8th International Congress on
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DE GUZMAN, Miguel (Spain)
"On the role of the mathematician in Mathematics
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
FREIRE, Paolo (Brazil)
"Social-philosophical aspects of mathematics
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
"Mathematics Teachers as decision makers: changes and
Moderator: Alan Bishop (Australia)
Participants: Gail Burrill (USA), Ruhama Even (Israel),
Francisco Hernan (Spain), Maria Salett (Brazil),
Thang Ruifen (China)
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
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
Didactical research developed around the conceptual field of
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
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
concepts and to give teachers some guides so they know (and
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
A drawing instrument is a plane articulated system, whose
degree of freedom is one
(during the motion, the points of the links draws algebraic
instruments have a long history both inside and outside
geometry. They constitute
a field of experience for geometrical activity in the research
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,
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
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
professional development. This session describes how a
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
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
A rationale and theoretical perspectives for conceptualizing
development will be presented. Research from longitudinal
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
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
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
Scenarios of the future can lead to considerations about the
next steps of the
DOERFLER, Willibald (Austria)
"Means for Meaning"
Three potential sources from which students could derive
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
use of the word "object").
ERNEST, Paul (UK)
"Social Constructivism as a Philosophy of
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
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
Attention will also be devoted to the relations between the
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
FORTUNY, Josep M. (Spain)
"Range of Abilities. Learning and Assessing Geometrical
Knowledge in Environmental
We tackle the complex problem of skill's processes in L & A
and present a brief
historic perspective about research approaches (factorial,
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
FUJITA, Hiroshi (Japan)
"High lights and shadows of recent Japanese curriculum for
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
targets (mathematical literacy and mathematical thinking), the
structure, and introduction of computers. Various difficulties
in implementation have
come up, while recently we are concerned with "Crisis of
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
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
GAULIN, Claude (Canada)
"Difficulties and challenges in the implementation of "problem solving" in school mathematics
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)
GJONE, Gunnar (Norway)
"A new role for curriculum documents - from inspiration to
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
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
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
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
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
methods at high school and university explicitly and
implicitly into conceptions of
aversion or avoidance of mathematics with students which
KIERAN, Carolyn (Canada)
"The changing face of school algebra"
In the past, school algebra has been viewed chiefly as
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
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,
mathematical background. Assessment designers feel not very
Mathematicians don't recognise the mathematics, let alone some
feel unable to help their children.
Both kind of problems will be addressed from experiences in
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
which argue that equity for females requires a reevaluation of
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
Teachers of mathematics at all levels are being urged to adopt
a new pedagogy that
emphasizes active learning and places more emphasis on group
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
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
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
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
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
In this talk the activities generated by mathematics
competitions in China will be
detailed. The influence of mathematics competitions into
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
The general content of this lecture will be related to the
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
Programs in this discipline. In each one of the current
programs, a number of
Doctoral Thesis have been defended, which state a core of
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
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
- What kind of help can such structures provide for the
SCHUPP, Hans (Germany)
"Regeometrization of school geometry - through
The decline of geometry at the secondary and its death at the
(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
intuition and reasoning.
SFARD, Anna (Israel)
"On metaphors and models for conceptual change in
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
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
SZENDREI, Julianna (Hungary)
"The role of mother tongue in mathematics learning"
THOMPSON, Alba (USA)
"Conceptual and Calculational Orientations in Teaching
We will contrast two orientations to mathematics teaching,
conceptual, focusing on what instructional patterns
characterize the two and the
knowledge base that teachers need to draw from in order to
TRI, Nguyen Dinh (Vietnam)
"Some aspects of the University Mathematics curriculum for
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
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
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
VIGGIANI-BICUDO, Maria Aparecida (Brazil)
"Philosophy of Mathematical Education: An Phenomenological
This lecture will focus the meaning of philosophy of
comparing it with that of Philosophy of Education and of
Mathematics. Then, it will focus the natural attitude and the
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
mathematics education. The report will try to explain how
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)
WG1. Communication in the classroom.
CO: Hermann Maier (Germany)
The work group offers an opportunity of exchanging ideas
and results, and
discussing problems, in:
AP: Susan Pirie (Canada), Heinz Steinbring (Germany)
LO: M. Victoria Sanchez (Spain)
- empirical research into every day classroom communication by
or qualitative methods, emphasizing a psychological, a
sociological or a
- theoretical analysis into every day classroom communication,
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
investigation or improvement (change in teaching style,
learning aids, different forms of social organization,
- empirical research into small group work or into
individual work of
pupils by means of overservation or (clinical) interview, with
e.g., processes of problem solving, pupils cognitions or
WG2. Forms of mathematical knowledge.
CO: Dina Tirosh (Israel)
Various types of knowledge are used in mathematical
algorithmic, formal, visual, and intuitive knowledge. In
the working group
we shall define, discuss and contrast these forms of
knowledge. We shall also provide examples of instruction that
integrate the various, sometimes insufficiently integrated, forms
AP: Tom Kieren (Canada), Lena Lindenskov (Denmark)
LO: Javier Brihuega (Spain)
Some of the issues to be discussed in this working group
1. The role
of intuitive, algorithmic and formal knowledge in various
2. The role of various forms of
knowledge in specific
mathematical domains (e.g., arithmetic, algebra,
3. Similarities and differences
between elementary and
advanced mathematical thinking.
aspects related to various
forms of mathematical knowledge.
5. Forms of
The case of the mathematics teacher.
WG3. Students' attitudes and motivation.
CO: Fong Ho Kheong (Singapore)
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.
AP: Douglas McLeod (USA)
LO: Manuel Torralbo (Spain)
WG4. Students' difficulties in learning mathematics.
CO: Ivan Jezik (Austria)
The aim of the working group is to identify the main
in learning mathematics and how teachers can face and
AP: Luciano Meira (Brazil), Jose M. Alvarez Falcon
LO Jose A. Ruperez (Spain)
WG5. Teaching mixed-ability classes.
CO: Liora Linchevski (Israel)
Every session will be devoted to a different topic
related to the Learning of
Mathematics in Mixed-Ability classes as follows:
AP: Margaret Cozzens (USA), Zmira Mevarech (Israel)
LO: Francisco Esteban (Spain)
ability grouping vs.
mixed ability classrooms: a look from a theoretical and
(b) innovative methods designed for
mixed ability classrooms;
(c) alternative assessments emerge from the mixed
ability classes needs;
teacher training for mixed ability classes.
WG6. Gender and mathematics.
CO: Barbro Grevholm (Sweden)
Gender and mathematics encompasses a broad range of
aspects have been explored at conferences and in recent
spite of this solid foundation, research perspectives and
practices and intervention may need to be re-examined and
topics relevant to gender and mathematics will be
research perspectives; manifestations of gender inequities;
and social conditions associated with equity issues;
and local cooperation in research; focus on directions
for change in
educational contexts. In each case, short presentations from
perspectives will be followed by discussions and work in
AP Jeff Evans (UK), Roberta Mura (Canada), Fidela
LO: M& Eugenia Jimenez (Spain)
WG7. Mathematics for gifted students.
CO: Vladimir Burjan (Slovak Republic)
WG7 will focus on: the notion (phenomenon) of "giftedness" (who
mathematically gifted students? which are the characteristics?
how can we recognize?...); approaches to identification and
mathematical giftedness within the educational systems; what
should be the gifted taught and how?, which out-of-class
activities must be organized for the mathematically
AP: Fou Lai Lin (China-Taiwan), John Webb (South
LO: Diego Alonso Canovas (Spain)
WG8. Mathematics for students with special needs.
CO: Jens Holger Lorenz (Germany)
The working group will try to identify which are the main
possible solutions, in the teaching and learning of
mathematics for students
with special needs.
AP: Marie-Jeanne Perrin-Glorian (France), Nuria
Rosich (Spain), Olof
LO: Luis M. Casas Garcia (Spain)
WG9. Innovation in assessment.
CO: Antoine Bodin (France)
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.
AP: Kenneth Travers (USA), Bengt Johansson (Sweden),
Movshovitz-Hadar (Israel), Vicente Riviere (Spain),
Gill Close (UK)
LO: Adela Jaime (Spain)
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)
The working group will focus the attention on activities which
transition from properties and relations dicovered in
and real situations to verbal an written presentations, and from
graphical languages (drawings, diagrams, graphs,...) and
AP: Ferdinando Arzarello (Italy), Joop van Dormolen
LO: Alicia Bruno (Spain)
WG11. A curriculum from scratch (zero-based).
CO: Anthony Ralston (USA)
Suppose mathematics education did not exist and you
needed to invent in
1996. What would the curriculum look like? The Working
address this question with the aim of assessing how far
from the current K-
12 curriculum an ideal curriculum would be and, also, how
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
testing and, as well, will consider what research in
can tell us about a zero-based curriculum. It is intended
to publish a
proceedings consisting of the papers presented and the
AP: Hugh Burkhardt (UK), Nerida Ellerton
(Australia), Susan Groves
(Australia), Rolf Hedren (Sweden)
LO: Salvador Guerrero (Spain)
WG12. Curriculum changes in the primary school.
CO: Mary Lindquist (USA)
Curriculum Changes in Primary Mathematics focus on
expectations of students, change in the mathematics
content, change in the
sequencing, research that supports change, recommendations for
change. Participants should bring curriculum documents
of their country,
region, or school and a brief description of the major
thrusts and recent
AP: Maria Canals (Spain), Michala Kaslova (Czech
Rep.), Hans Nygaard
LO: Carmen Burgues (Spain)
WG13. Curriculum changes in the secondary school.
CO: Martin Kindt (Netherlands)
In this group we will focus the discussions on the
Geometry; Discrete Mathematics (graph theory, combinatorics,
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
changing view on learning; changing societ, changing
AP: Abraham Arcavi (Israel), Margaret Brown (UK),
Eizo Nagasaki (Japan),
F. Villarroya (Spain).
LO: Francisco Garcia (Spain)
WG14. Linking mathematics with other school subjects.
CO: Fred Goffree (Netherlands)
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
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
teaching, reports from development and research on this
presentations of paradigms of integrated math lessons,
concerning low and
high achievers when maths is linked with other school
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
school subjects needs a balance between maths learning
in contexts and
maths learning in isolation".
AP: Rolf Biehler (Germany), Mario Carretero (Spain),
Kurt Kreith (USA),
Howard Tanner (UK).
LO: Mariano Dominguez (Spain)
WG15. The impact of technology on the mathematics Curriculum.
CO: Michal Yerushalmy (Israel)
Technology is currently central in many of the attempts to reform
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
manipulating mathematical objects, and in carrying out
The development of many new technology-intense
around the world suggests a serious discussion of the
problems raised by widespread use of technology in school
The group will concentrate on three major characterizations of
technology-intense curriculum reform:
AP: David Chazan (USA), Al Cuoco (USA), Koeno
(Netherland), John Monaghan (UK)
LO: Jacinto Quevedo (Spain)
1. Modeling based curricula: curriculum which is
organized around "real
life" applications that create opportunities to learn
2. Curricula organized around big mathematical ideas:
re-think the organization and the emphases of the current
content of the curriculum.
3. Curricula organized around new themes and topics:
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)
The aim of this working group is to discuss both from a
practical point of view the changes in the mathematics
computers and graphing calculators are introduced in the
AP: Manuel Armas (Spain), Jim Fey (USA), Maria Mas-
LO: Miguel de la Fuente (Spain)
WG17. Mathematics as a service subject at the tertiary
CO: Eric Muller (Canada)
This group aims to provide participants with opportunities to
share experiences relating to their teaching of
mathematics as a service
subject. The group will consider, but will not be limited
by, the following
AP: Jairo Alvarez (Colombia),
Fred Simons (Netherlands)
LO: Ceferino Ruiz (Spain)
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
3. What service course experiences assist
development of mathematical reasoning as it pertains to
their area of
specialization? The overall aim is to suggest methods by
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)
The goal of this WG is to propose a set of recomendations related
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
should be considered, what achievements levels should be
aimed at, what
teaching, strategies can be used, etc.
AP: Diana Cohen (UK)
LO: Antonio Renguiano (Spain)
WG19. Preparation and enhancement of teachers.
CO: Marjorie Carss (Australia)
The mathematics curriculum in all countries faces the
challenge of social
change, developments in information technology, and
mathematics itself. How do we prepare teachers to be
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
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
if they are to continue as effective teachers and as
teachers who can reliably
describe classroom interactions and evaluate and record
AP: Barbara Jaworski (UK), Milan Koman (Czech Rep.)
LO: Jose Ramon Pascual (Spain)
WG20. Evaluation of teaching, centers, and systems.
CO: David Robitaille (Canada)
One focus of the Working Group will be on prominent cases
activity in mathematics education around the world which
role of teachers and teacher education in mathematics
education, how the
role of teachers is changing. A second focus will be on
approaches to evaluation including the use of portfolios,
assessment, and others. A panel discussion will be a
featur of the first
session of the WG, and subsequent sessions will include
presentations and group discussions.
AP: Fernando Hernandez-Guarch (Spain), Norman L. Webb (USA)
LO: Antonio Molano (Spain)
WG21. The teaching of mathematics in different cultures.
CO: Jerry Becker (USA)
The program will provide for presentation, discussion and
current research on culture and mathematics teaching and
exchanging perspectives (e.g., the role of language in
relationships between teachers and students); consideration of
prior experiences as a basis for constructing knowledge;
contributions to the development of specific mathematics
systems, arithmetic, problem solving); development of new
research and cross-cultural research of critical aspects
understanding and problem solving inside and outside
AP: Sunday A. Ajose (USA), Andy Begg (New Zealand),
T. Fujii (Japan),
Martha Villavicencio (Peru)
LO: Andres Marcos (Spain)
WG22. Mathematics, education, society, and culture.
CO: Richard Noss (UK)
The group will focus on the social and cultural dimensions of
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
AP: Cyril Julie (South Africa), Jean M. Kantor
(France), Catherine Vistro-Yu
LO: Jose L. Alvarez (Spain)
WG23. Cooperation among countries and regions in mathema-
CO: Bienvenido Nebres (Philippines)
WG23 will focus on the possible cooperation among
countries and regions
in order to improve mathematics education at the
AP: Emma Garcia Mora (Spain), John Egsgard (Canada), Murak Jurdak (Lebanon), Aderemi Kuku (Nigeria), Bernardo Montero
LO: Mercedes Garcia (Spain)
WG24. Criteria for quality and relevance in mathematics
CO: Kenneth Ruthven (UK)
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:
AP: Robert Davis (USA), Angel Gutierrez (Spain)
LO: Salvador Llinares (Spain)
- the award of a doctoral degree in mathematics
- publication in a refereed journal in mathematics
- inclusion in a course aimed at the professional
preparation or development
of mathematics teachers;
- to inform policy formation in mathematics teaching and
of professional guidelines;
- to design resources for mathematics teaching, such as
textbooks and other
WG25. Didactics of mathematics as a scientific
CO: Nicollina Malara (Italy)
The working group will face the following questions:
AP: Carmen Azcarate (Spain), Hans-Georg Steiner
LO: Maria del Carmen Batanero (Spain)
1. Which paths have we followed in order to arrive at the
Didactis of Mathematics as a scientific discipline? Is
the vision agreed on
internationally? To what extent?
2. Is the difference between "Didactics of Mathematics"
Education" only a linguistic problem due to different
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,
anthropology, etc. In what way is it related to each of
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
CO: Beatriz D'Ambrosio (USA)
Throughout the sessions of this working group we hope to
discussions in which participants share their experiences in
bridging the gap
between research and practice. We will explore the
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
our discussions. Examples of questions that may arise
include the following:
AP: Luciana Bazzini (Italy), Morten Blomhoj (Denmark), Sandy
LO: Lorenzo Blanco (Spain)
What practices seem effective in bridging the gap
between research and
practice? What counts as research? What counts as
practitioner research be considered a form of scholarship? Does
research help bridge the gaps between theory and
practice? What are the
means through which scholarly work impacts the work of
These are but a few of the questions that we anticipate will
the working group discussions.
TG1. Primary school mathematics.
CO: Regine Douady (France)
In present-day society, every citizen needs to have at
his/her disposal a
certain mathematical knowledge. Work starts at elementary school
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
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
on their ability to make hypotheses, choices, arguments, to
misdirected choices and make new ones, in order to deal
context? Can one detect regularities beyond the diversity of
The group TG1 will be devoted to debating on the
elementary school is concerned, of such questions and
other ones arising
from the points mentionned above. Pieces of work will be
are related to the above problematic - possibly opposed to it
arguments, and which have been produced since ICME 7.
AP: J. Klep (Netherlands), Helen Mansfield (USA)
LO: Francisco T. Sanchez-Cobo (Spain)
TG2. Secondary school mathematics.
CO: Glenda Lappan (USA)
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
focus on work that helps illuminate questions such as the
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
Between secondary school and higher education? Between
and the world of work?
AP: Dirk Janssens (Belgium), Hans C. Reichel
LO: Juan Gallardo (Spain)
TG3. University mathematics.
CO: Joel Hillel (Canada)
This group will examine how the traditional university
curriculum is being influenced by general phenomena such
as: changes in
the student clientele in terms of their mathematical
and aspirations; results of research in mathematics
education related to
undergraduates' learning of specific topics; computer
specific mathematical software; new emphases within the
mathematics; changes in employment prospects for students
AP: Francine Gransard (Belgium), Habiba El Bouaz-
zaoui (Marocco), Lee
Peng Yee (Singapur)
LO: Jose Carmona Alvarez (Spain)
TG4. Distance learning of mathematics.
CO: Haruo Murakami (Japan)
The group will examine the latest innovations on the
distance learning of
mathematics with special reference to the use of
AP: David Crowe (UK), Nerida Ellerton (Australia)
LO: Jose M. Gairin (Spain)
TG5. Education for mathematics in the working place.
CO: Annie Bessot (France)
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
situations? what are the appropriate research methods for
of the vocational use of mathematics? what changes in the
mathematics will be brought about by technologica
progress (including the
growing use of computers) in vocational education?
AP: Marilyn Mays (USA), Jim Ridgway (UK)
LO: M. Dolores Eraso (Spain)
TG6. Mathematics teaching from a constructivist point of
CO: Ole Bjoerkqvist (Finland)
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
Another focus is on the reverse process, the impact of
current practice and
educational policy on theories of learning mathematics
and the nature of
AP: Jere Confrey (USA), Tadao Nakahara (Japan)
LO: M.V. Garcia-Armendariz (Spain)
TG7. The fostering of mathematical creativity.
CO: Erkki Pehkonen (Finland)
Creativity is a topic which is often neglected within
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
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
creativity within school situations? What scientific
knowledge, i.e. research
results, do we have on mathematical creativity?
AP: J.G. Greeno (USA), Yoshihiko Hashimoto (Japan)
LO: Lluis Segarra (Spain)
TG8. Proofs and proving: Why, when and how.
CO: Michael de Villiers (South Africa)
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
"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
students spontaneously produce themselves? What are
students' needs for
conviction and explanation? How can we demystify the
auxiliary lines in geometry proofs? What contexts can be
utilized to present
proof as meaningful activity?
AP: Fulvia Furinghetti (Italy), David Pimm (UK)
LO: Encarnacion Castro (Spain)
TG9. Statistics and probability at the secondary
CO: Brian Phillips (Australia)
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
statistics and probability can best be incorporated in
the overall school
AP: Ruma Falk (Israel), Juan A. Garcia-Cruz (Spain),
LO: Eliseo Borras (Spain)
TG10. Problem solving throughout the curriculum.
CO: Kaye Stacey (Australia)
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
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
organisation and structures, and empirical and
studies into thinking, learning and teaching.
AP: Maria L. Callejo (Spain), Mary Falk (Colombia),
Diana Lambdin (USA)
LO: Jose Carrillo (Spain)
TG11. The future of calculus.
CO: Ricardo Cantoral (Mexico)
The aim of the group is to support the improvement of the
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
Calculus. We want to organize the interaction (reflection and
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
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
Mathematics and Differential Equations? Which conceptions of the
of the Calculus and of its teaching are at the base of
How has the new technology affected the teaching
Calculus? What does
mean "understand" in the Calculus domain?
AP: Peter Bero (Slovaquia), Paul Zorn (USA)
LO: Jordi Deulofeu (Spain)
TG12. The future of geometry.
CO: Joe Malkevitch (USA)
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
tilings, and computational geometry, to name but a few.
This rapid growth
has been accompanied with broadening applicability to
processing and computer graphics, knotting of DNA, etc.
developments create challenges for mathematics educators
emerging with traditional geometry. One important
consideration is the use
of software systems to help with visualization and
AP: Maria A. Mariotti (Italy), Richard Pallascio (Canada)
LO: Francisco Castro (Spain)
TG13. The future of algebra and arithmetic.
CO: Joaquin Gimenez (Spain)
In this topic group there will be selected presentations on
aspects, projects and proposals for the new ways of
treating algebra and
airthmetic throughout the curriculum.
AP: Teresa Rojano (Mexico), Barbara Wittington (USA)
LO: Bernardo Gomez-Alfonso (Spain)
TG14. Infinite processes throughout the curriculum.
CO: Bruno D'Amore (Italy)
Numbers, sequences, functions, iterative methods,
fractals,... infinite processes play a role throughout
the curriculum. The
topic group will treat the various aspects of this
AP: Raymond Duval (France), Vera W. de Spinadel
LO: M. Carmen Penalva (Spain)
TG15. Art and mathematics.
CO: Dietmar Guderian (Germany)
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
AP: Nat Friedman (USA), Doris Schattschneider (USA)
LO: Rafael Perez-Gomez (Spain)
TG16. History of mathematics and the teaching of
CO: Louis Charbonneau (Canada)
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.
AP: Evelyne Barbin (France), Man Kenng Siu (Hong
LO: Santiago Fernandez (Spain)
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
contribution of history.
TG17. Mathematical modelling and applications.
CO: Joao Pedro da Ponte (Portugal)
The topic group Mathematical modeling and applications
consider the questions addressed at the previous ICME
philosophy of MMA, role of computers, assessment, and
and then turn to the questions left open. Through invited
general discussion, the group will consider both the
student and the
teacher: what are appropriate learning objectives
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?
AP: Werner Blum (Germany), Qi-Xiao Ye (China)
LO: Carles Llado (Spain)
TG18. Roles of calculators in the classroom.
CO: Pedro Gomez (Colombia)
The main goals of the group will be to inform, develop
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
relationship between calculator use and Mathematics
curriculum. Some of
the topics that can be treated are those concerning the
calculators and: Goals of Mathematics Education;
to be taught (nature, programs, materials, content,
(understanding, achievement, attitudes) and Teaching
AP: Nestor Aguilera (Argentina), Bert Waits (USA)
LO: Juan M. Garcia-Dozagarat (Spain)
TG19. Computer-based interactive learning.
CO: Nicolas Balacheff (France)
In recent years, our computer-based ability to connect
representations of knowledge in mathematics have become
powerful and flexible. The reification of mathematical
computer-based learning environments, and accompanying
mathematical experience due to progress in interface
design and knowledge
representation (ie internal structures), widen and deepen
experiential learning. Some of these environments even
involve tools or
models that adapt to the learner or guide their learning. Such
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?
mathematical knowledge transformed when instantiated in
computational environments (the computational
mathematics)? How can teachers bridge between low
technology and high
technology approaches to teaching and learning? Dealing
questions is essential to the productive use of technology by
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
from the collaboration of at least two communities,
mathematics-educators, TG 19 will address each of them
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:
the new realism of mathematics; Managing didactical
learning, collaborative learning and distributed or
Problems, limits, and potentials of the teacher/machine
Understanding learners' understanding and the issue of
Computational transposition of mathematics and related
issues; the contribution and limits of AI; the
contribution and limits of the
WWW as a Computer-based interactive learning environments
AP: James J. Kaput (USA), Tomas Recio (Spain)
LO: Claudio Sanchez (Spain)
TG20. Technology for visual representation.
CO: Rosamund Sutherland (UK)
The advent of fast and sophisticated computer graphics
has made dynamic
and interactive visual images accessible to mathematics
potentially changes the ways students work with
mathematics and the
mathematics they work with. This topic group will centre
following themes as they relate to the use of technology for
representation: the relationship between internal and
representations; the role of diagrams (static, dynmic,
mathematical thinking; using the visual as an analytic
differences influencing students' use of visual
computational environments which promote the use of the
AP: Gerd Doctorow (Canada), Joel Schneider (USA)
LO: Francisco Martin Casadelrrey (Spain)
TG21. Mathematics instruction based on manipulative
CO: Ana Garcia-Azcarate (Spain)
In this group we will focus the attention on manipulative
can be used in the classroom in order to improve
AP: David Fielker (UK), Marion Walter (USA)
LO: Ladislao Navarro (Spain)
TG22. Mathematical games and puzzles.
CO: Aviezri Fraenkel (Israel)
Among the main questions to be explored at TG22: Why are
so complex? Any new tools to analyze them? New ways of
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?
applications? How do games contribute to education?
AP: David Singmaster (UK), Fernando Corbalan (Spain)
LO: Manuel Garcia-Denis (Spain)
TG23. Future ways of publishing in mathematics
CO: Don Albers (USA)
1. In this reapidly evolving electronic world, what is
meant by a
AP: Gerhard Koenig (Germany), David L. Rodgers (USA),
LO: Jose Cobos-Bueno (Spain)
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
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
6. How should copyright and issues of intellectual
property rights be
handled in the electronic environment?
TG24. Mathematics competitions.
CO: Patricia Fauring (Argentina),
The group will present many recent experiences on the
mathematics competitions in different levels, regions,
international perspectives. The implications of such
competitions for the
improvement of mathematics education will be faced.
AP: Claude Deschamps (France)
LO: Pedro J. Martinez (Spain)
TG25. Mathematics clubs.
CO: Jenny Henderson (Australia)
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.
AP: Pedro Esteves (Portugal)
LO: Jose M. Sanchez Molina (Spain)
TG26. International comparative investigations.
CO: Gabriele Kaiser (Germany)
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
comparative study. Both large and small-scale studies
will be examined
including, among others: Second International Mathematics
Third International Mathematics and Science Study
(TIMSS), Survey of
Mathematics and Science Opportunities (SMSO), First and
of International Assessment of Educational Progress
Japanese Comparative Studies, Mathematics Teaching and
The second session will be a panel discussion focusing on the
can we learn from international comparative investigations.
Experts in the
field will discuss selected relevant aspects such as
classroom reality, global cooperation, regionalization.
AP: Juan Diaz-Godino (Spain), Murad Jurdak
(Lebanon) Eduardo Luna
(Dominican Republic), Eduardo Lacasta (Spain)
LO: Juan Calderon (Spain)
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17 June 1996