[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 
Editor: Jaime Carvalho e Silva, Dep. Matematica, 
Universidade de Coimbra, Portugal


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


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 

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 

Frederick.K.S. Leung, Member-at-large, ICMI-EC, 
The University of Hong Kong, frederickleung at hku.hk


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

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 
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 
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 

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: 

Jaime Carvalho e Silva, Member-at-large, ICMI-EC, 
Organizing Committee, jaimecs at mat.uc.pt


4. ICMI AWARDS - Call for Nominations

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 

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


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 

*    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 
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)
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 
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 

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,

Ricardo Cantoral, Director, RELIME, rcantor at cinvestav.mx


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

Bridges Banff - Mathematics, Music, Art, Architecture, Culture
The Banff Centre, Banff, Alberta, Canada, July 26-29, 2009

CIEAEM61 - Commission internationale pour l'étude 
et l'amélioration de l'enseignement des 
Université de MONTRÉAL, Montréal, Québec, Canada, July 26-31, 2009

ICTMA 14 - 14th International Conference on the 
Teaching of Mathematical Modelling and 
University of Hamburg, Germany, July 27-31, 2009

SEMT '09 - 10th bi-annual conference on Elementary Mathematics Teaching,
"The development of mathematical understanding"
Prague, August 23-28, 2009

4th general meeting of European Women in Mathematics (EWM)
University of Novi Sad, Serbia, August 25-28, 2009

"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 

CoSMEd -Third International Conference on Science and Mathematics Education
Improving Science and Mathematics Literacy: Theory, Innovation and Practice
Penang, Malaysia, November 10-12, 2009

2009 SAMSA Conference
Southern Africa Mathematical Sciences Association
Belinda Hotel, Dar es Salaam, Tanzania, November 23-27, 2009

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

"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


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 

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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