The International Commission on Mathematical Instruction
ICMI
Bulletin No. 42
June 1997
Editor:
Mogens Niss
IMFUFA, Roskilde University
P.O.Box 260, DK 4000 Roskilde
DENMARK
Table of Contents
(The page numbers below refer to the hardcopy version of this Bulletin.)
Executive Committee 1
Report on ICMI activities in 1996 3
ICMI Accounts 1996 6
ICMI Study on The Role of the History of Mathematics
in the Teaching and Leraning of Mathematics - Discussion Document 9
The International Programme Committee for ICME-9 17
ICMI Study on University Mathematics 18
ICMI WMY 2000 Committee 18
French Donation for ICMI's Solidarity Fund 19
Mathematics Education in Germany 19
A Tribute To David Wheeler 20
Announcement concerning 'For the Learning of Mathematics' 28
Future Conferences 29
ICMI and the ICMI Bulletin on the World Wide Web and on E-Mail 37
National Representatives 38
The International Commission on Mathematical Instruction
Executive Committee 1995-1998
President:
Miguel de GUZMAN,
Facultad de Ciencias Matematicas, Universidad Complutense,
28040 Madrid, SPAIN
Vice-Presidents:
Jeremy KILPATRICK,
Department of Mathematics Education, University of Georgia,
105 Aderhold Hall, Athens, GA 30602-7124, USA
Anna SIERPINSKA,
Department of Mathematics and Statistics, Concordia University,
7141 Sherbrooke St. W., Montreal, Quebec H4B 1R6, CANADA
Secretary:
Mogens NISS,
IMFUFA, Roskilde University,
P.O. Box 260, DK-4000 Roskilde, DENMARK
Members:
Colette LABORDE,
Laboratoire IMAG - Leibniz, Universite Joseph Fourier - CNRS,
46 avenue Felix Viallet, 38031 Grenoble Cedex 1, FRANCE
Gilah LEDER,
Graduate School of Education, La Trobe University,
Bundoora, VIC 3083, AUSTRALIA
Carlos E. VASCO,
Depto. de Matematicas y Estadistica, Universidad Nacional de Colombia,
Ciudad Universitaria, Santafe de Bogota, D.C., COLOMBIA
ZHANG Dianzhou,
Department of Mathematics, East China Normal University,
3663 Zhongshan Rd. (Northern), 200062 Shanghai, CHINA
Ex-Officio Members:
David MUMFORD,
Department of Mathematics, Harvard University,
Cambridge, MA 02138-2901, USA
(President of IMU)
Jacob PALIS Jr.,
IMPA, Estrada Dona Castorina, 110,
Jardim Botanico, 22460 Rio de Janeiro, RJ, BRAZIL
(Secretary of IMU)
Legend: IMU stands for The International Mathematical Union.
Report on
ICMI activities in 1996
1. Organisation
The General Assembly of ICMI held its quadriennial session in
conjunction with the 8th International Congress on Mathematical
Education, ICME-8, held at Reina Mercedes campus of the Universidad de
Sevilla, Spain, in July 1996. The General Assembly was held on 17th
July 1996. The minutes of the Assembly are published in the ICMI
Bulletin No. 41, December 1996, pp 3-9.
The Ececutive Committee had its second meeting at ICME-8 as well. The
EC meeting was devided into three sessions, held on the 13th, 14th,
and 19th July. Beside in meetings, the work in the EC is conducted by
correspondence and electronic communication under the direction of the
President and the Secretary.
In recent years, applications from a number of countries to be
co-opted as non-IMU member states of ICMI have been received by the
EC. At the end of 1996 ICMI decided, with the endorsement of the
International Mathematical Union, to co-opt Thailand as a non-IMU
member of ICMI. The Adhering Organisation is the Mathematical
Association of Thailand under the Patronage of His Majesty the
King. Other applications were considered by the EC in 1996. Decisions
are likely to be made in 1997.
It is part of ICMI's general policy to encourage member states to
establish National Sub-Commissions of ICMI. In 1996 the EC was not
informed of the establishment of new National Sub-Commissions.
2. ICMEs
The latest of the quadriennial International Congress on Mathematical
Education, ICME-8, was held at Universidad de Sevilla, Reina Mercedes
campus, 14-21 July. The congress had an attendance of about 3500
delegates from almost a hundred different countries. The programme was
very rich and intensive. Proceedings of the Congress are in
preparation. A novel feature in the ICME series was instigated at
ICME-8. A 10% solidarity tax was imposed on all registration fees in
order to provide (partial) financial support of the attendance of
about 250 delegates from about 55 different non-affluent
countries. The amount thus generated was distributed by a specially
appointed Grants Committee which worked incognito in order to minimise
potential problems of pressure. The Grants Committee will publish a
separate report of its work.
The next congress, ICME-9, will be held in Makuhari, Chiba, Japan, in
2000. Preliminary dates are 31 July to 7 August. An International
Programme Committee was appointed in 1996. It is chaired by Professor
Hiroshi Fujita, Meiji University, Tokyo, Japan. The IPC is expected to
begin its work early in 1997.
3. ICMI Studies
The mounting and conducting of so-called ICMI studies on crucial
themes and issues in mathematics education was continued in 1996. The
ICMI studies are published by Kluwer Academic Publishers, Dordrecht,
the Netherlands, under the general editorship of the President and the
Secretary of ICMI.
The study on What is Research in Mathematics Education, and What Are
Its Results?, the corresponding conference of which was held at the
University of Maryland in College Park, USA, May 1994, is edited by
Jeremy Kilpatrick and Anna Sierpinska. The volume is expected to
appear in the beginning of 1997.
The study on Perspectives on the Teaching of Geometry for the 21st
Century, the corresponding study conference of which was held at
Universita di Catania, Italy, September-October 1995, is edited by
Vinicio Villani and Carmelo Mammana. The volume is expected to appear
in the course of 1997.
Reports on the these studies, and on one a previously completed,
Gender and Mathematics Education, were given at special ICMI study
sessions at ICME-8, in Sevilla, July 1996.
The next study in the series is devoted to the theme The Role of the
History of Mathematics in the Teaching and Learning of mathematics. An
International Programme Committee was appointed in 1996, with John
Fauvel, the Open University, UK, and Jan van Maanen, the University of
Groningen, the Netherlands as co-chairs. The study conference will be
held in France, most probably at CIRM Luminy (Marseille) in April
1998, with Jean-Luc Dorier, Grenoble, France, in charge of the Local
Organisation.
The ICMI EC has also decided to mount a study on the Teaching and
Learning of Mathematics at Tertiary level. The IPC is expected to be
appointed in beginning of 1997. The site of the corresponding study
conference is under negotiation.
4. Regional Conferences
In 1996, 3-7 June, SEACME-7 (The 7th South East Asian Conference on
Mathematical Education) was held in Hanoi (Vietnam) with 135
participants from 17 countries. A brief report of the conference,
which was sponsored by ICMI as an ICMI Regional Meeting, was published
in the ICMI Bulletin, No. 41, December 1996.
5. Affiliated Study Groups
ICMI continues to have four affiliated study groups, HPM (The
International Study Group for the Relations Between the History and
Pedagogy of Mathematics), IOWME (The International Organisation of
Women and Mathematics Education), and PME (The International Group for
the Psychology of Learning Mathematics), and WFNMC (The World
Federation of National Mathematical Competitions). Separate reports of
their activities were published in the ICMI Bulletin Nos. 40 (HPM,
PME, and WFNMC) and 41 (IOWME), 1996.
6. The Solidarity Programme
In 1992 ICMI established a Solidarity Programme to help the
development of mathematics education in countries in which there is a
need for it that justifies international assistance. The first stage
in this programme was the mounting of a Solidarity Fund based on
private contributions by individuals, associations, etc. The Fund is
to be activated to support concrete initiatives and activities that
may foster solidarity in mathematics education between well-defined
quarters in developed and less developed countries. The Solidarity
Fund has received donations from various organisations and individuals
in mathematics education for which it is most grateful. In 1996 no
projects were supported by the Solidarity Fund. Although the total
funds are not excessive, the ICMI EC would welcome applications
concerning projects which are worthy of support in line with the
general aims of the Fund.
7. ICMI Bulletins
In 1996, ICMI Bulletin Nos. 40 and 41 were published under the
editorship of the Secretary of ICMI. Furthermore, the ICMI Bulletin is
available in the following electronic forms: In ASCII-format on direct
request to the editor. On the World Wide Web, where it can be found
under the following coordinates on the IMU-server, through URL:
http://elib./zib-berlin.de/imu.icmi.bull.[no.]
8. ICMI on WWW
Since the end of 1995, information concerning ICMI can be found on the
ICMI-pages of the IMU-server on the World Wide Web. The pages are
located through URL:
http://elib./zib-berlin.de/imu.icmi
Mogens Niss, Secretary, 3 February 1997
Roskilde University, Roskilde, Denmark
ICMI Accounts 1996:
1 January - 31 December
Swiss Francs Account:
Income:
balance 1995 118.685,25
IMU (Schedule A: Administration) 11.000,00
IMU (Schedule B: Scientific Activities) 22.000,00
IMU Contribution to ICME-8 12.000,00
interest 61,51
total 163.746,76
Expenditure:
transfer charges 19,22
transfer to US$ Account 10.000,00
ICMI balance 1996 153.727,54
total 163.746,76
Den Danske Bank exchange rate, ult. 1996: 1 CHF = 0,74 US$
Danish Kroner Account:
Income:
ICMI balance 1995 23.860,34
2. payment (US$ 1.000) of UNESCO 5.825,60
grant to ICMI Study on Geometry1)
total 29.685,94
Expenditure:
ICME-8, Secretary's expenses 11.069,84
EC meeting in Sevilla, at ICME-8 5.513,56
ICMI Study on Geometry, IPC/Editorial board 5.614,00
meeting, Secretary's expenses
typing of Bulletin 40 & 41 2047,50
credit card charge 150,00
transfer charges 30,00
ICMI Balance 1996 5.261.04
total 29.685,94
Den Danske Bank exchange rate, ult. 1996: 1 DKR = 0,16 US$
Sterling Account:
Income:
balance 1995 16.279,88
CUP royalties for studies 31,96
interest 560,20
total 16.872,04
Expenditure:
ICMI Study on Geometry, IPC/Editorial 514,08
board meeting, Trento
transfer charges 6,66
ICMI balance 1996 16.352,30
total 16.872,04
Den Danske Bank exchange rate, ult. 1996: 1 GBP = 1,61 US$
US Dollars Account:
Income:
ICMI balance2) 1995 541,17
Solidarity Fund balance2) 1995 32.761,69
ICMI interest, 29% of total (corresponding 348,32
to 1996 balance share)
Solidarity Fund interest, 71% of total 853,15
(corresponding to 1996 balance share)
transfer from Swiss Franc Account (10.000) 8.306,34
reimbursement of loan to ICME-8, given in 1994 10.000,00
Individual contribution to the Solidarity Fund 41,00
total 52.851,67
Expenditure:
ICME-8, including EC meeting 2.885,04
Contribution to the publication 2.500,00
'The History of the Inter-American Committe
on Mathematics Education'
transfer charges 63,55
Solidarity Fund balance 1996 33.655,84
ICMI balance 1996 13.747,24
(account balance 47.403,08)
total 52.851,67
Notes:
1. The UNESCO/ROSTE office generously contributed a grant of US$ 3.000
to the ICMI Study Conference on Perspectives of the Teaching of
Geometry for the 21st Century, held in Catania, Sicily (Italy), 28
September - 2 October 1995. The second installment of the payment,
which was initially divided into two parts - US$ 2.000 and 1.000,
respectively -
was made in 1996.
2. As a consequence of the ICMI General Assembly and Executive
Committee meetings held in Quebec, August 1992, it was decided to
establish an ICMI Solidarity Fund based on private contributions. The
Solidarity Fund is mounted to assist mathematics education and
mathematics educators in less affluent countries. Its money can only
be spent (by a committee chaired by Professor Jean-Pierre Kahane) to
serve such purposes and is therefore not part of ICMI's general
resources. However, the appearance of the Solidarity Fund on the ICMI
accounts for 1996 is due to the wish to keep ICMI's number of
different bank accounts low. The accounts exhibit the ICMI balances
and the Solidarity Fund balances separately. In 1996 the Solidarity
Fund balances were all concentrated in the US Dollar Account.
3. In addition to the amounts displayed directly in the accounts,
considerable extra sums should appear but do not and cannot. In 1995
Roskilde University (the Secretary's home institution) has contributed
a substantial support to ICMI's work (e.g. telephone and -fax, e-mail
facilities, postage, all the printing and distribution costs of the
Bulletin, plus secretarial help of various sorts). It is estimated
that the total contribution of Roskilde University is equivalent about
US$ 5.000. The ICMI Executive Committee expresses its gratitude for
this generous support.
The Executive Committee's thanks also go to the institutions of its
other members. These institutions, too, have given invisible support
to ICMI's work in a variety of ways. For instance, in many cases these
institutions have paid travel and other expenses related to
participation in EC meetings and soforth.
Mogens Niss
5 February 1997
ICMI Study on
The role of the history of mathematics
in the teaching and learning of mathematics:
Discussion Document
Introduction
In recent years there has been growing interest in the role of history
of mathematics in improving the teaching and learning of
mathematics. Educators throughout the world have been formulating and
conducting research on the use of history of mathematics in
mathematics education. Some of the results of this research have been
communicated at meetings of interested organisations, and through
papers in various journals.
A research programme is beginning to emerge, with contributions from
many places over the globe. Such a programme involves a consolidated
critical bibliography of work that has been done, and a programme for
developing a deeper understanding of the factors involved in the
relations between history and pedagogy of mathematics, in different
areas of mathematics, and with pupils and students at different stages
and with different environments and backgrounds. It also involves the
identification and spreading of information and good practice in
learning and teaching situations.
ICMI, the International Commission on Mathematics Instruction, has set
up a Study on this topic, to report back in time to form part of the
agenda at the next International Congress in Mathematics Education
(ICME) in Japan in the year 2000. The present document sketches out
some of the concerns to be addressed in the ICMI Study, in the hope
that many people across the world will wish to contribute to the
international discussions and the growing understandings reached in
and about this area.
It is hoped that this discussion document will lead to a number of
responses and intimations of interest in contributing to the Study. It
will be followed by an invited conference (to be held in France in
April 1998), from which a publication will be prepared to appear by
2000. The next section of the present document surveys the questions
to be addressed. Your views are solicited both on the questions and on
how to take the issues forward as implied in the commentary.
Some research questions
The overall intention is to study the role of history of mathematics,
in its many dimensions, at all the levels of the educational system:
in its relations to the teaching and the learning of mathematics as
well as with regard to teacher training and in educational
research. History of mathematics as a component of the teaching of
mathematics is, as any educational project, directed towards more or
less explicit expectations in terms of (better) learning of some
mathematics.
Research on the use of history of mathematics in teaching is thus an
important part of research in mathematical education. To study such a
large and multi-faceted theme we propose to analyse it in a number of
(inter-related) questions which together will give insight into the
whole process. The order in which the questions are put down here
carries no implication about their relative importance or
significance.
1. How does the educational level of the learner bear upon the role of
history of mathematics?
The way history of mathematics can be used, and the rationale for its
use, may vary according to the educational level of the class:
children at elementary school and students at university (for example)
do have different needs and possibilities. Questions arise about the
ways in which history can address these differences. This may, again,
be reflected in different training needs for teachers at these
levels. (To speak about the ``use'' of the history of mathematics may
seem to presuppose that history of mathematics is something external
to mathematics. This assumption would not be universally agreed,
however.
2. At what level does history of mathematics as a taught subjectbecome
relevant?
In analysing the role of history of mathematics, it is important to
distinguish issues around using history of mathematics in a situation
whose immediate purpose is the teaching of mathematics, and teaching
the history of mathematics as such, in a course or a shorter
session. It could be that courses in the history of mathematics, and
its classroom use, should be included in a teacher training curriculum
(see question 3). There is also a third area, related but separate,
namely the history of mathematics education, which is a rather
different kind of history.
3. What are the particular functions of a history of mathematics
course or component for teachers?
History of mathematics may play an especially important role in the
training of future teachers, and also teachers undergoing in-service
training. There are a number of reasons for including a historical
component in such training, including the promotion of enthusiasm for
mathematics, enabling trainees to see pupils differently, to see
mathematics differently, and to develop skills of reading, library use
and expository writing which can be neglected in mathematics
courses. It may be useful here to distinguish the training needs for
primary, secondary and higher levels (see question 1).
A related issue is what kinds of history of mathematics is appropriate
in teacher training and why: for example, it could be that the history
of the foundations of mathematics and ideas of rigour and proof are
especially important for future secondary and tertiary teachers. (This
issue is also relevant for other categories than future teachers, and
is picked up again in question 5.)
4. What is the relation between historians of mathematics and those
whose main concern is in using history of mathematics in mathematics
education?
This question focuses on the professional base from which
practitioners emerge, and relates to the social fabric of today's
mathematics education community as well as to issues about the nature
of history. There are, gratifyingly, a number of leading historians of
mathematics with an interest in educational issues, as there are
leading mathematicians and mathematics educators with an interest in
history. But as well as minor misapprehensions of the nature of the
others' activities, there may be deeper tensions and conflicting aims
which it is important to bring to the surface. For example, historians
may underestimate the difficulty of transmuting the historical
knowledge of the teacher into a productive classroom activity for the
learner. It is important that historians and mathematics educators
work co-operatively, since historical learning and classroom
experience at the appropriate level do not always co-exist in the same
person.
5. Should different parts of the curriculum involve history of
mathematics in a different way?
Already research is taking place to investigate the particularities of
the role of history in the teaching of algebra, compared with the role
of history in the teaching of geometry. Different parts of the
syllabus make reference, of course, to different aspects of the
history of mathematics, and it may be that different modes of use are
relevant. Looking at the curriculum in a broad way, we may note that
the histories of computing, of statistics, of core "pure" mathematics
and of the interactions between mathematics and the world are all
rather different pursuits.
Even for the design of the curriculum historical knowledge may be
valuable. A survey of recent trends in research, for example (bearing
in mind that history extends into the future) could lead to
suggestions for new topics to be taught.
6. Does the experience of learning and teaching mathematics in
different parts of the world, or cultural groups in local contexts,
make different demands on the history of mathematics?
A historical dimension to mathematics learning helps bring out two
contrary perceptions in a dialectical way. One is that mathematical
developments take place within cultural contexts and it is valid to
speak of Islamic mathematics, Greek mathematics and so on, as
developments whose style is characteristic of the generating
culture. The antithesis to this is the realisation that all human
cultures have given rise to mathematical developments which are now
the heritage of everyone; this therefore acts against a narrow
ethnocentric view within the educational system.
The Study should explore the benefit to learners of realising both
that they have a local heritage from their direct ancestors --in the
way in which Moslem children in countries where they are in a minority
are known to derive pride and strength from learning about Islamic
mathematical achievements-- but also that every culture in the world
has contributed to the knowledge and experience base made available to
today's learners.
There are many detailed studies of the interplay betwen history of
mathematics and culture in educational contexts throughout the world,
notably in Brazil, the Maghreb, Mozambique, China, Portugal etc, which
should be drawn upon in analysing and responding to this question.
7. What role can history of mathematics play in supporting special
educational needs?
The experience of teachers with responsibility for a wide variety of
special educational needs is that history of mathematics can empower
the students and valuably support the learning process. Among such
areas are experiences with mature students, with students attending
numeracy classes, with students in particular apprenticeship
situations, with hitherto low-attaining students, with gifted
students, and with students whose special needs arise from
handicaps. Here the many different experiences need to be researched,
their particular features drawn out, and an account provided in an
overall framework of analysis and understanding.
8. What are the relations between the role or roles we attribute to
history and the ways of introducing or using it in education?
This question has been the focus of considerable attention over recent
decades. Every time someone reports on a classroom experience of using
history and what it achieved they have been offering a response to
this question. So a search of the literature is a fundamental part of
researching the response to this question.
The question also involves also a listing of ways ofintroducing or
incorporating a historical dimension: for example anecdotal, broad
outline, content, dramatic etc. Then one would draw attention to the
range of educational aims served by each mode of incorporation: the
way that historical anecdotes are intended to change the image of
mathematics and humanize it, for example. Or again, the way that
mathematics is not, historically, a relentless surge of progress but
can be a study in twists, turns, false paths and dead-ends both
humanizes the subject and helps learners towards a more realistic
appreciation of their own endeavours.
There are rich issues for discussion and research in, for example, the
use of primary sources in mathematics classrooms at appropriate
levels.
This question is a very broad one that could involve a large number of
people: it may be wise to distinguish the taxonomic question --the
range of different classroom aims and modes of activity-- from the
further exploration of each issue.
9. What are the consequences for classroom organisation and practice?
The consequences of integrating history are far-reaching. In
particular, there are wider opportunities for modes of
assessment. Assessment can be broadened to develop different skills
(such as writing and project activity), and consequences for students'
interest and enjoyment have been noted. Teachers may well need
practical guidance and support both in fresh areas of assessment, and
in aspects of classroom organisation. This in turn may have
consequences for teacher training as well as curriculum design.
10. How can history of mathematics be useful for the mathematics
education researcher?
This question provides an opportunity for an exploration of the
relations between the subject of this study and researchers in the
mathematical education community (whose aims are, in turn, to provide
insights into the processes of learning and teaching). One example is
the use of history of mathematics to help both teacher and learner
understand and overcome epistemological breaks in the development of
mathematical understanding. A constructive critical analysis of the
view that 'ontogeny recapitulates phylogeny' --that the development of
an individual's mathematical understanding follows the historical
development of mathematical ideas-- may be appropriate. Another
example is of research on the development of mathematical concepts. In
this case the researcher applies history as possible 'looking glasses'
on the mechanisms that put mathematical thought into motion. Such
combinations of historical and psychological perspectives deserve
serious attention.
These issues could be studied in teaching experiments in which the
above questions are addressed, and also questions like: What is good
for the learner? How do you know it is good for the learner? and so
on. Even if a teaching experiment does not use history of mathematics
explicitly, the elaboration of the teaching project may have made use
of the results of history of mathematics. For instance, such a
question as 'is it good for the learner?' may be better understood in
the light of the history of mathematics. So the question here is: how
can research in mathematics education profit from historical
knowledge? The answer to this question might deal with themes such as
the historical genesis of a concept and an epistemological analysis of
the interplay between history and the teaching of a subject. Moreover,
history of mathematics helps to understand the distance between the
way in which concepts function in the mathematics community and the
way they function in the school.
There are also fundamental questions about the style and evaluation of
research in this area. Different styles which have been used in the
past range from the anecdotal (in effect) to quasi-scientific surveys
with questionnaires and statistical apparatus. A process of such
considerable complexity evidently calls for a research methodology of
some sophistication. Fortunately the wider mathematics education
community has been studying this problem for some time: it is indeed
the subject of an earlier ICMI Study (What is research in mathematics
education and what are its results?). So a group could be encouraged
to draw upon the wider community experience and consider its
application to our area of concern.
11. What are the national experiences of incorporating history of
mathematics in national curriculum documents and central political
guidance?
This is not so much a question for discussion as a fairly
straightforward empirical question, needing input from knowledgeable
people in as many countries and states as possible. But of course it
has policy implications too, and could lead to a sharing of experience
among members of the community about how they have reached the
policy-making level in their countries to influence the content or
rhetoric of public documents. Perhaps this study could be carried on
in parallel with the more discursive questions, organised by a small
group who could put the results (in the sense of public documents or
quotations from them as well as brief historical accounts of national
curriculum change) on the WorldWideWeb as they are collected.
In some parts of the world a different relationship between history
and mathematics may have been developed. For example, in Denmark and
Sweden history of mathematics is regarded as an intrinsic part of the
subject itself. There are also differences in styles of examination
and assessment. If everyone with access to examples of such different
approaches, from different countries and states, could pool their
experience it would be a most valuable input to the Study.
12. What work has been done on the area of this Study in the past?
The answer is: quite a lot. But it is all over the place and needs to
be gathered together and referenced analytically. A major annotated
critical bibliographical study of the field, which might well take up
a sizable proportion of the final publication, would be an enormously
valuable contribution that the ICMI Study could make. It should
include a brief abstract of each paper or piece of work included, and
indications of the categories to which the work relates in an
analytical index.
The organisation of this sub-project will need to be different from
that of the rest of the Study. It will need to be even more pro-active
to achieve a useful result. A small group should perhaps take this in
hand and work out how it can be achieved collaboratively. Some
progress on such a bibliography is already in hand in various places,
notably by Fred Rickey in the US, John Fauvel in the UK. This seems
another place where work in progress could be available on the
WorldWideWeb.
Bibliography
Here are, as a small selection to start with, some of the places in
which work on the above topics has appeared in recent years.
Calinger, Ronald (ed), Vita mathematica: historical research and
integration with teaching, Mathematical Association of America 1996
Fauvel, John (ed), History in the Mathematics Classroom. The IREM
Papers, The Mathematical Association 1990 (translation from the French
of papers by the Committee Inter-IREM, combined with classroom
resources)
Fauvel, John (ed), For the learning of mathematics 11 no 2 (June 1991;
special issue on using history of mathematics in the mathematics
classroom)
Fuehrer, Lutz (ed), mathematik lehren 19 (December 1986; special issue
entitled 'Geschichte -- Geschichten')
IREM de Franche-Comte (coll.ed), Contribution d'une approche
historique de l'enseignement des mathematiques, Besancon 1996
(proceedings of the 6th Summer University, Besancon July 1995)
IREM de Montpellier (coll.ed), Histoire et epistemologie dans l'
education mathematique, Montpellier 1995 (proceedings of the
first European Summer University, Montpellier August 1993)
McKinnon, Nick (ed), The mathematical gazette 76 no 475 (March 1992;
special issue on using history of mathematics in the teaching of
mathematics)
Nobre, Sergio (ed), Meeting of The International Study Group on
Relations Between History and Pedagogy of Mathematics. Blumenau/
Brazil 25--27 July 1994, UNESP 1994
Schoenebeck, Juergen (ed.), mathematik lehren 47 (August 1991; special
issue about 'Historische Quellen fuer den Mathematikunterricht')
Swetz, Frank, et al (ed), 'Learn from the Masters!', Mathematical
Association of America 1995
Veloso, Eduardo (ed), Historia e Educac o
Matematica. proceedings/actes/actas, Braga/Lisbon 1996
Call for contributions
The ICMI Study on The role of the history of mathematics in the
teaching and learning of mathematics will investigate the above
questions over the next two years. The Study has three components: an
invited study conference, related research activities, and a
publication to appear in the ICMI Study series that will be based on
contributions to and outcomes of the conference and related research
activities. The conference will be held in April 1998 in France. The
major outcomes of the study will be published as an ICMI Study in 1999
and presented at the International Congress of Mathematics Education
in Japan in 2000.
The International Programme Committee (IPC) for the study invites
members of the educational and historical communities to propose or
submit contributions on specific questions, problems or issues
stimulated by this discussion document no later than 1 October 1997
(but earlier if possible). Contributions, in the form of research
papers, discussion papers or shorter responses, may address questions
raised above or questions that arise in response, or further issues
relating to the content of the study. Contributions should be sent to
the co-chairs (addresses below). Proposals for research that is on
its way, or still to be carried out, are also welcome; questions
should be carefully stated and a sketch of the outcome --actual or
hoped-for-- should be presented, if possible with reference to earlier
and related studies. All such contributions will be regarded as input
to the planning of the study conference.
The members of the International Programme Committee are
Abraham Arcavi (Israel),
Evelyne Barbin (France),
Jean-Luc Dorier (France),
Florence Fasanelli (USA),
John Fauvel (UK, co-chair),
Alejandro Garciadiego (Mexico),
Ewa akoma (Poland),
Jan van Maanen (Netherlands, co-chair),
Mogens Niss (Denmark, ex officio)
Man-Keung Siu (Hong Kong).
This document was prepared by John Fauvel and Jan van Maanen with the
help of Abraham Arcavi, Evelyne Barbin, Alphonse Buccino, Ron
Calinger, Jean-Luc Dorier, Florence Fasanelli, Alejandro Garciadiego,
Torkil Heiede, Victor Katz, Manfred Kronfellner, Reinhard
Laubenbacher, David Robertson, Anna Sfard, and Daniele Struppa.
Contributions should be sent to the co-chairs at the following
addresses:
John Fauvel, Mathematics Faculty, The Open University, Milton
Keynes MK7 6AA, England UK (j.g.fauvel@open.ac.uk)
Jan van Maanen, Department of Mathematics, University of
Groningen, P O Box 800, 9700 AV Groningen, The Netherlands
(maanen@math.rug.nl)
This document is also available on the World Wide Web at
http://www.math.rug.nl/indvHPs/Maanen.html#dd
The International Programme Committee for ICME-9
The International Programme Committee (IPC) for ICME-9, The Ninth
International Congress on Mathematical Education, to be held in
Makuhari, Chiba, near Tokyo, Japan, in July/August 2000 has now been
appointed by the Executive Committee of ICMI. The members are as
follows
Professor Hiroshi Fujita, Tokyo, Japan, Chair
Professor Claudi Alsina, Barcelona, Spain
Professor Jerry Becker, Carbondale, Illinois, USA
Professor Tania Campos, S o Paulo, Brazil
Professor Gila Hanna, Toronto, Ontario, Canada
Professor Cyril Julie, Belville, South Africa
Professor Gilah Leder, Bundoora, Victoria, Australia, representative of ICMI
Professor Lee, Peng Yee, Singapore, liaison officer between the IPC and the
Congress Organisers
Dr. Stephen Lerman, London, United Kingdom
Professor Tadao Nakahara, Hiroshima, Japan
Professor Nabuhiko Nohda, Tsukuba, Japan
Professor Toshio Sawada, Tokyo, Japan
Professor Heinz Steinbring, Dortmund, Germany
Professor Julianna Szendrei, Budapest, Hungary
Professor Wang, Chang-Pei, Beijing, China
Professor Miguel de Guzman, Madrid, Spain, ex officio, President of ICMI
Professor Mogens Niss, Roskilde, Denmark, ex officio, Secretary of ICMI
The IPC can be contacted through its Chair:
Professor Hiroshi Fujita,
Department of Mathematics,
Meiji University,
Higashimita, Tama-ku
Kawasaki-shi, 214
JAPAN
Tel: +81 44-934-7456
Fax: +81 44-934-7913 or +81 3-3822-2986
e-mail: fujita@math.meiji.ac.jp
ICMI Study on University Mathematics
The Executive Committee of ICMI has decided to mount an ICMI Study on
the Teaching and Learning of Mathematics at University Level. The
Study is directed by an International Programme Committee (IPC) which
is composed as follows:
Professor Derek Holton, Dunedin, New Zealand, Chair
Professor Nestor Aguilera, Santa Fe, Argentina
Professor Michele Artigue, Paris, France
Dr. Frank Barrington, Melbourne, Victoria, Australia
Professor Mohamed El Tom, Doha, Qatar
Dr. Joel Hillel, Montreal, Quebec, Canada
Professor Urs Kirchgraber, Zuerich, Switzerland
Professor Lee, Peng Yee, Singapore
Professor Alan Schoenfeld, Berkeley, California, USA
Professor Hans Wallin, Umeaa, Sweden
Professor Ye, Qi-xiao, Beijing, China
Professor Mogens Niss, Roskilde, Denmark ex officio, Secretary of ICMI
The first task of the IPC is to produce a so-called Discussion
Document for world-wide circulation. This Discussion Document will be
published in the next (December 1997) issue of this Bulletin, and
elsewhere. The next task is to organise an international Study
Conference which is to be held 8-12 December 1998 in Singapore.
Contacts with the IPC can be made through its chair
Professor Derek Holton
Department of Mathematics and Statistics,
University of Otago,
P.O Box 56, Dunedin,
NEW ZEALAND
Tel: +64 3 478-7759
Fax: +64 3 479-8427
e-mail: dholton@maths.otago.ac.nz
ICMI WMY 2000 Committee
In order to consider, plan and prepare the main aspects of ICMI's
involvement in the World Mathematical Year 2000, The ICMI WMY 2000
Committee has been formed. The Committee will work under the
chairmanship of ICMI's President, Professor Miguel de Guzman. The
Committee has the following members:
Professor Miguel de Guzman, Madrid, Spain, Chair
Professor Bernard Hodgson, Quebec City, Quebec, Canada
Professor Jean-Pierre Kahane, Orsay, France
Professor Hikosaburo Komatsu, Tokyo, Japan
Professor Lee, Peng Yee, Singapore
Professor Eduardo Luna, Miami Shores, Florida, USA
Professor Michael Neubrand, Flensburg, Germany
Professor Kaye Stacey, Melbourne, Victoria, Australia
The Committee may be contacted through its chair, Professor de Guzman,
at the address given at the beginning of this Bulletin, or by e-mail:
French Donation for ICMI's Solidarity Fund
The French National Sub-Commission of ICMI, C.F.E.M, has decided to
make a contribution to ICMI's Solidarity Fund and Programme
(established 1992) of French Francs 5.000. The Executive Committee of
ICMI is very grateful for this generous donation towards the
furtherance of mathematics education research and development through
projects and activities in places in which there is a need for it.
Mathematics Education in Germany
The German Sub-Commission of ICMI offers information about
'Mathematics Education in Germany', for all who are interested, and
especially for participants in The International Congress of
Mathematics, to be held in Berlin, Germany, in 1998. The information
is available on the WWW at the following address
http://www.mathematik.uni-wuerzburg.de/History/mathed.html
A Tribute to David Wheeler
The publication this summer of the 50th issue of For the Learning of
Mathematics (FLM) will herald the end of David Wheeler's editorship of
this well-known and respected mathematics education journal, a journal
he founded close to two decades ago and which he has produced almost
single-handedly by himself ever since then. Moreover, this year marks
the 50th anniversary of the beginning of David's remarkable career as
a mathematics teacher. David retired from Concordia University
(Montreal) in 1990, and has recently relinquished his position as
the Canadian national representative to ICMI. Thus it was felt by
many to be an excellent occasion to pay tribute to David's manifold
achievements and contributions to mathematics education.
We would like to thank all the authors below who kindly agreed to
collaborate with us in the preparation of this tribute. The personal
perspectives they provide in their testimony will undoubtedly help the
reader gain a sense of the variety and the depth of David's
involvement in mathematics education over half-a-century. We would
also like to thank Mogens Niss, editor of this Bulletin, for providing
a publication outlet through which this tribute to David Wheeler could
be shared broadly with the mathematics education community.
Bravo and thank you, dear friend David!
Bernard R. Hodgson
Universite Laval, Quebec, Canada
bhodgson@mat.ulaval.ca
A.J. (Sandy) Dawson
Simon Fraser University, Vancouver, Canada
dawson@sfu.ca
Some notes on David Wheeler's years as a mathematics educator in Britain
I first met David Wheeler in the late fifties at a local branch
meeting of ATAM (the Association for Teaching Aids in Mathematics,
later to become ATM, the Association of Teachers of Mathematics). When
the meeting broke up into small discussion groups I found myself in
one chaired by this amazingly impressive man with a generous laugh, a
warm and inviting manner yet with a sharp eye for fraud or
insincerity. Not for the last time, I found myself simultaneously
encouraged and challenged by his presence in the group. Such personal
influence has been the experience of many teachers who were fortunate
enough to work with him in some way during his professional life in
England.
David was already a key figure in the Association which had been
founded by Caleb Gattegno in 1952. He became an increasingly important
influence in mathematics education in Britain over the next two
decades. He was tirelessly active in a number of fields: after many
years teaching mathematics in London schools, he moved into
post-graduate teacher education at Leicester University, where he soon
became involved in the setting up of a study group with colleagues
from other universities (some readers will know the sort of influence
he had in this study group which was not unlike the one he initiated
many years later in Canada).
He continued to be involved in the work of ATM: he wrote regularly for
the journal of the association, "Mathematics teaching", contributed to
various books and edited a number of these (notably "Notes on
mathematics for children", Cambridge University Press, 1977). He
served on the committee of the association for many years, including a
particularly fertile spell as Secretary, and he was a regular seminar
leader at conferences. He became an outstanding editor of the journal
whose magisterial editorials still get re-printed from time to time;
his own wide interests and contacts ensured that the journal moved
from being something more like a local house magazine into an
authoritative and internationally respected journal.
Apart from all that, and apart from his normal university teaching and
administrative responsibilities, he was often running courses for
teachers outside his immediate local area, serving on national
committees, attending international conferences, giving radio talks on
the teaching of mathematics, writing articles in other educational
journals, commissioning and editing a series of textbooks, preparing
courses for the Open University - this latter yielding a remarkable
book, "R is for Real" (Open University Press, 1974) which deserves to
be more widely known.
Lists of achievements like the above are formal pieties which do not
convey the very special nature of the legacy that David left to his
many friends and colleagues in Britain. Perhaps this can be best be
captured in some of his own words. For many years I would ask groups
of prospective teachers to read his article on the Role of the Teacher
("Mathematics Teaching", no. 50, 1970, p23) . Discussion of this
article was always fruitful. For students who were on the edge of
their first experience of teaching, it was exhilarating and very
helpful to read his pungent reversal of the usual traditional advice
that a teacher faced with a new class needs first to establish
relationship. (A typically shrewd aside noted that "teacher-trainers
have one sort of language for this: experienced teachers another!")
For, "if the teacher takes the initiative in establishing
relationships before there are any tasks, the children will know that
the tasks do not have first priority; they are being thoroughly
logical in subsequently working on the relationships instead of the
tasks."
The article opened with the following paragraph: "If we know that
ineffective teaching of mathematics is not due to the difficulty of
the subject matter, and if we know that changing the classroom
environment .... does not contain within itself the possibility of
acting directly on the awarenesses of children, and if we then do not
re-examine in the most fundamental way how as teachers we should act,
we are guilty of a total failure of seriousness, for we have stopped
our progress towards a better education for children just short of the
point at which we can make a contribution to it."
David himself never stopped short of making a contribution, one that
was serious, challenging but sympathetic, and always tinged with
humour. In the words of the title of one of his ATM conference
lectures, he helped "humanise mathematical education". During the
sixties, he had been a central figure in the ATM research and develop-
ment group. He had not himself been a student of Gattegno's like many
other members of the group, but he was certainly the one who had the
most understanding in theory and practice of what Gattegno was
eventually to call the science of education.
It is perhaps typical of his own research in mathematics education
that at the height of a professional career in England he chose to
leave a tenured post and familiar ways to work with new challenges in
New York.
Dick Tahta
(retired) Exeter University, UK
d.tahta@open.ac.uk
Reminiscences of David Wheeler in New York
I don't have a clear recollection of my first meeting with David
Wheeler, although it was certainly in the early 1970's at Caleb
Gattegno's Educational Solutions. I started working for Educational
Solutions in various public schools in 1970 and Wheeler's name was
often mentioned (somewhat reverently) around the office. ATM
(Association of Teachers of Mathematics), MT (Mathematics Teaching),
David's connection to Gattegno and David, himself, were unknown to
me. These were all to change in the next couple of years.
I didn't see much of David when he first arrived. He mostly worked in
the downtown 5th Avenue office of Education Solutions and I in the
uptown 5th district of the New York City Public Schools. I don't know
how we came to know each other better, but it was undoubtedly through
some combination of seminars at Educational Solutions, the many
lunches at Brew Burger, and concerts at Carnegie Hall.
I appreciated David's wit and humor from our first meetings, but a
true respect for his mathematical insights came a short bit later. The
occurrence was a weekend workshop that he conducted using the black
and white Nicolet geometry films. He guided the participants through a
careful study of several of the films, revealing insight after
insight. What a tour de force! And I still have my notes.
There were occasions in New York when I was leading a workshop that he
was able, at a critical moment, to focus an uncertain
discussion. Then, and in many working groups of CMESG/GCEDM (Canadian
Mathematics Education Study Group / Groupe canadien d'etude en
didactique des mathematiques) that we participated in since, I have
come to value his uncanny ability to contribute when he is not the
leader, not by adding more layers of detail to an existing viewpoint,
but by illuminating it through the suggestion of complementary and
countervailing viewpoints.
David and I used to trade what seemed to us to be interesting math
problems. There must have been some discussion about their usefulness
in school settings, but the memory of the joy of solving them is more
prominent. After leaving New York he continued to send me problems and
I have maintained them in a file which I still utilize. Recently, a
discussion among members of my department on an equivalent of
Wythoff's Nim sent me back to that file. There it was, clearly
presented with follow-up suggestions from twenty years ago that the
current discussion had yet to consider.
There was one question that I used to frequently ask David to which he
did not have (or chose not to have) an unequivocal answer: "What do
you do in that office?" It was asked partly out of curiosity and
partly from the knowledge that I would have found it very difficult to
work in such close physical proximity to Gattegno.
In retrospect I think a partial answer to the question comes from
viewing his short stay in New York as a bridge spanning his
significant accomplishments with ATM and MT in the UK and with FLM
(For the Learning of Mathematics) and CMESG/G- CEDM in Canada. The
office allowed him to cross that bridge at an ideal pace;
contemplating the past, learning in the present and preparing for the
future. I feel fortunate to have accompanied him for even a small part
of that crossing.
Marty Hoffman
Queen's College, CUNY, New York, USA
martin_hoffman@qc.edu
Some aspects of David Wheeler's career in Canada
David Wheeler came to Canada in 1976 as professor of mathematics at
Concordia University in Montreal. From that date until the time of
his retirement and relocation to Vancouver a decade and a half later,
he played a major role in a number of international organizations and
activities. In the Canadian context he was instrumental in the
formation and growth of two significant initiatives: the development
of Concordia as a centre for teaching and research in mathematics
education, and the creation of the Canadian Mathematics Education
Study Group / Groupe canadien d'etude en didactique des
mathematiques (CMESG/GCEDM).
When David Wheeler came to Concordia, the Mathematics Department's
main commitment to education was through the Master's in the Teaching
of Mathematics programme (M.T.M.). At the time, the M.T.M. consisted
essentially of content courses in mathematics and did not provide a
broader based vision of mathematics education. Wheeler brought a
wider perspective to the programme by weaving in the pedagogical,
psychological, historical and philosophical connection to mathematics
education. He introduced faculty and students alike to Piaget's work
in developmental psychology, to Polya's classical writing on
heuristics and problem solving, to Lakatos' perceptive insights of the
process of mathematization and proof. He brought the international
mathematics education community to Concordia by attracting visiting
scholars and lecturers. By co-directing the first FCAR (Fonds pour la
formation de chercheurs et l'aide a la recherche du Quebec) three year
research project on problem-solving, he helped launch the research
aspect of the mathematics education group. Within five very short
years, the group has achieved an international reputation, with a very
high research profile and an active role in many national and
international organizations.
CMESG/GCEDM in the 1990's has become an active and influential group
involving a high percentage of the population of Canadian mathematics
educators and mathematicians with a strong interest in education, as
well as a few regular, 'offshore', participants. In its early days,
however, it was almost exclusively Wheeler's brainchild. In the
evolution of CMESG/GCEDM we have a clear picture of Wheeler at work --
imaginative, sensitive, ambitious, disciplined, diligent and
determined; it is a story worth recounting in some detail.
Shortly after his arrival in Montreal, David composed a letter in
which he noted his perception of the lack of any national forum for
the discussion of ideas about the teaching and learning of
mathematics. He went on to ask a large number of mathematicians and
mathematics educators in Canada whether this perception was correct,
and if it was, whether there was merit in trying to create such a
forum. The response to this request was largely negative. Of the
individuals who responded, the majority either did not see such a
venture as particularly important, or felt that their needs were
already being met adequately by the National Council of Teachers of
Mathematics (USA) and its allied interest groups. In the minority
group of 'positive' respondents there was a small 'cluster point' in
Kingston, Ontario where, independently, two individuals had expressed
some interest in Wheeler's suggestion. One was John Coleman, the
long-time head of the Department of Mathematics at Queen's University,
and the second was William Higginson, recently appointed as an
assistant professor in the Faculty of Education at the same
university. [It would later be suggested, neither unkindly nor totally
inaccurately, that CMESG/GCEDM was a function of Wheeler's
imagination, Coleman's influence and Higginson's energy.] With this
rather thin potential base for a national organization Wheeler moved
quickly and decisively taking advantage of the fact that Coleman had
recently completed a major study of the "Mathematical Sciences in
Canada" (Science Council of Canada, 1976) and was able to support an
invitational meeting at Queen's in the summer of 1977. The format
established for that gathering [invited speakers -- in this case, John
Coleman, Tom Kieren of the University of Alberta, and Claude Gaulin of
Universite Laval -- and working groups] has been one of the
'constants' of the organization which evolved out of that meeting. It
was clear to many by the end of that first Kingston meeting [which was
to be followed by three more at that location in the next three years,
by which time a formally constituted organization -- whose elected
president for the first ten years was David Wheeler -- had come into
being] that the 'new boy' on the Canadian mathematics education block
had much to offer to this previously very loosely organized
community. Take, for instance, these observations from his
contribution, "Reflections after the Conference" from the Conference
Proceedings (pp. 56 - 61 in "Educating Teachers of Mathematics: The
Universities' Responsibility", A. J. Coleman, W. C. Higginson and
D. H. Wheeler, eds.; Ottawa: Science Council of Canada, 1978):
"...it would be premature to say that mathematics education is on the
verge of a breakthrough comparable to that experienced by
mathematics... Yet the real message of the implied parallelism is that
there 'may' be a current flowing that could liberate education from
its ideological constraints... It is always a possibility that those
who enter with curiosity and sensitivity and persistence into a
dialogue with the facts may, like Kepler or Faraday or Cantor, find
themselves carried into a new world that others will inherit."
William Higginson
Queen's University, Kingston, ON, Canada
higginsw@educ.queensu.ca
Joel Hillel
Concordia University, Montreal, Canada
jhillel@vax2.concordia.ca
David Wheeler's international legacy
David Wheeler's fifty years in mathematics education have left
indelible marks on the international scene.
Evidence of these can be found in his exceptional contribution as
writer and as editor of the internationally renowned British journal
"Mathematics Teaching" as well as in his remarkable work as founder,
editor, fund-raiser, administrator, and much more, of "For the
Learning of Mathematics" (FLM), a journal with a well-established
world-wide reputation. These are discussed by others in this Bulletin.
Other evidence is David's involvement in activities of the
International Commission on Mathematical Instruction (ICMI) and
International Congresses on Mathematical Education (ICMEs). Concerning
ICMI, he was the first and the only Canadian official representative
until his retirement from this post in 1996, and he actively
participated in a number of ICMI study seminars, always providing deep
insights and thoughtful reflections. On the other hand, David Wheeler
has been a member of the International Programme Committees for ICME-5
(1984), ICME-6 (1988) and ICME-7 (1992). For the latter, he chaired
the IPC and played other very important roles, being in the forefront
organizing and developing the successful bid to host the congress in
Quebec City, and sitting on the Executive Committee and the
Canadian National Committee. He contributed much to the success of
ICME-7 and was an important member of the Editorial Panel for the two
volumes of its Proceedings. As Chair of the IPC, he insisted that
members reflect and question all parts of the programme: What was the
role of Working Groups, Topic Groups, etc.? Was there a proper balance
between these and the more traditional lecture presentations? How
could the committee facilitate real participation by those who already
had and those who were new to the ICME experience? etc. Undoubtedly
David Wheeler has left his mark on the evolving spirit and
organization of the ICMEs. Moreover, through many invited
presentations he has made during ICMEs, PME and HPM conferences, ICMI
study seminars and other events around the globe, he has influenced
mathematics educators from the elementary to the tertiary levels.
It is clear that David has been consistently recognised
internationally not only for his thought provoking and rich articles
and presentations, but perhaps even more for his brilliant, original
and spontaneous interventions during meetings, often raising questions
or putting in question what others assumed of no consequence or
accepted without question. Always aspiring to improve knowledge and
understanding, he eagerly and patiently encouraged the participation
and development of others.
We take the liberty to personalize the aims which he had originally
spelt out for FLM: David Wheeler... "aims to stimulate reflection on
and study of the practices and theories of mathematics education at
all levels; to generate productive discussion; to encourage enquiry
and research; to promote criticism and evaluation of ideas and
procedures current in the field." In his fifty years of activities in
mathematics education, David has certainly achieved that and we are
most grateful for it.
Claude Gaulin
Universite Laval, Quebec, Canada
cgaulin@fse.ulaval.ca
Eric Muller
Brock university, St. Catharines, ON, Canada
emuller@spartan.ac.brocku.ca
David Wheeler and the FLM adventure
In July 1980, the first issue of "For the Learning of Mathematics"
(FLM) appeared -- conceived, edited and financed (with some support
from Concordia University in Montreal) by David Wheeler. By June
1997, the fiftieth issue will have appeared, David's final one as
editor of his journal. Although the journal's synchronic appearance
was on occasion aleatory, its diachronic presence is now an
established regularity in the academic world (reflecting the most
important factor when calling the June issue the June issue).
One of the many lasting impressions David has made in this realm has
been produced through the pages of this journal, despite his almost
never appearing as a named presence in the pages themselves. (He had a
short editorial on page 1 together with a few briefly-worded questions
and comments in his interview/discussion with Caleb Gattegno in issue
number 1, and a second editorial to end things off in issue number
50. And that's it.) The incoming editor might be permitted a gleam in
his eye about the pieces David might finally be inveigled into
writing.
There are a number of orienting influences. One is that of the
Association of Teachers of Mathematics (ATM), of whose journal David
Wheeler was an early editor. In FLM issue 1, ATM is "represented" by
Tahta, Trivett and Gattegno. The very name of the journal is
deliberately resonant of the collections of Caleb Gattegno's writings,
entitled "For the Teaching of Mathematics".
The title also signals the journal editor's strong interest in
learning mathematics, without necessarily delimiting this as the
journal's sole or even primary focus. The editorial on page 1 of issue
1 claims: "I want to do something to serve the interests of those who
have to learn mathematics." A wide range of things can be offered "for
the learning of mathematics": the title signals one answer to the
question of what the journal is for.
FLM, like its editor-creator, is strongly orientated toward the
mathematical, including its history and philosophy, in order to offer
illumination of some of the issues at work within mathematics
classrooms at all levels. FLM takes mathematics seriously. This has
little to do with the age of pupils or complexity of mathematical
content. It is possible to take mathematics in infant schools very
seriously, as authors such as Gattegno, Rotman, Tahta and Walkerdine
have shown, illuminating the referential and symbolic complexity of
early arithmetic.
Elsewhere, in particular regard to mathematics, David Wheeler has
written: "Dewey said somewhere that subject matter is a prime source
of pedagogical insights. Almost no educators really believe this, I
think, except in the trivial sense of hoping that teachers, textbook
writers, and curriculum designers "know their mathematics". Even many
mathematicians, who ought to know better, have no interest in looking
below the instrumental or formal surface of mathematics in order to
get clues about how to present it more effectively."
Wheeler has published, indeed championed, some pioneering work in the
use of history of mathematics in classrooms, as well as strongly
underpinning by his support a continuing exploration of the notion of
"ethnomathematics". There is actually something of an irony here, as
this latter notion in its various manifestations has proved a source
of ambivalence to him (not least in connection to his own work on the
notion of mathematising). Yet, as psychoanalyst Adam Phillips has
noted, "ambivalence makes us vulnerable, because we are always on the
side of the enemy".
For the Learning of Mathematics has proved itself to be open to some
unfamiliar and unexpected writing (not least on occasion unexpected by
the editor himself, a consequence of engaging guest editors). The
special issue on psychodynamic influences brought together a number of
such pieces, though other writing drawing on similar elemental themes
(such as by Early or Blanchard-Laville) had appeared in the journal
prior to this collection. As David has often pointed out, he doesn't
have to agree with his authors. Even the Radatz article on student
errors in the first ever issue contained a citation by Freud.
David Wheeler's sense of the mathematical and the educational, of what
is worthwhile attending to, is well represented in the pages of his
journal. It reflects a disciplined eclecticism and an appreciation of
a wide variety of writing, both in content and style, corralled by a
clear and unflinching eye for material of value shining through a wide
range of forms. The letters he wrote to authors, whether of acceptance
or rejection (producing occasional difficulty in recipients of the
former in not construing them as the latter), were always motivated by
a desire to make the journal the best he possibly could.
For the Learning of Mathematics will no longer be confluent with David
Wheeler. But in handing its management over to the Canadian
Mathematics Education Study Group / Groupe canadien d'etude en
didactique des mathematiques (CMESG/GCEDM) and in taking part in
the choosing of a subsequent editor, he has continued the link and
underlined his continued involvement with and commitment to the
journal. And it is we, its readers, who benefit and it is on behalf of
the readers that I offer my appreciation.
David Pimm
Open University, Milton Keynes, UK
d.j.pimm@open.ac.uk
Announcement
The journal For the Learning of Mathematics (FLM) changes hands.
At this time, it is fitting to announce that David Wheeler, founder,
editor, etc. of FLM, has generously agreed that his journal should
continue under the auspices of the Canadian Mathematics Education
Study group / Groupe canadien d'etude en didactique des
mathematiques. Starting with issue 17(3) the new editor will be Dr
David Pimm of the Open University, U.K. The Canadian home of FLM will
be Queen's University in Kingston, Ontario.
FUTURE CONFERENCES
ATCM '97, June 1997
The Second Asian Technology Conference in Mathematics, focusing on
computer technology in mathematical research and teaching, will be
held 16- 20 June, 1997, in Penang, Malaysia, organised by School of
Mathematical Sciences, Universiti Sains Malaysia.
The conference will provide an interdisciplinary forum where
researchers in the fields of mathematics, education, computers and
technology, together with teachers can present results and exchange
ideas and information. The conference will cover a broad range of
topics relevant to the use of technology in mathematics. These topics
include: The potential use of technology in teaching and learning of
mathematics; Development of user-friendly softwares; Computational
mathematics. The programme will include plenary sessions, special
sessions, short communications and exhibitions. Selected papers
presented at the conferecne will be published in the proceedings.
For further information, please contact
Dr. Yahya Abu Hassan, Chair of the Organising Committee
School of Mathematics
Universiti Sains Malaysia
11800 Penang
MALAYSIA
Tel: +60 4 6577888 Ext. 3284 or +60 4 8603284
Fax: +60 4 6570910
e-mail:
or
Dr. Wei-Chi Chang, Chair of the International Programme Committee
Department of Mathematics and Statistics
Radford University,
Radford University, VA 24142
USA
Tel: +1 540 831-5232
Fax: +1 540 831-6452
e-mail:
PME-1997, July 1997
The 1997 annual conference of the International Group for the
Psychology of Mathematics Education, PME, will be held in Lahti,
Finland, 14-19 July 1997.
The Richard Skemp Memorial Fund of PME has limited funds available to
support both academics who find difficulties in attending PME
conferences for racial, political, or philosophical reasons, and those
from developing countries that are under-represented within the
PME. Applications for an allowance from the Travel Fund containing
relevant information my be sent to the Executive Secretary, Dr. Joop
van Dormolen, Rehov Harofeh 48 Aleph, 34367 Haifa, ISRAEL, before 1
March 1997. Applicants are supposed to play an active part in a
Working Group or Discussion Group, or otherwise). PME members may
nominate recipients for support from this fund by writing to the
Executive Secretary.
For further information about PME-1997, please contact
Marja-Liisa Neuvonen, Conference Secretary
University of Helsinki, Lahti Research and Training Centre
Kirrkkikatu 16
SF-15140 Lahti
FINLAND
tel: +358 3 892 299
fax: +358 3 892 219
e-mail:
http://frodo.helsinki/kongress or ftp://frodo.helsinki.fi
CIEAEM 49: The interactions in the mathematics classroom, July 1997
La Commission Internationale pour l'etude et l'Amelioration de
l'Enseignement des Mathematiques (CIEAEM) organises its 49th
conference on the above-mentioned theme, 24-30 July 1997, at the
Escola Superior de Educac o, Instituto Politecnico de Setubal,
Portugal. The sub-themes of the conference are 'The interactions among
students', 'The teacher's role', 'Task, curriculum materials and
problems', 'Images/-views of mathematics', 'The observation and
analysis of classroom interactions'.
The International Programme Committee is chaired by
Paulo Abrantes,
Fax: +351 1 750082
e-mail:
from whom further information can be obtained.
International Symposium on DERIVE and the TI-92:
Fun in Learning Mathematics, August 1997
The Austrian Centre for Didactics of Computer Algebra organises this
conference in Kungsbacka (near Gothenburg) in Sweden, 7-9 August
1997. For further information please contact the chair of the
programme committee and local organiser
David Sjoestrand
Mejerivaegen 31
S-539 36 Onsala,
SWEDEN
Tel & Fax: +46 300 641 60
e-mail:
Justification and Enrolment Problems
in Education Involving Mathematics or Physics, August 1997
On the occasion of the 25th anniversary of Roskilde University
(Denmark), IMFUFA (the Department of Mathematics and Physics and their
Functions in Education, Research and Applications) is pleased to
invite mathematics and physics educators; scholars and scientists
working in areas to which mathematics or physics are essential;
representatives of institutions, agencies and organisations of
research, industry or commerce; educational administrators, planners,
authorities, and politicians; and other interested parties to attend
this international conference which is going to be held at IMFUFA,
Roskilde University, 22-26 August 1997.
Mathematics and physics play objectively significant roles in a large
number of educational subjects and study programmes in various areas,
not only as subjects in their own right but even more, perhaps, as
essential components in other subjects and fields of study. Yet, in
many places pupils and students have considerable difficulty in
finding mathematics and physics relevant, and in coming to grips with
their study. Similarly, in many countries students, to a manifest
extent, are opting away from tertiary studies in which mathematics or
physics form a key component.
Although national and local conditions and circumstances are
undoubtedly important in this context, the problems are clearly
international and non-superficial. This implies that attempts to
explain or counteract the problems have to rely on in-depth analyses
of their scientific, socio-economic, cultural, didactial,
philisophical, and pedagogical aspects. The main purpose of the
international conference Justification and enrolment problem in
education involving mathematics or physics is to elucidate and analyse
the problems with respect to these aspects, and to do so from a
variety of different perspectives, such as educational sector and
level, geography and culture.
If you are interested in receiving further information about this
conference please contact the organisers:
Jens Hoejgaard Jensen (physics)
e-mail:
or
Mogens Niss (mathematics)
e-mail:
or the Conference Secretariat:
Ms. Karina Larsen,
IMFUFA, Roskilde University
P.O. Box 260,
DK-4000 Roskilde,
DENMARK
Fax: +45 46755065
e-mail:
ICTMT-3, September-October 1997
The Third International Conference on Technology in Mathematics
Teaching will take place 29 September - 2 October 1997 at the
University of Koblenz, Germany. The conference will bring together
classroom practitioners, curriculum developers and mathematics
education researchers who share a desire to improve the quality of
student learning. Main lectures by distinguished speakers will be
complemented by a programme of specialist short talks and
workshops. There will be an exhibition of books and IT materials. The
conference languages are English and German.
Conference themes include: 'Impact of technology on teaching and
learning'; 'Access to education through technology'; 'Technology and
assessment'; 'Ways forward - future trends'. Deadline for the
submission of abstracts is 30 June 1997. Abstracts should be submitted
to Professor Wolfgang Fraunholz, Mathematisches Institut der
Universitaet, Rheinau 1, D-56075 Koblenz, Germany.
For further information about this conference, please contact
Institut fuer Mediendidaktik
der Universitaet in Koblenz,
Rheinau 1, D-56075 Koblenz,
GERMANY
Tel: +49 261 9119651
Fax: +49 261 9119652
International Conference on Mathematical Education, October 1997
This conference, which is co-sponsored by Hangzhou Teachers College
and California State University at San Marcos, USA, is going to be
held in Hangzhou, China, 3-5 days in the middle of October 1997. The
exact dates have not yet been decided. The topics for discussion in
the conference include: 'continuing education in mathematics',
'middle-school mathematics education', 'university mathematics
education', 'modern technology and mathematics education', '"literacy"
in mathematics education'. The deadline for the submission of
abstracts (not exceeding two pages) to the address below is 31 July.
For further information, please contact
Yu, Xiuyuan, Conference Co-Chair
Hangzhou Teachers College,
91 Wenyi Road, Hangzhou 310012,
CHINA
Tel: +86 571 808 1082 or 808 7339
Fax : +86 571 808 1082
PME-NA XIX, October 1997
Illinois State University is proud to host the 1997 PME-NA (Psychology
of Mathematics Education - North America) meeting at Chateau,
Bloomington/Normal, Illinois, USA, 18-21 October 1997. A rich and
stimulating program is in the planning stages. Tentative program
planning features several plenary sessions with a focus on mathematics
education research on learning and instruction. Suggestions for other
plenary topics and/or speakers are invited.
At present the planned session formats include research paper
sessions, symposia, discussion groups, short oral presentations, and
poster sessions. As usual, decisions about acceptance will rely on
peer review, which shortens the timeline for proposal subsmission. It
is not too early to be thinking about your propossal, which will be
due by 27 January, 1997.
Bloomington/Normal is located in Central Illinois, 125 miles south of
Chicago. Weather in October will be moderate with trees and fields in
fall harvest colors. Planned excursions may include an evening at the
theatre or a barn dance. Accommodations will be availabe at
Jumeris Chateau, a five-storey hotel offering the warmth and charm
of a French country estate. A walking-jogging trail in back of
Jumeris leads all the way to the University and can be particularly
colorful in October. We look forward to your participation in the
program and to your presence among us in 1997.
For further information about the 1997 PME-NA meeting, please contact:
Jane Swafford, 1997 PME-NA Annual Conference
Department of Mathematics
Campus Box 4520
Ilinois State University
Normal, IL 61790-4520
USA
tel: +1 309 438-7797
fax: +1 309 438 5866
e-mail: swafford@math.ilstu.edu
IFIP Working Group 3.1. Working Conference, October 1997
Working Group 3.1 (Secondary Education) of the International
Federation for Information Processing (IFIP) is organising a Working
Conference on the topic Secondary School Mathematics in the World of
Communication Technology: Learning, Teaching and the Curriculum. This
Working Conference is a sequel to two previous ones organised by IFIP
WG 3.1 on similar themes in Varna (Bulgaria) in 1977, and in Sofia
(Bulgaria) in 1987. It was felt appropriate to look again, ten years
later, at the rich relationships between mathematics and the new
technologies of information and communication. The conference will
take place in Villard de Lans, a mountain resort located in the Alps
35 km from Grenoble (France), from October 26 to 31, 1997.
The programme of the conference will be built around four themes:
A. Curriculum: curriculum evolution; relationships with informatics
B. Teachers: professional development; methodology and practice
C. Learners: tools and techniques; concept development; research and theory
D. Human and social issues: culture and policy; personal impact
Participation at the Working Conference is by invitation only and will
be limited to 80-90 participants. Both the philosophy underlying such
a working conference and the physical capacities of the venue impose
this limitation on the number of participants.
For further information, please contact
Bernard R. Hodgson
Chair of the Programme Committee (Grenoble 1997)
Departement de mathematiques et de statistique
Universite Laval
Quebec G1K 7P4,
Canada
e-mail: bhodgson@mat.ulaval.ca
Fax : +1 418 656 2817
If such is the case, you should briefly explain the reasons why you
wish to take part in the Working Conference.
This Working Conference is being organised by IFIP WG 3.1, with the
help of the IUFM (Institut Universitaire de Formation des Maitres)
of Grenoble and the Leibniz Laboratory of IMAG (Institut
d'informatique et de mathematiques appliquees de Grenoble).
Teaching in mathematics, July 1998
An International Conference of the title indicated above will take
place 3-6 July 1998 in the island of Samos, Greece. The main objective
of the conference is to examine new ways of teaching undergraduate
mathematics. It will provide a unique and centralised forum and bring
together faculty members from various countries who are committed to
introducing and using innovative teaching methods. The conference will
be of great interest to mathematics faculty as well as to anyone
involved in the teaching and learning process of undergraduate
mathematics. Conference themes include: Integration of computing
technology; Innovative ways of teaching; Reform issues related to
calculus and other math courses; Distance learning technologies;
Assessment of student learning; The role of mathematics in other
disciplines.
For further information, please contact the conference chair:
Ignatios Vakalis
Department of Math & Computer Science, Capital University
e-mail:
or consult the World Wide Web at http://icg.harvard.edu/ samos98
Third International DERIVE and TI-92 Conference, July 1998
This conference will be held 14-17 July 1998, on the campus of
Gettysburg College in Gettysburg, Pennsylvania, USA. Papers submitted
for consideration by the Conference Committee should reach conference
organiser Professor Carl Leinbach (see below) no later than 15
November 1997. For further information please contact either of the
following conference organisers
Carl Leinbach,
Gettysburg College, Gettysburg, PA 17235,
USA
e-mail:
or
Bert K. Waits,
Mathematics Department, The Ohio State University
231 W. 18th Avenue, Columbus, OH 43210
USA
e-mail:
ICMI-EARCOME 1, August 1998
The First ICMI East Asia Regional Conference on Mathematics Education
(ICMI-EARCOME 1) will be held 17-21 August 1998 at the Korea National
University of Education, Chungbuk, Republic of Korea. See announcement
elsewhere in this Bulletin.
International Congress of Mathematicians, ICM-98, August 1998
This congress will be held, under the auspices of the International
Mathematical Union, 18-27 August 1998 in Berlin, Germany. The Board of
Directors of the Organizing Committee consists of
President: M. Groetschel, Berlin
Vice-President: M. Aigner, Berlin
Honorary President: F. Hirzebruch, Bonn
Treasurer: J. Sprekels, Berlin
Secretary General: J. Winkler, Berlin
The International Programme Committee is chaired by
Phil. J. Griffiths, Princeton, USA.
The current plans for the congress include the following sections:
1. Logic; 2. Algebra; 3. Number Theory and Arithmetic Algebraic
Geometry; 4. Algebraic Geometry; 5. Differential Geometry and Global
Analysis; 6. Symplectic Geometry and Hamiltonian Theory; 7. Topology;
8. Lie Groups and Lie Algebra; 9. Analysis; 10. Ordinary Differential
Equations and Dynamical Systems; 11. Partial Differential Equations;
12. Mathematical Physics; 13. Probability and Statistics;
14. Combinatorics; 15. Mathematical Aspects of Computer Science;
16. Numerical Analysis and Scientific Computing; 17. Applications;
18. Control Theory and Optimization; 19. Teaching and Popularization
of Mathematics; 20. History of Mathematics.
Further information about ICM-98 can be obtained through the World
Wide Web, through URL:
http://elib.zib-berlin.de/icm98
Third European Congress of Mathematics, July 2000
The Third European Congress of Mathematics will be held in Barcelona,
Spain, 10-14 July, 2000. Further information will be released in due
course.
ICME-9, July-August 2000
The Ninth International Congress on Mathematical Education, ICME-9, is
going to be held 31 July - 7 August 2000, at the Chiba Convention
Centre, Makuhari, at the Tokyo Bay, near Narita Airport. Further
information will be available in forthcoming issues of this Bulletin.
ICMI and the ICMI Bulletin on the World Wide Web
and on E-mail
Information about ICMI, including the most recent issue of the ICMI
Bulletin, is now availabe from the ICMI pages of the IMU server at the
Konrad-Zuse-Zentrum fuer Informationstechnik Berlin,
(Germany). These pages can be found through URL:
http://elib.zib-berlin.de/imu.icmi
Direct access to the ICMI Bulletin on the WWW, through the IMU-server,
is obtained by the URL:
http://elib.zib-berlin.de/imu.icmi.bull.[no]
The ICMI Bulletin is also stored as an ASCII file in the editor's
(i.e. the ICMI Secretary's ) electronic post system. If you want to
receive a copy of this issue as an ASCII text through e-mail, please
contact Mogens Niss at .
NATIONAL REPRESENTATIVES
(Readers are asked to notify the Secretary of any errors in or changes
to this list)
ARGENTINA Professor J. C. Dalmasso,
Director de Olimpiada Matematica
Santa Fe 3312, 90 piso
1425 Buenos Aires
ARGENTINA
AUSTRALIA Dr. Jane Watson,
Department of Education,
University of Tasmania, G.P.O Box 252 C
Hobart, Tasmania 7001
AUSTRALIA
AUSTRIA Professor F. Schweiger,
Institut fuer Mathematik, Universitaet Salzburg,
Heilbrunnerstr. 34, A-5020 Salzburg,
AUSTRIA
BANGLADESH Professor S.M. Sharfuddin,
58 Lake Circus, Kalabagan, Dhaka-1205,
BANGLADESH
BELGIUM Professor Gontran Ervynck,
K.U.L.K, Department of Mathematics,
Universitaire Campus, 8500 Kortrijk,
BELGIUM
BOTSWANA Mr. B.J. Radipotsane,
Ministry of Education,
Private Bag 005, Gaborone,
BOTSWANA
BRAZIL Professor Elon Lages Lima,
IMPA/CNPq
Estrada Dona Castorina, 110
Rio de Janeiro, RJ 22460-320
BRAZIL
BULGARIA Academician Blagovest Sendov,
Bulgarian Academy of Sciences, 1,7 Noemvry, Sofia 1040,
BULGARIA
CAMEROUN Professor Henri Hogbe Nlend,
Societe Mathematique du Cameroun,
BP 12041 Yaounde,
CAMEROUN
CANADA Professor Bernard Hodgson,
Departement de mathematiques et de statistique
Universite Laval,
Quebec, QC G1K 7P4
CANADA
CHILE Professor Rubi Rodriquez
Facultad de Matematicas
Pontificia Universidad Catolica de Chile
Casilla 306, Correo 22
CHILE
CHINA Chinese Mathematical Society. Professor Li Daqian,
INstitute of Mathematics, Fudan University, Shanghai 200433,
CHINA
Mathematical Society located in Taipei, China.
Professor Fou-Lai Lin, Institute of Mathematics
National Taiwan Normal University, Taipei,
TAIWAN
COSTA RICA Professor B. Montero,
Associacion Matematica Costarricense,
Escuela de Matematica, Universidad de Costa Rica,
San Jose,
COSTA RICA
CROATIA Professor Mirko Polonijo,
Matemati ki odjel PMF
Bijeni ka cesta 30
41000 Zagreb
CROATIA
CUBA Professor M. Prieto,
Facultad de Matematica, Universidad de le Habana,
Habana 4,
CUBA
CZECH Professor Franti ek Ku ina
REPUBLIC Katedra matematiky
Pedagogicka fakulta
500 00 Hradec Kralove
The CZECH REPUBLIC
DENMARK Professor Martin P. Bendsoee,
Department of Mathematics,
The Technical University of Denmark,
Building 303,
DK-2800 Lyngby
DENMARK
EGYPT Professor W. Ebeid,
Faculty of Education, Einshams University,
Roxy, Heliopolis, Cairo,
EGYPT
FINLAND Professor Tuomas Sorvali,
University of Joensuu, P.O.Box 111, SF-80101 Joensuu 10,
FINLAND
FRANCE Professor Regis Gras,
Universite de Rennes 1, UFR de Mathematiques, IRMAR,
35042 Rennes Cedex
FRANCE
GEORGIA Recently a new member state of the IMU, and hence of ICMI.
National Representative to be appointed
GERMANY Professor, Dr. H.-J. Vollrath,
Mathematisches Institut der Universitaet Wuerzburg
Am Hubland
DW-97074 Wuerzburg
GERMANY
GHANA Professor D.A. Akyeampong,
Department of Mathematics, University of Ghana,
P.O.Box 62, Legon, Accra,
GHANA
GREECE Not known
HONG KONG Mr. Pak-Hong Cheung
Department of Curriculum Studies,
The University of Hong Kong,
Pokfulam Road,
HONG KONG
HUNGARY Professor, Dr. J. Szendrei,
Juhasz Gyula Teacher Training College,
Boldogasszony sgt. 6
H-6701 Szeged,
HUNGARY
ICELAND Dr. Kristin H. Jonsdottir,
Kennarah skola slands, Stakkahli, IS-105 Reykjavik,
ICELAND
INDIA Professor R. C. Cowsik,
Department of Mathematics,
University of Bombay, Vidyanagari,
Bombay 400098
INDIA
IRAN Professor Megherdich Toomanian,
Department of Mathematics, Faculty of Science,
University of Tabriz, Tabriz,
IRAN
IRELAND Professor A.D. Wood
The National Sub-Commission for Mathematical Instruction
The Royal Irish Academy, Academy House,
19 Dawson Street, Dublin 2,
IRELAND
ISRAEL Professor Theodore Eisenberg
Department of Mathematics,
Ben-Gurion University
P.O.Box 653, Beer Sheva 84105
ISRAEL
ITALY Professor Benedetto Scimeni,
Prato delle Valle 80, 35123 Padova,
ITALY
IVORY COAST Professor Pierre Nezit,
Societe Mathematique de Cote d'Ivoire (S.M.C.I.),
08 B.P. 2030 Abidjan 08,
IVORY COAST
JAPAN Professor Shigeru Iitaka,
Department of Mathematics, Gakushuin University,
Mejiro, Toshima, Tokyo, 171
JAPAN
KUWAIT Mr. Mansour Hussein,
Mathematics Advisory, Ministry of Education, P.O.Box 7,
Safat,
KUWAIT
LUXEMBOURG Professor Rene Klopp,
Mathematics, Centre Universitaire de Luxembourg
162 A, avenue de la Faiencerie
L-1511 Luxembourg
LUXEMBOURG
MALAWI Inspector for Mathematics,
c/o Secretary for Education & Culture,
Ministry of Education & Culture,
Private Bag 328, Capital City, Lilongwe 3,
MALAWI
MALAYSIA Professor C.K. Lim,
Department of Mathematics, University of Malaya,
Kuala Lumpur,
MALAYSIA
MEXICO Not known
MOZAMBIQUE Dr. Abdulcarimo Ismael,
Head of Department of Mathematics,
Higher Pedagogical Institute (I.S.P.), C.P. 3276, Maputo,
MOZAMBIQUE
NETHERLANDS Professor Fred Simons,
Department of Mathematics
Eindhoven University of Technology,
P.O.Box 513, 5600 MB Eindhoven,
The NETHERLANDS
NEW ZEALAND Ms. Megan Clark,
Institute of Statistics and Operations Research
Victoria University of Wellington,
P.O.Box 600, Wellington,
NEW ZEALAND
NIGERIA Dr. Sam O. Ale,
Abubakar Tafawa Balewa College,
School of Science and Science Education,
Ahmadu Ballo University, Bauchi Campus, Bauchi,
NIGERIA
NORWAY Dr. Kari Hag,
Department of Mathematical Sciences,
University of Technology of Norway
N-7034 Trondheim,
NORWAY
PAKISTAN Not known
PHILIPPINES Professor B.F. Nebres S.J.,
Ateneo de Manila University, P.O.Box 154, Manila,
The PHILIPPINES
POLAND Professor Stefan Turnau,
Institute of Mathematics, Pedagogical University (WSP),
P.B. 115, PL-35-959 Rzeszow,
POLAND
PORTUGAL Professor M.R.F. Moreira,
Department of Mathematics, University of Porto,
4000 Porto,
PORTUGAL
ROMANIA Not known
RUSSIA Professor A.S. Miscenco,
Faculty of Mathematics, Moscow State University,
117324 Moscow,
RUSSIA
SENEGAL Professor S. Niang,
Faculte des Sciences, Universite de Dakar, Dakar,
SENEGAL
SINGAPORE Dr. Cheng Kai Nah,
Department of Mathematics,
National University of Singapore,
10 Kent Ridge Crescent, Singapore 0511,
SINGAPORE
SLOVAK Dr. Vladimir Burjan
REPUBLIC EXAM
P.O. Box 215
852 99 Bratislava
The SLOVAK REPUBLIC
SLOVENIA Recently a new member of the IMU, and hence of ICMI. National
Representative to be appointed
SOUTH AFRICA Professor Cyril Julie,
Faculty of Education and Didactics, University of Western Cape
Private Bag X17, Belville 7535
SOUTH AFRICA
SOUTH KOREA Professor Han Shick Park,
Faculty of Mathematics,
Korea National University of Education,
Chongwon-kun,
Chungbuk, 363-791,
SOUTH KOREA
SPAIN Professor Claudi Alsina,
Department of Mathematics & Statistics, ETSAB,
Universitat Politecnica de Catalunya,
Diagonal 649, Barcelona 08028,
SPAIN
SWAZILAND Mr. E.D. Bicknell,
William Pitcher College, P.O.Box 1473, Manzini,
SWAZILAND
SWEDEN Dr. Gerd Brandell,
Department of Mathematics, University of Luleaa,
S-97187 Luleaa,
SWEDEN
SWITZERLAND Professor Urs Kirchgraber,
Mathematik ETH-Zentrum, CH-8092 Zurich,
SWITZERLAND
THAILAND Dr. Suwimon Hall
Department of Mathematics, Faculty of Science
Chulalongkorn Universitty, Bangkok 10330
THAILAND
TUNISIA Dr. S. Aidi,
18 rue des Suffetes, Salammbo,
TUNISIA
UNITED Professor Margaret Brown
KINGDOM Centre for Educational Studies
University of London
Waterloo Road, London SE1 8TX
ENGLAND
USA Dr. John A. Dossey, Distinguished University Professor
4520 Mathematics
Illinois State University
Normal, IL 61790-4520
USA
VIETNAM Professor Nguyen Dinh Tri
Hanoi National University of Technology
Dai Co Viet Road, Hanoi
VIETNAM
EX-YUGOSLAVIA Dr. Milica Ili Dajovo ,
Gospodar Jevremova 45, 11000 Beograd
SERBIA
ZAMBIA Dr. S.M. Bayat,
Secretary, Mathematical Association of Zambia,
P.O.Box RW 204, Ridgeway, Lusaka,
ZAMBIA