[ICMI-News] ICMI News 10: June 2009
J Carvalho e Silva
jaimecs at mat.uc.pt
Fri Jul 24 15:59:32 CEST 2009
ICMI News 10: June 2009
A Bimonthly Email Newsletter from the
ICMI-International Commission on Mathematical
Instruction
Editor: Jaime Carvalho e Silva, Dep. Matematica,
Universidade de Coimbra, Portugal
CONTENTS
1. Editorial: Mathematics Education in East Asian Countries
2. The Klein Project
3. A XXIst century Felix Klein's follow up workshop
4. ICMI AWARDS - Call for Nominations
5. ICMI Digital Library
6. ICME-13 Bids Intention - November 1
7. The 14th Asian Technology Conference in Mathematics
8. Online version of the Journal of Mathematics Education (JME)
9. RELIME (Latin American Journal of Mathematics Education)
10. Calendar of Events of Interest to the ICMI Community
11. ICMI encounters: George Polya (1887-1985) and Lev Pontryagin (1908-1988)
12. Subscribing to ICMI News
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1. Editorial: Mathematics Education in East Asian Countries
In the last issue of this Newsletter, Kumaresan
talked about the issues and problems faced by
India in mathematics education. Coming from East
Asia, perhaps I should briefly talk about issues
concerning mathematics education in East Asia.
These descriptions and discussions reflect the
truly international nature of ICMI. I will
however be tackling the topic following an
approach totally different from that adopted by
Kumaresan.
There are quite a number of countries which may
be considered as being in East Asia, but here I
will confine myself to those countries or systems
which are under the influence of the Confucian
Heritage Culture (or CHC), namely China, Hong
Kong, Japan, Korea, Singapore and Taiwan.
Interest in the mathematics education of CHC
countries has been aroused and intensified by the
superior performance of CHC students in recent
international studies of mathematics achievement
such as TIMSS and PISA. Traditionally, student
achievement was explained in terms of learner
attributes and the quality of teaching, but the
high achievement of students from these East
Asian countries which share a common culture
points to the necessity of understanding
teaching, learning and achievement from the
perspective of the underlying cultural values.
In response to this, ICMI devoted a Study (Study
13) to discussing mathematics education in East
Asia and the "West".
In the Study Volume of Study 13 and elsewhere, I
have discussed the possible cultural values which
may be used for explaining the high achievement
of CHC students. These include,
1. a strong emphasis on the importance of
education and the high expectation for students
to achieve,
2. the examination culture,
3. the role of practice and memorization in learning, and
4. the pragmatic philosophy in CHC countries
This is not the place to elaborate on these
values, but in recounting the superior
achievement of CHC students, one must not forget
that in the literature, CHC students were also
found to be situated in an environment that is
not conducive to effective learning. CHC class
size is often large, and teaching is typically
very traditional and teacher centered with
minimal student involvement. Students' attitude
towards mathematics is rather negative, and
students are not confident in their mathematics
ability. This is the so-called Paradox of the
Chinese or CHC Learner. What can we learn from
the discussion above and from the Paradox of the
CHC Learner? I will just mention two points here.
First, cultural factors are important
determinants of student learning and achievement.
The student is not a white sheet of paper waiting
for the teacher to write knowledge onto. This
realization is especially important for a subject
such as mathematics, which is often considered a
universal subject not affected by culture. The
Paradox of the CHC Learner should remind us of
the powerful cultural factors that are at work in
student learning and achievement, often
transcending the influences of other factors such
as student ability and classroom instructional
practices. Teachers should take the culture of
the students into consideration in designing
their instructional activities, and should
capitalize on the favourable elements in
students' culture(s) to promote learning.
Secondly, we need to view the high achievement of
CHC students in the light of their negative
attitudes towards mathematics. Some of these
negative attitudes may also be explained by
cultural factors, and the lesson to learn here is
that we need to take into account the price that
has been paid in achieving good results. The
negative effects of a high expectation for
students to achieve, the examination culture, and
the stress on practice and memorization are
surfacing. In Korea for example, many children
attend private tutoring schools after their
formal schooling, often until mid-night, and this
has become an acute social problem. No wonder
the attitudes of CHC students towards mathematics
are so low!
In mathematics education, one should of course
aim for good academic results. But a positive
attitude towards mathematics should also be an
important goal of mathematics education. The
issues and problems faced by CHC countries in
mathematics education should remind us that in
education, it is important to strike a delicate
balance.
Frederick.K.S. Leung, Member-at-large, ICMI-EC,
The University of Hong Kong, frederickleung at hku.hk
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2. The Klein Project
In 2008 IMU and ICMI commissioned a project to
revisit the intent of Felix Klein when he wrote
Elementary Mathematics from an Advanced
Standpoint. That is, to produce a book for
secondary teachers that communicates the breadth
and vitality of the research discipline of
mathematics and connects it to the senior
secondary school curriculum.
The international Design Team for the project met
recently. The team confirmed the production of a
300-page book written to inspire teachers to
present to their students a more complete picture
of the growing and interconnected field
represented by the mathematical sciences in
today's world. We expect this will be backed up
by web, print, and DVD resources. The project is
expected to take about four years.
The book will be neither comprehensive, nor
definitive of the field. Whatever chapter
structure is chosen the text will emphasise links
between branches of the field and generic themes
(such as the impact of computing). Insights from
mathematics education will not be addressed
specifically but will be implicit in many places.
The Design Team seeks input from all those
working in the mathematical sciences, researchers
and educators alike. We welcome written
communications, but will also be holding several
"Klein conferences" around the world where
feedback on draft ideas and material can be
given, and original contributions offered. The
actual writing will be done by invited authors of
proven experience in expert and inspiring
authorship. Anyone wishing to be on a mailing
list to be kept up to date and receive draft
material is invited to send an email in the first
instance to <b.barton at auckland.ac.nz>. A website
is in the process of being established.
Comments are invited on the choice of Chapter
titles (bearing in mind the comments above):
* Introduction
* Topic Chapters
- Arithmetic
- Logic
- Algebra & Structures
- Geometry
- Functions & Analysis
- Discrete & Algorithmic mathematics
- Mathematics of Computation
- Probability & Statistics
* Theme Chapters
- Intradisciplinarity (i.e. internal connections)
- Mathematics as a living discipline inside science and society
- How mathematicians work
Bill Barton, Vice-President of ICMI, b.barton at auckland.ac.nz
------------------------------------------------------------------------
3. A XXIst century Felix Klein's follow up workshop
Didactics of Mathematics as a Mathematical Discipline
(a XXIst century Felix Klein's follow up)
An international workshop, Funchal (Madeira), Portugal, October 1-4, 2009
http://glocos.org/index.php/dm-md/
A century ago Felix Klein's lectures on
mathematics for secondary teachers were first
published: "Elementarmathematik vom höheren
Standpunkte aus" (1908). This comprehensive view
challenged both teachers and mathematicians to
consider the relationship between mathematics as
a school subject, and mathematics as a scientific
discipline. As Klein wrote: "we first raise the
question as to how these things are handled in
the schools; then we shall proceed to the
question as to what they imply when viewed from
an advanced standpoint." To this we must add
"another point in this instruction which is
usually neglected in university teaching. It is Š
the application of numbers to practical life."
This last 100 years have witnessed many changes
in mathematics that provoked major changes and
challenges for school mathematics. The role of
mathematics in the education of scientists,
economists and engineers seems to have achieved
unprecedented societal unanimity. While Klein's
writing remains a valuable source insight, it
seems timely to revisit this theme by linking the
topics and approaches of upper secondary with the
field of mathematics. This is an important
challenge for Mathematics Education.
Can we analyse the new challenges for mathematics
in the XXIst century? Can we devise a XXIst
century book that will be "read with pleasure and
profit alike by the scholar, the student, and the
teacher" (AMS Book Reviews 1940) taking into
account all the dimensions Klein stressed:
intuitive, genetic, applications?
This workshop aims at discussing this subject,
contemplating the following strands:
a) Which special characteristics can be
found in mathematics as a school subject for the
XXIst century?
b) Which kind of relationships between
mathematics as a school subject and mathematics
as a scientific discipline must be
developed/implemented?
c) Which challenges are national and which
are international? Which are individual and which
are societal?
d) Which new mathematics should be included
(apart from arithmetic, algebra, analysis and
geometry), why and from which "advanced
standpoint"?
e) What should be the methodology of such a
book in order to be read by "the scholar, the
student, and the teacher"?
f) How to integrate "elementary" recent applications in such a book?
g) Which kind of multimedia tools would be
most useful to accompany and amplify the impact
such a book?
The workshop will include 20-30 invited speakers
will present their views in 30m lectures,
followed by discussions; there will be a slot for
some other presentations selected by the
organizing committee from the proposals received
(20m presentations). The deadline for proposals
is September 7. Please register at the website
http://glocos.org/index.php/dm-md/
Already confirmed invited speakers include John
Mason, Ulrich Kortenkamp, M. Artigue, U.
Bottazzinni, Abraham Arcavi, Arselio Martins,
João Pedro Ponte, Tomás Recio, Gert Schubring, T.
Banchoff, R. Strasser, S. Xambó, M. Hohenwarter,
Bernard R. Hodgson and Bill Barton.
The Organizing Committee is Elfrida Ralha (Univ.
Minho), Jaime Carvalho e Silva (Univ. Coimbra),
Suzana Nápoles (Univ. Lisboa), José Manuel
Castanheira (Univ. Madeira), Elsa Fernandes
(Univ. Madeira), Sandra Mendonça (Univ. Madeira).
The workshop is organized by CIM-Centro
Internacional de Matemática and announcements can
be found in http://www.cim.pt/?q=events and a
short note about the workshop can be found in the
CIM Bulletin:
http://www.cim.pt/files/publications/b26.pdf
Jaime Carvalho e Silva, Member-at-large, ICMI-EC,
Organizing Committee, jaimecs at mat.uc.pt
------------------------------------------------------------------------
4. ICMI AWARDS - Call for Nominations
THE ICMI AWARDS COMMITTEE
Announcement: Call for Nominations
As is probably well known to most mathematics
educators around the world, the Executive
Committee of the International Commission on
Mathematical Instruction (ICMI) a number of years
ago created two awards, each in the form of a
diploma and a medal, to recognise outstanding
accomplishments in mathematics education research:
. the Hans Freudenthal Award, for a major
programme of research on mathematics education,
. the Felix Klein Award, for lifelong
achievement in mathematics education research.
An ICMI Awards Committee has been appointed for
selecting the awardees. The President of ICMI has
appointed Professor Mogens Niss to chair this
committee, the other members of which are
anonymous until their terms have come to an end.
The first recipients of these two awards,
Professor Guy Brousseau (France) for the Felix
Klein Award and Professor Celia Hoyles (UK) for
the Hans Freudenthal Award, formally received
these at the opening ceremonies of ICME-10 in
Copenhagen, in July 2004. The two 2005 awards
went to Professors Ubiratan D'Ambrosio (Brazil)
(the Klein Award) and Paul Cobb (USA) (the
Freudenthal Award), and for 2007, Professors
Jeremy Kilpatrick (USA) and Anna Sfard
(Israel/UK/USA) received the Klein and the
Freudenthal Awards, respectively. The awards for
2005 and 2007 were formally presented to the
recipients at the opening ceremony of ICME-11 in
Monterrey, México, in July 2008.
The ICMI Awards Committee is now entering a
fourth cycle of selecting awardees for 2009. The
result of this process will be known by the end
of 2009. The 2009 Awards will be presented to the
recipients at ICME-12 in Seoul, Korea in 2012. As
was the case with the previous cycles, the ICMI
Awards Committee welcomes suggestions coming from
the mathematics education community, hence this
call for nominations.
A nomination of a candidate for the Felix Klein
or the Hans Freudenthal Award has to be
accompanied by a summary presenting the vita and
the achievements of person nominated, as well as
the reasons for the nomination. Moreover,
nominations also have to include the names and
coordinates of two or three persons from whom the
committee may seek further information. All
proposals must be sent by e-mail (mn at ruc.dk) to
the Chair of the Committee no later than 15
September 2009.
Mogens Niss, Chair of the ICMI Awards Committee,
IMFUFA, NSM, Building 27, Roskilde University,
P.O.Box 260, DK-4000 Roskilde, DENMARK
------------------------------------------------------------------------
5. ICMI Digital Library
The International Commission on Mathematical
Instruction (ICMI) is pleased to announce the
inauguration of its Digital Library.
The project of an ICMI Digital Library, where
eventually "all" publications related to ICMI and
its activities will be made freely available
online, has been under discussion for a long
time. Thanks to the support received from the
International Mathematical Union, and especially
the IMU Committee on Electronic Information and
Communication (CEIC), much progress has been made
recently as regards this project, and in
particular the digitisation of past ICMI material.
ICMI is celebrating this opening with the posting
online of the Proceedings of the symposium
organised in 2000 on the occasion of the
centennial of L'Enseignement Mathématique, the
official organ of ICMI. The ICMI Executive
Committee wishes to express its gratitude to the
editors of L'EM for generously granting
permission to post on the ICMI website the book:
One Hundred Years of L'Enseignement Mathématique:
Moments of Mathematics Education in the Twentieth
Century. Proceedings of the EM-ICMI Symposium
(Geneva, 20-22 October 2000) Edited by D. Coray,
F. Furinghetti, H. Gispert, B.R. Hodgson, G.
Schubring (ISBN 2-940264-06-6) softbound; 336
pages, 2003; 63 CHF (L'Enseignement Mathématique,
Monograph no. 39).
More material will be made accessible
progressively, including all the issues of the
ICMI Bulletin, the volumes resulting from the
ICMI Studies or the Proceedings of the ICME
congresses. It is also our intent to include in
the Digital Library other documents related to
activities organised under the auspices of ICMI,
such as the proceedings of ICMI regional
conferences.
Comments and suggestions about the ICMI Digital
Library Project and how to make it a useful tool
for the community are most welcome and should be
sent to the Secretary-General of ICMI, Bernard R.
Hodgson (bhodgson at mat.ulaval.ca).
The Digital Library can be directly accessed via the ICMI website
http://www.mathunion.org/ICMI/
Bernard R. Hodgson, Secretary-General of ICMI, bhodgson at mat.ulaval.ca
------------------------------------------------------------------------
6. ICME-13 Bids Intention - November 1
The deadline for submitting bids for hosting
ICME-13, to be held in 2016, is November 1, 2010.
However countries considering making such a
proposal should inform the Secretary-General of
ICMI of their intention by November 1, 2009. The
decision about the site of ICME-13 will be
announced before the end of 2013.
Preparing a Bid to Host an ICME
The main aspect to keep in mind when preparing a
bid proposing to host the International Congress
on Mathematical Education is to provide
conviction for the ICMI Executive Committee that
the candidate country is in a favorable position
of accomplishing this non-trivial task. The
document submitted should thus address aspects
such as the following.
* Inviting bodies
The bid should define the set of inviting bodies,
i.e. those who submit the bid. In most cases
this set consists of a coalition of bodies (like
learned societies, associations, academies,
universities, official national or provincial
authorities). This aspect is to ensure that the
invitation has sufficiently broad support in the
proposed host country and that all major parties
concerned with mathematics education stand behind
the bid. Also of importance is the actual
involvement of the local mathematics education
community so as to create a nice ambiance around
and during the meeting.
* Scientific infrastructure
The document should present the scientific
infrastructure in the bidding country that will
be supporting the congress. This is to
demonstrate the presence of a sufficiently large
group of mathematics educators in the country to
provide national backup of the scientific
program. In particular, the document should
clarify whether there is a substantial core of
educators in the country with experience in
international meetings.
* Venues
The bid should indicate possible venues within
the country (city and institutions in which the
congress would take place), describing their
advantages and disadvantages in relative terms.
This includes a presentation of the technical
congress facilities (in particular the
availability of rooms of various types and sizes,
among others for the plenary sessions, or usual
standards such as air conditioning or
presentation equipment), transportation to the
site as well as on-site, and the variety of local
accommodation facilities, ranging from
inexpensive student residence type accommodation
to high-class international hotels. Eventually,
the bid should address other local concerns, such
as the security of participants.
* Logistic infrastructure
The document submitted should outline the
logistic infrastructure of the congress in order
to demonstrate that a sufficiently advanced,
varied and capable organization system is - or
can be put - in place to deal with all matters
pertinent to the local organization of a
multi-faceted and complex congress of about 3500
participants.
* Financial infrastructure
The bid should describe the financial
infrastructure of the congress, indicating the
size of the funds that are expected to be
available to the congress, and listing the
organizations, institutions, and bodies in the
bidding country that are ready - or may be
expected - to support the congress financially in
terms of money, services, equipment or manpower.
The bid should also address the specific issue of
possible help to participants from non-affluent
countries, as well as the expected level of
registration fees for congress participants.
The above is not meant to be an exhaustive
check-list of matters to be considered one after
the other in preparing a bid, but it gives the
flavor of the natural questions the decision
makers, namely the Executive Committee of ICMI,
will be considering, in addition to other issues
such as the broad geographical distribution of
the ICME congresses.
The best general guidance in preparing a bid may
be found in the following summary: the document
has to have two properties, namely,
(a) an existence proof (or at least a good
sketch of one) that the inviting consortium can
actually manage all aspects of the Congress;
(b) features that make the Executive Committee
of ICMI think that the present bid is not only
feasible, but also better than other potential
bids.
Of course, as the quality of a bid is a
multi-faceted concept, there is freedom to
balance weaker points in a potential bid with
stronger ones.
Requests for further information about the
preparation of a bid to host an ICME should be
addressed to the Secretary-General of ICMI.
Bernard R. Hodgson, Secretary-General of ICMI, bhodgson at mat.ulaval.ca
------------------------------------------------------------------------
7. The 14th Asian Technology Conference in Mathematics
(ATCM 2009), December 17-21, 2009, Beijing Normal University, Beijing, China
The ATCM 2009 is an international conference to
be held in China that will continue addressing
technology-based issues in all Mathematical
Sciences. Thanks to advanced technological tools
such as computer algebra systems (CAS),
interactive and dynamic geometry, and hand-held
devices, the effectiveness of our teaching and
learning, and the horizon of our research in
mathematics and its applications continue to grow
rapidly. The aim of this conference is to provide
a forum for educators, researchers, teachers and
experts in exchanging information regarding
enhancing technology to enrich mathematics
learning, teaching and research at all levels.
English is the official language of the
conference. There will be over 400 participants
coming from over 33 countries around the world.
Be sure to submit your abstracts or full papers
in time.
Plenary Speakers
Bogumila KLEMP-DYCZEK (Poland) Nicolaus Copernicus University, Poland.
Sung Je Cho (South Korea) Chair of the
International Program Committee, ICME 12.
Wei-Chi YANG (USA) Founder-ATCM and eJMT.
Jing-zhong ZHANG (China) Academician of the Chinese Academy of Science.
Yingbo ZHANG (China) Member of the Executive
Committee of the ICMI, Director of Education
Committee of the Chinese Mathematical Society.
Invited Speakers
Keng Cheng ANG (Singapore)
Douglas BUTLER (UK)
Jen-chung CHUAN (Taiwan)
Miroslaw MAJEWSKI (UAE)
Changpei WANG (China)
We invite you to submit original and unpublished
work to the conference for review. Each
submission will be reviewed and the author(s)
will be notified of recommendation by the
International Program Committee. Only scholarly
work that has not been published elsewhere should
be submitted for consideration. Accepted
abstracts and refereed Full Papers will be
published at the Proceedings of ISSN 1940-2279
(CD) and ISSN 1940-4204 (Online). We also will
publish a hard copy Proceeding for ATCM 2009.
Selected referred papers will be invited for
consideration of publication at the Electronic
Journal of Mathematics and Technology.
Important Notes:
* For all Authors and Reviewers, we
are using a new reviewing system, you need to log
in the online reviewing system and fill out a
simple form by clicking on 'register' next to
'Login' when you login first time. Especially, be
sure to select the fields best describe your
paper and your interests, this will provide the
best match between Authors and Reviewers.
* If you want to send in more than
one submission, you can log in the reviewing
system (after entering your user name and
password) again and select 'Upload Submission'.
* If you plan to present your talk
or poster session with an abstract, you may
submit your abstract without a full paper by July
30, 2009 (extended).
* If you plan to present your talk
and consider publishing your full paper at the
ATCM 2009 Proceedings, you may submit your FULL
Paper by July 30 of 2009 for reviewing.
* We will distribute a hard copy of
accepted abstracts at the conference. The
accepted Full Papers will appear in Electronic
format: A CD will be distributed at the
conference and an Electronic Proceedings will be
available after the conference.
Wei-Chi Yang, Co-chair of IPC, wyang at radford.edu
------------------------------------------------------------------------
8. Online version of the Journal of Mathematics Education (JME)
I am pleased announce that the Journal of
Mathematics Education (JME) online version is
ready for free public review. The website is
http://educationforatoz.com/journalandmagazines.html.
We would like to invite all mathematics educators
to review these online articles and provide
feedback, if any.
The Journal of Mathematics Education (JME) is a
semi-annual and peer-reviewed professional
academic research journal. JME aims at promoting
communication in mathematics education between
the United States and China as well as between
the West and East in general. The goal of JME is
to provide opportunities for all scholars to
conduct research on mathematics education, with
emphasis on assessment, curriculum, instruction,
theory, technology, equity, and other issues
relating to mathematics education. The Journal of
Mathematics Education is published semi-annually
in hard copy (ISSN 1945-7502) and online (ISSN
1945-7 448) by Education for All.
We welcome all mathematics education researchers
to contribute to JME, and we also welcome all
mathematics educators to be a reviewer and join
our peer review process.
Thanks for your support.
Zhonghe (John) Wu, Mathematics Education @
National University - Costa Mesa, CA, zwu at nu.edu
------------------------------------------------------------------------
9. RELIME (Latin American Journal of Mathematics Education)
The "Revista Latinoamericana de Investigación en
Matemática Educativa", RELIME (Latin American
Journal of Mathematics Education), published by
the "Comité Latinoamericano de Matemática
Educativa", CLAME (Latin American Committee of
Mathematics Education), recently has been
incorporated to the "Social Sciences Citation
Index of the ISI Web of Knowledge". With this,
two of the research journals in our field have
been included in ISI Web, the other one being
JRME, the Journal for Research on Mathematics
Education.
RELIME invites you to submit your research papers
in any of the following languages: Spanish,
English, French or Portuguese. For form of
manuscripts and other guides for authors, please
check RELIME webpage,
http://www.clame.org.mx/relime.htm
Ricardo Cantoral, Director, RELIME, rcantor at cinvestav.mx
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10. Calendar of Events of Interest to the ICMI Community
PME33 - 33rd Annual Meeting of the International
Group for the Psychology of Mathematics Education
Thessaloniki, Greece, July 19-24, 2009
http://www.pme33.eu
Bridges Banff - Mathematics, Music, Art, Architecture, Culture
The Banff Centre, Banff, Alberta, Canada, July 26-29, 2009
http://bridgesmathart.org/bridges-2009/
CIEAEM61 - Commission internationale pour l'étude
et l'amélioration de l'enseignement des
mathématiques
Université de MONTRÉAL, Montréal, Québec, Canada, July 26-31, 2009
http://www.cieaem.net/
ICTMA 14 - 14th International Conference on the
Teaching of Mathematical Modelling and
Applications
University of Hamburg, Germany, July 27-31, 2009
http://www.ictma14.de/
SEMT '09 - 10th bi-annual conference on Elementary Mathematics Teaching,
"The development of mathematical understanding"
Prague, August 23-28, 2009
http://kmdm.pedf.cuni.cz
4th general meeting of European Women in Mathematics (EWM)
University of Novi Sad, Serbia, August 25-28, 2009
http://ewm2009.wordpress.com/
"Models in Developing Mathematics Education"
The Mathematics Education into the 21st Century Project
Dresden, Saxony, Germany, September 11-17, 2009
<mailto:arogerson at inetia.pl>alan at rogerson.pol.pl
ICREM4 - The 4th International Conference on
Research and Education in Mathematics 2009
K u a l a L u m p u r , M a l a y s i a, October 2 1 - 2 3 , 2 0 0 9
http://einspem.upm.edu.my/icrem4/
CoSMEd -Third International Conference on Science and Mathematics Education
Improving Science and Mathematics Literacy: Theory, Innovation and Practice
Penang, Malaysia, November 10-12, 2009
http://www.recsam.edu.my/cosmed/
2009 SAMSA Conference
Southern Africa Mathematical Sciences Association
Belinda Hotel, Dar es Salaam, Tanzania, November 23-27, 2009
http://www.samsajournal.org/
SRD'09 - Southern Right Delta'09
7th Southern Hemisphere Conference on the Teaching
and Learning of Undergraduate Mathematics and Statistics
Gordons Bay, South Africa, 29 November-4 December 2009
http://www.delta2009.co.za
"Numeracy: Historical, philosophical and educational perspectives"
St Anne's College, Oxford, England, December 16-18, 2009
benjamin.wardhaugh at all-souls.ox.ac.uk
ATCM 2009 - The 14th Asian Technology Conference in Mathematics
Beijing Normal University, Beijing, China, December 17-21, 2009
http://atcm.mathandtech.org or http://atcm.mathandtech.com
10th Islamic Countries Conference on Statistical Sciences (ICCSS-10)
Cairo, Egypt, December 20-23, 2009
http://www.iccs-x.org.eg/
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11. ICMI encounters: George Polya (1887-1985) and Lev Pontryagin (1908-1988)
Brief Encounters
It was suggested that instead of the usual
historical vignette I should write a note about
some of the great mathematicians that I have met
during my work for ICMI. There have been very
many, of which there is space here to describe
only two, but I hope that this selection together
with an indication of their work in mathematics
education will prove of interest.
The first, George Polya (1887-1985), was an
invited guest at ICME2 in 1972. He did not
lecture there but submitted a paper consisting of
ten quotations that 'helped Š clarify [his]
opinions' on the teaching of mathematics. As the
editor of the proceedings I was initially
disappointed not to receive a longer contribution
from him, but soon realised that value and length
are independent variables and Polya's selection
can still inspire thought and admiration. This
was not the first time I had met Polya for he had
been an invited lecturer at the First
Commonwealth Conference on Mathematical Education
held in Trinidad in 1968. There I had been asked
to chair a working group and it was with
considerable trepidation that I learned that
Polya was to be a member of it. Would he
dominate it? Would his presence inhibit others
from putting forward their views? My fears were
ungrounded. Polya, whom I soon discovered to be
a most likeable person, made his contributions to
the discussion but in a gentle and seemingly
tentative way, and throughout listened to what
others had to say while giving the impression
that this was the first time he had heard such
interesting ideas. Polya was, of course, not
only a great mathematician, but also he made
important contributions to mathematics education.
Polya did not originally study mathematics at
university and it was only when he switched to
philosophy that his professor suggested that he
should also learn some mathematics in order
better to understand philosophy. It was
mathematics though that was to retain Polya.
After study at Budapest, Vienna and Göttingen
(with mathematicians such as Klein and Hilbert),
Polya was to accept a post in Zurich. There
during the war years he was separated from his
native Hungary. If he returned he would be
conscripted for service in a war that he, a
pacifist, could not support. Later, if he
returned he could be charged with having evaded
conscription. It was 54 years before he returned
to his native land. Yet in the meantime he,
together with his compatriot Szegö, wrote what
was a totally novel text, Problems and Theorems
in Analysis (Springer, 1925 - in German), which
classified problems not by subject but by their
methods of solution. It was the first indication
of that interest in heuristics which was later to
produce the books How to solve it, Mathematics
and Plausible Reasoning and Mathematical
Discovery. Perhaps the title of the first of
these - widely translated, still in print and
having sold well over a million copies - might
transgress the present-day Trades Descriptions
Act, for it does not guarantee that the reader
will always find a solution, but it remains a key
work: as Schoenfeld wrote, work on problem
solving is now divided into two eras: 'before and
after Polya'.
The second mathematician I have chosen to write
about is that remarkable Russian, Lev Pontryagin
(1908-1988). In the 1950s I owned his book,
Topological Groups, and I had heard of this
remarkable person who, although blinded in an
accident at the age of 14, had become one of the
word's greatest mathematicians. One of the joys
of attending international congresses is that one
can see, even if one cannot talk to, the people
who have so greatly influenced one's subject. I
was thrilled then at the Stockholm 1962 congress
of mathematicians to see this legendary person.
I did not imagine at that time that I would ever
have the chance of speaking with him. This came
about when just after being appointed secretary
of ICMI, but before taking up office, I went to
Moscow in 1982 with a team of 12 British
mathematics educators in order to discuss common
problems and possible methods of solution with a
similar team drawn from the USSR. My USSR
colleagues then suggested that I might attend a
meeting of what I believe was called the USSR
Committee on Secondary School Mathematics in
order to tell them about the planned 1984
Adelaide ICME in the hope that this would
encourage the USSR to send a delegation to it.
This provided me with the opportunity to talk
with and listen to Pontryagin. He it was who
chaired that meeting in the absence through
illness of Pavel Alexandrov (1896-1982)
(Pontryagin's teacher who had inspired his work
in topology) and Andrei Kolmogorov (1903-1987).
Shortly before I went to Moscow, Hassler Whitney
(at that time president of ICMI) had visited our
home and when told about my planned trip he
reminisced about how he had visited Moscow in the
mid-1930s to attend a conference on topology and
had met Pontryagin then. I was able to convey
Hass's good wishes to Pontryagin, which prompted
his memories of that occasion. But it was a
chance remark made by Pontryagin at the committee
meeting that seized my attention. The committee
was discussing the place of complex numbers in
the higher grades of school and Pontryagin gently
remarked that the subject was in the curriculum
in Tsarist times. It suddenly struck me what
turbulent times this man had lived through: he
would have been 9 at the time of the Russian
revolution, and would have attended school at the
time that Nadja Krupskaya (1869-1939) (Lenin's
wife) and Anatoly Lunacharsky (1875-1933) were
attempting to reform education along socialist
lines (which included abolishing examinations).
He would have witnessed Stalin's overthrow of
these schemes, the Stalinist purges of the 1930s,
the arrival of Hitler's forces at the outskirts
of Moscow, and the 'cold war' that followed the
cessation of hostilities. What a story he would
have to tell. But what of his personal
struggles? Blinded at 14 and from a poor family
he relied on his mother effectively to be his
secretary and to read mathematics texts and
papers to him although she herself knew no
mathematics and had to fall back on describing
rather than naming symbols. Aged 17 he entered
the University of Moscow where, without being
able to take notes and without present-day
recorders to help, he had to memorise lectures as
they were given. Yet aged 19 he already began to
produce important mathematical results within
topology.
The committee that I attended had, then, three of
the greatest mathematicians of the twentieth
century - Russian or otherwise - on its secondary
schools mathematics committee. The word
gerontocracy might spring to mind, but these were
men who were passionately interested in the
mathematics taught in schools. Kolmogorov had led
far reaching innovations in the 1960s (which
Madam Maslova described at ICME 1) and was
responsible for the establishment of schools for
highly gifted mathematics students which not only
allowed their mathematical talents to be
developed but also ensured they had a rounded
education with music and literature given special
emphasis. Kolmogorov was invited to speak at
ICME 2 but at the last moment was replaced by
Sergei Sobolev (1908-1989) another outstanding
mathematician with a close involvement in
mathematics education whom I had the pleasure of
meeting both at Exeter and later in Tokyo. By
the 1980s Pontryagin and Kolmogorov were in open
disagreement about the nature of the school
mathematics curriculum and it was the former's
more conservative views that now prevailed.
Indeed Brezhnev, no less, proclaimed that, in
line with Pontryagin's views, a vector should
again be taught as something having magnitude and
direction. Yet what is important for ICMI is the
interest that these great mathematicians had in
education. And it was not just a case of saying
what should be done. Kolmogorov wrote textbooks
for schools as did, for example, the leading
Academicians, Alexei Pogorelov (1919-2002, and
one of the members of the USSR team that we met
with in Moscow) and Sergei Nikolskii (1905-) the
remarkable centenarian who served on the IPC for
ICME 6 and, aged 99, gave a talk at the Russian
exhibition at ICME 10.
It is good that ICMI has achieved a degree of
independence from the International Union of
Mathematicians, but I believe that if ICMI
proceeds further in narrowly focusing on research
in mathematics education at the expense of
accumulated professional wisdom, then it will be
to the detriment of what we, hopefully, are
seeking to do: to improve mathematics education
at all levels. We cannot sensibly ignore the
contributions that mathematicians such as those
to whom I have here referred made and which
mathematicians, even if of lesser standing, can
still make.
Geoffrey Howson, former Secretary-General of ICMI
------------------------------------------------------------------------
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