
8th International Congress on Mathematical Education
SCIENTIFIC PROGRAM 
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Index
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)
"Socialphilosophical 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 weekends. On weekdays 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.
"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)
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
socialconstructivist 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.
BARTOLINIBUSSI, 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
schoolbased
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 sixyearold 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) Reinterpreting the mathematical discourse: we speak
(and think) as if there
were specific objects with the ascribed properties and
relations though we
only can access socalled 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 postmodernist
philosophy of mathematics,
since it dethrones logic as the foundation of mathematical
knowledge in favour of
decentred human practices and contextbound 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
doublefocused
targets (mathematical literacy and mathematical thinking), the
CoreOptions
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
nongeneralisable 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 undergraduate 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 selfcritical 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
problemsolving 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 "ComputerBased 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
alHaytham 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
postsecondary level
(s. ICME4) 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,
noneuclidean geometries, algebraic curves and surfaces and
computer graphics.
VIGGIANIBICUDO, 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)
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 mixedability 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 MixedAbility 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 reexamined 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 (ChinaTaiwan), 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 outofclass
and outofschool
activities must be organized for the mathematically
gifted?
WG8. Mathematics for students with special needs.
CO: Jens Holger Lorenz (Germany)
AP: MarieJeanne PerrinGlorian (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
MovshovitzHadar (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; selfassessment 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 uptodate 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 email 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 (zerobased).
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 ICME8 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 zerobased idea on pedagogy, teacher
education and
testing and, as well, will consider what research in
mathematics education
can tell us about a zerobased curriculum. It is intended
to publish a
proceedings consisting of the papers presented and the
discussions at
ICME8.
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
CHANGEnew
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 (1216; 1619) 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 technologyintense
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
technologyintense 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
rethink 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 twentyfirst 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 HernandezGuarch (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 crosscultural 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 VistroYu
(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 socioeconomic 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), HansGeorg 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 worksessions 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.
TG1. Primary school mathematics.
CO: Regine Douady (France)
AP: J. Klep (Netherlands), Helen Mansfield (USA)
LO: Francisco T. SanchezCobo (Spain)
In presentday 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" (ICME7). 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. GarciaArmendariz (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
socalled
"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. GarciaCruz (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
interdisciplinary 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
teachinglearning
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 GomezAlfonso (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 PerezGomez (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), QiXiao 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. GarciaDozagarat (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. Computerbased interactive learning.
CO: Nicolas Balacheff (France)
AP: James J. Kaput (USA), Tomas Recio (Spain)
LO: Claudio Sanchez (Spain)
In recent years, our computerbased ability to connect
and manipulate
representations of knowledge in mathematics have become
ever more
powerful and flexible. The reification of mathematical
knowledge in
computerbased 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 computerintensive 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 computerbased interactive learning
environments results
from the collaboration of at least two communities,
computerscientists and
mathematicseducators, 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 Computerbased 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 GarciaAzcarate (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 GarciaDenis (Spain)
Among the main questions to be explored at TG22: Why are
2player 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, errorcorrecting
codes, graph and
matroid theory, networks, online 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 CobosBueno (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 DiazGodino (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
stateoftheart 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 smallscale 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