroom, on the one hand, and in research on mathematics education, on the other hand.
1) The use of history in the classroom : an overview of the different approaches actually experimented, methodological implications of each approach, positive, as well as negative, aspects.
2) The use of history in mathematics education research : fields in which history has been actually used, methodological constraints, evaluation of the effective contribution of history.

TG17. Mathematical modelling and applications.

CO: Joao Pedro da Ponte (Portugal)
AP: Werner Blum (Germany), Qi-Xiao Ye (China)
LO: Carles Llado (Spain)
The topic group Mathematical modeling and applications (MMA) will consider the questions addressed at the previous ICME regarding philosophy of MMA, role of computers, assessment, and empirical research and then turn to the questions left open. Through invited speakers and general discussion, the group will consider both the student and the teacher: what are appropriate learning objectives (cognitive/affective) regarding MMA at different grade levels and ability groups?; what is the role of the teacher in initiating, sustaining, summing up, and assessing MMA activities?; what are successful strategies for articulating the learning of the structure of mathematics and its applications?

TG18. Roles of calculators in the classroom.

CO: Pedro Gomez (Colombia)
AP: Nestor Aguilera (Argentina), Bert Waits (USA)
LO: Juan M. Garcia-Dozagarat (Spain)
The main goals of the group will be to inform, develop and support reflection and discussion concerning the roles that calculators have played and can play in the teaching and learning of Mathematics. For this, the presentations and discussions will deal with the complex and dynamic relationship between calculator use and Mathematics curriculum. Some of the topics that can be treated are those concerning the relationship between calculators and: Goals of Mathematics Education; Mathematical Knowledge to be taught (nature, programs, materials, content, etc.); Learning (understanding, achievement, attitudes) and Teaching (teachers, instruction, assessment).

TG19. Computer-based interactive learning.

CO: Nicolas Balacheff (France)
AP: James J. Kaput (USA), Tomas Recio (Spain)
LO: Claudio Sanchez (Spain)
In recent years, our computer-based ability to connect and manipulate representations of knowledge in mathematics have become ever more powerful and flexible. The reification of mathematical knowledge in computer-based learning environments, and accompanying enrichment of mathematical experience due to progress in interface design and knowledge representation (ie internal structures), widen and deepen access to experiential learning. Some of these environments even involve tools or models that adapt to the learner or guide their learning. Such developments raise questions regarding the use of these tools in the classroom: How can teachers and others assess and make sense of what students learn? How can they manage computer-intensive classroom situations? How is mathematical knowledge transformed when instantiated in such computational environments (the computational transposition of mathematics)? How can teachers bridge between low technology and high technology approaches to teaching and learning? Dealing with such questions is essential to the productive use of technology by teachers and designers of instruction. We would like to examine these questions from the research point of view as well as from practice. Since the design and implementation of computer-based interactive learning environments results from the collaboration of at least two communities, computer-scientists and mathematics-educators, TG 19 will address each of them regarding the difficulties and success in the past and the problems to be investigated by research and development in the future? Among the possible key issues to addressed we identify: Microworlds and the new realism of mathematics; Managing didactical interaction; Distance learning, collaborative learning and distributed or virtual classrooms; Problems, limits, and potentials of the teacher/machine partnership; Understanding learners' understanding and the issue of learner modeling; Computational transposition of mathematics and related epistemological issues; the contribution and limits of AI; the contribution and limits of the WWW as a Computer-based interactive learning environments

TG20. Technology for visual representation.

CO: Rosamund Sutherland (UK)
AP: Gerd Doctorow (Canada), Joel Schneider (USA)
LO: Francisco Martin Casadelrrey (Spain)
The advent of fast and sophisticated computer graphics has made dynamic and interactive visual images accessible to mathematics students. This potentially changes the ways students work with mathematics and the mathematics they work with. This topic group will centre around the following themes as they relate to the use of technology for visual representation: the relationship between internal and external visual representations; the role of diagrams (static, dynmic, computerised) in mathematical thinking; using the visual as an analytic tool; cultural differences influencing students' use of visual representations; computational environments which promote the use of the visual.

TG21. Mathematics instruction based on manipulative materials.

CO: Ana Garcia-Azcarate (Spain)
AP: David Fielker (UK), Marion Walter (USA)
LO: Ladislao Navarro (Spain)
In this group we will focus the attention on manipulative materials which can be used in the classroom in order to improve mathematics instruction.

TG22. Mathematical games and puzzles.

CO: Aviezri Fraenkel (Israel)
AP: David Singmaster (UK), Fernando Corbalan (Spain)
LO: Manuel Garcia-Denis (Spain)
Among the main questions to be explored at TG22: Why are 2-player games so complex? Any new tools to analyze them? New ways of utilizing existing tools? Can games be used to contribute significantly to areas such as complexity, logic, surreal numbers, error-correcting codes, graph and matroid theory, networks, on-line algorithms and biology? Any other applications? How do games contribute to education?

TG23. Future ways of publishing in mathematics education.

CO: Don Albers (USA)
AP: Gerhard Koenig (Germany), David L. Rodgers (USA), Sixto Romero (Spain)
LO: Jose Cobos-Bueno (Spain)
1. In this reapidly evolving electronic world, what is meant by a publication?
2. How will researchers in mathematics education deal with issues of promotion and tenure in an electronic environment?
3. How will the Web and other electronic forms of communication impact existing mathematics education journals?
4. New electronic journals come into existence at a rapid rate. How will these be substained and who will pay for them?
5. Who will bear the responsbility for archiving electronic journals?
6. How should copyright and issues of intellectual property rights be handled in the electronic environment?

TG24. Mathematics competitions.

CO: Patricia Fauring (Argentina),
AP: Claude Deschamps (France)
LO: Pedro J. Martinez (Spain)
The group will present many recent experiences on the organization of mathematics competitions in different levels, regions, countries and international perspectives. The implications of such competitions for the improvement of mathematics education will be faced.

TG25. Mathematics clubs.

CO: Jenny Henderson (Australia)
AP: Pedro Esteves (Portugal)

LO: Jose M. Sanchez Molina (Spain)
This topic group is new to the ICME program this year. We aim to examine the role of clubs in supporting the mathematical development of high school (and possibly older) students. The group will focus on those enrichment and challenge activities which bring students together in groups. Although some of these activities may be directed toward preparations for competitions, the purpose of most of them is simply to stimulate, challenge and support able students in their mathematical interests. Each session of the group will include some short talks from speakers with experience in either running clubs or participating in clubs. We will discuss the motivation for forming clubs, the methods of operation, the mathematical material used and the impact (mathematical and social) on the students who participate. There will be ample opportunity for wide discussion.

TG26. International comparative investigations.

CO: Gabriele Kaiser (Germany)
AP: Juan Diaz-Godino (Spain), Murad Jurdak (Lebanon) Eduardo Luna (Dominican Republic), Eduardo Lacasta (Spain)
LO: Juan Calderon (Spain)
The work of the topic group will begin with a state-of-the-art description of international comparative investigations, in which the aims and incentives of the international studies as well as their limitations will be explored. In small groups, and based on short descriptions of each study distributed in advance, participants will then discuss in more depth one selected comparative study. Both large and small-scale studies will be examined including, among others: Second International Mathematics Study (SIMS), Third International Mathematics and Science Study (TIMSS), Survey of Mathematics and Science Opportunities (SMSO), First and Second Study of International Assessment of Educational Progress (IAEP), American- Japanese Comparative Studies, Mathematics Teaching and Learning Worldwide Study. The second session will be a panel discussion focusing on the theme: What can we learn from international comparative investigations. Experts in the field will discuss selected relevant aspects such as curriculum analysis, classroom reality, global cooperation, regionalization.

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17 June 1996