[ICMI-News] ICMI News 11: August 2009

[J Carvalho e Silva]

ICMI News 11: August 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: Continuing Professional Development 
and Effective integration of Digital Technologies 
in Teaching and Learning Mathematics: Two 
Challenges for ICMI
2. A XXIst century Felix Klein's follow up workshop
3. Deadline Extended: ICMI / ICIAM STUDY
4. EARCOME5: First Announcement
5. Chilean Journal of Statistics (ChJS)
6. Calendar of Events of Interest to the ICMI Community
7. ICMI encounters: Hassler Whitney, Laurence C. 
Young and Dirk J. Struik: Personal recollections
8. Subscribing to ICMI News

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1.  Editorial: Continuing Professional 
Development and Effective integration of Digital 
Technologies in Teaching and Learning 
Mathematics: Two Challenges for ICMI

I will take the opportunity in writing this 
editorial of focussing on two major concerns in 
mathematics education, both of which have been 
the subjects of recent ICMI Studies and both of 
which are central to my own professional life. 
The first is the professional development of 
teachers of mathematics, and the second the use 
of digital technologies in mathematics teaching 
and learning.

The Continuing Professional Development (CPD) of Teachers of Mathematics
CPD was the subject of 15th ICMI Study 'The 
Professional Education and Development of 
Teachers of Mathematics'. The book has appeared 
in 2008 as Vol 11 in the New ICMI Study Series. 
It was edited by Ruhama Even, and Deborah 
Loewenberg Ball, who were co-chairs of the Study. 
The premise of this ICMI Study is that teachers 
are key to students' opportunities to learn 
mathematics, and what teachers of mathematics 
know, care about, and do is a product of their 
experiences and socialisation, together with the 
impact of their professional education. The book 
shows how preparing and maintaining a 
high-quality, professional teaching force that 
can teach mathematics effectively and prepare 
youth for a future of social responsibility is a 
worldwide challenge.

Issues around CPD for teachers of mathematics the 
Study volume argues offer 'a cross-cultural 
conversation' about mathematics teacher education 
with 'attention given to research, theory, 
practice and policy'. Clearly there are 
differences between countries as to how the 
challenge of mathematics-specific CPD is faced. 
Is CPD regarded as important?  A crucial tension, 
I would argue is that there is (and cannot be) an 
exact way of measuring the 'effects of CPD' on 
learners' achievement in and engagement with 
mathematics. This means that in the face of 
financial constraints, CPD is often the first to 
suffer. Yet we know that it is important to value 
our mathematics teachers and to ensure they are 
given the support they need to enhance their 
professional expertise - for themselves. CPD is 
not something 'to be done to teachers'. But how 
best can this be achieved given time (as well as 
funding) constraints? How can CPD be informed by 
the best research in mathematics education while 
remaining relevant to practice with its 
day-to-day pressures? How can the case for 
mathematics-specific CPD be made effectively to 
policy -makers and politicians? The National 
Centre for Excellence in the Teaching of 
Mathematics (NCETM), www.ncetm.org.uk, was set up 
in England by the UK Government in 2006 to face 
up to these challenges. I have been its Director 
since 2007. The National Centre oversees 
mathematics-specific CPD provision at a strategic 
level nationally across all phases of education, 
and coordinates its operation nationally. It is 
the first time such a national infrastructure has 
been put in place in England. The NCETM takes as 
its starting point the premise that effective CPD 
has three interrelated strands:

  - broadening and deepening mathematics content knowledge;
  - developing mathematics-specific pedagogy, 
which includes appreciating how learners engage 
with mathematics and likely obstacles to 
progression; and,
  - embedding effective mathematics pedagogy in practice.

Thus, the key aims of the NCETM are:

  - to stimulate demand for mathematics-specific 
CPD contributing to strengthening the 
mathematical knowledge of teachers and improving 
school and college performance in mathematics
  - to lead and improve the coordination, 
accessibility and availability of 
mathematics-specific CPD
  - to enable all teachers of mathematics to 
identify and access high-quality CPD that will 
best meet their needs and aspirations.


The National Centre has a virtual presence 
through its online web portal (www.ncetm.org.uk) 
and an on-the-ground presence through a network 
of Regional Coordinators (RCs) and teacher 
associates that cover all of England. They 
encourage teachers of mathematics to engage in 
collaborative teacher enquiry, to identify 
opportunities for high-quality professional 
development and to share examples of excellence 
across the region. This effort includes 
supporting the spread of dynamic networks in 
which teachers take the lead in developing their 
own communities -virtual and actual - thus both 
spreading ideas further and providing another and 
different type of CPD for teacher-leaders. Many 
of these networks are catalysed by the NCETM 
Teacher Enquiry Funded projects in which teachers 
are given some funds to work together on a shared 
problem, usually with some outside support. The 
National Centre works with a range of partners to 
promote CPD opportunities that are cumulative and 
sustained over the career of a teacher. Higher 
Education Institutions (HEIs), are important 
among these as they are already offering CPD 
opportunities for teachers and can provide 
expertise in mathematics and mathematics 
education, as well as bring new perspectives on 
the subject and on effective pedagogies.
National and regional events play an important 
part in the NCETM's work, but its unique offer is 
of course its web portal, a cutting-edge, online 
resource that allows the NCETM to reach those 
teachers that other more low-tech conventional 
means cannot reach. The portal signposts a wealth 
of excellent resources and is a dynamic means of 
sharing strategies for teaching mathematics 
through online networks and communities. Teachers 
of mathematics can also monitor their own 
learning chart their individual CPD progress 
through Self Evaluation tools and their Personal 
Learning Space (PLS).

Teachers' engagement with the NCETM has grown 
hugely and we have outstripped every target set 
us by the Government, with over 25000 users of 
the portal. In particular the use of the Personal 
Learning Space (including the Self Evaluation 
Tools) has been remarkably successful in engaging 
teachers: before April 2009 there was an average 
of 11,000 interactions per month, June 2009 there 
were 247,000 interactions per month!  There is 
still much to do however and many challenges to 
face before CPD for all teachers of mathematics 
in England is recognised as key by all, including 
politicians and policy makers, and is universally 
demanded. The National Centre continues to seek 
to engage more teachers and senior leaders in all 
sectors and to find further ways to work with 
partners to help grow all aspects of provision.

The use of digital technologies in mathematics teaching and learning

One focus of the NCETM's effort has been the 
promotion of the use of ICT (information and 
communication technologies) in the teaching and 
learning of mathematics alongside as a medium for 
enhancing teacher professional learning. We held 
a national one-day event on 'The Potential of ICT 
in Mathematics Teaching and Learning' at which we 
showcased the work of teachers using ICT in their 
mathematics teaching. We are actively working to 
promote and support networks of teachers working 
together on mathematics with different software. 
This is indeed challenging with complex issues to 
be faced related to teaching and learning, 
diversity and equity, many of which were 
discussed in ICMI Study 17. 'Mathematics 
Education and Technology: Rethinking the Terrain' 
with myself and Jean-Baptiste Lagrange as 
co-chairs. The Study Volume is to be published 
Dec 2009. The volume also addresses issues such 
as design of learning environments and curricula 
using digital technologies, learning and 
assessing mathematics with and through digital 
technologies and the emerging challenge of 
connectivity and virtual networks for learning, 
The volume comes out over twenty years after the 
first ICMI study on technology. The scenery of 
digital technology in mathematics education has 
radically changed and will continue to change. We 
look forward to still more dramatic changes that 
enhance engagement in our subject.

Celia Hoyles, Member-at-large, ICMI-EC, 
University of London, c.hoyles at ioe.ac.uk

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2. 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. 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.

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 will include around 20 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 9. Please register at the 
website http://glocos.org/index.php/dm-md/

Some of the talks at the workshop will be:

"Mathematics as a school subject in the XXI 
century: trends, promises and dilemmas".
Abraham Arcavi

"Functions and Analysis: Elements of reflection 
within the perspective of the Felix Klein project"
Michèle Artigue

"Felix Klein's vision on the relation: Between abyss and hysteresis"
Gert Schubring

"Algorithmic thinking in mathematics"
Manuel Silva

"Exploring and investigating mathematics: A key 
element in the activity of mathematicians, 
students and teachers"
João Pedro Mendes da Ponte

"Some considerations about the advances of 
Mathematics in 20th century and the possible 
implications to modernize the school curriculum"
Yuriko Baldin

"A Clifford perspective on Klein's Geometry".
Sebastià Xambó

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

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3. Deadline Extended: ICMI / ICIAM STUDY

JOINT ICMI / ICIAM STUDY
Educational Interfaces between Mathematics and Industry  (EIMI)

The deadline for submitting contributions to the 
Study has been extended until OCTOBER 15.

Instructions on submission of contributions and 
general information on the Study, organised by 
the International Commission on Mathematical 
Instruction (ICMI) and the International Council 
for Industrial and Applied Mathematics (ICIAM), 
can be found on the study website:
http://eimi.mathdir.org/

The Study Conference will be held in Lisbon on April 19-23, 2010.

Bernard R. Hodgson, Secretary-General of ICMI, bhodgson at mat.ulaval.ca

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4. EARCOME5: First Announcement

The Fifth East Asia Regional Conference on Mathematics Education
August 18-22, 2010, Tokyo, Japan
http://www.earcome5.jp/

IN SEARCH OF EXCELLENCE IN MATHEMATICS EDUCATION

Organizer: Japan Society of Mathematical Education (JSME)
Co-organizers: The Association of Mathematics Instruction
Mathematical Society of Japan
Mathematical Education Society of Japan
ICMI-International Commission on Mathematical Instruction

Conference Theme

The theme of conference is "In search of 
excellence of mathematics education". Countries 
in East Asia are well-known for their high 
achievement in international comparisons in 
mathematics. Exploring the factors behind this 
excellence, such as curriculum, teachers, and 
teaching-learning processes among others, is of 
special interest to researchers and practitioners 
not only in this region but also around the world.

Scientific Programs

The program of the conference includes several 
activities: Plenary Lectures, Round Table 
Discussions, Regular Lectures, Paper 
Presentations, Posters, Workshops, and 
Observation of Mathematics Lessons (Lesson 
Study). The official language of the conference 
is English.

Call for Papers

We hope that all participants will contribute 
actively to the conference by sharing their 
experiences and views in the various sessions. 
Moreover, you are encouraged to send a proposal 
for an oral presentation of your paper.

Submission of the Proposal

Intending participants are invited to present 
individual papers either in parallel paper 
sessions or in poster exhibitions. Proposals 
should be sent by email as Microsoft Word 
attachment to earcome5 at sme.or.jp BEFORE JANUARY 
15, 2010, including the following:

-Title, authors' names, affiliations, postal 
address, fax, telephone numbers and email address
-Aim and the main idea of the reported study, 
methodology and the expected conclusions (in 500 
words)
-Related essential references

The proposal should be submitted as a single file 
in Microsoft Word format saved as ".doc" or 
".rtf" using Times New Roman 11-point font size 
and single-spacing. To avoid confusion or loss of 
proposals, please name your file as follows:
EARCOME5_<your name>_country.doc. For example:
EARCOME5_S.Shimizu_JP.doc.

Important Dates
JANUARY 15, 2010: Deadline for the Submission of a proposal
MARCH 15, 2010: Notification of Acceptance:
MAY 31, 2010: Submission of Final Paper

Venue
National Olympics Memorial Youth Center, Tokyo
Address: 3-1, Yoyogi Kamizono-cho, Shibuya-ku, Tokyo, 151-0052
TEL. +81-3-3469-2525
http://nyc.niye.go.jp/e/

Registration
Before MAY 31, 2010 18,000 JPY
After JUNE 1, 2010 20,000 JPY

Accommodation
There are many HOTELS in the Tokyo area. A 
limited numbers of rooms are available at the 
National Olympics Memorial Youth Center at lower 
cost.

Committees
International Program Committee
Shizumi Shimizu, Chair of IPC, Frederick K.S. 
Leung (Hong Kong), ICMI-ECÅCToshiakira Fujii 
(Japan), Maitree Inprasitha (Thailand), 
Berinderjeet Kaur (Singapore), Shiqi Li (China), 
Masataka Koyama (Japan), Chap Sam Lim (Malaysia), 
KyungMee Park (South Korea), Yoshinori Shimizu 
(Japan)

Advisory Board
HeeChan Lew (South Korea), Fou-Lai Lin (Taiwan), 
Cham Roatch (Cambodia), Peter Sullivan 
(Australia), Catherine Vistro-Yu (The 
Philippines), Hiroshi Fujita, Yukihiko Namikawa, 
Yoshishige Sugiyama, Toshio Sawada, Tadao 
Nakahara, Akihiro Nozaki, Michimasa Kobayashi, 
Tomoko Ninomiya (Japan)

Local Organizing Committee
Shizumi Shimizu (Chair), Sigeru Iitaka, Yasuo 
Morita, Yoshihiko Hashimoto, Toshiakira Fujii, 
Ryousuke Nagaoka, Takayuki Kodera, Toshikazu 
Ikeda, Hiroyuki Ninomiya, Masami Isoda, Masataka 
Koyama, Yoshinori Shimizu, Yasuhiro Sekiguchi, 
Keiko Hino, Mikio Miyazaki, Tatsuo Morozumi, 
Nanae Matsuo, Hiroyuki Kumakura, Kazuya Kageyama, 
Hideo Emori

For Contact: earcome5 at sme.or.jp

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5.  Chilean Journal of Statistics (ChJS)

Dear colleague:

I am very pleased to inform you that on August, 2009, we are launching the
new version of the Chilean Journal of Statistics (ChJS).

More details about the journal, that now is including papers in statistics
education, can be checked in the journal web page
http://www.soche.cl/chjs

In this way, the Chilean Society of Statistics (SOCHE, http://www.soche.cl )
materializes the dream of publishing an international journal, and we hope this
will serve to begin a new stage for statistics in Chile.

We greatly appreciate any diffusion that you can make of ChJS.

Best regards,

Victor Leiva, Executive Editor, Chilean Journal 
of Statistics, victor.leiva at uv.cl

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6. Calendar of Events of Interest to the ICMI Community

"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

The 43rd Korean National Meeting of Mathematics Education,
Hannam University, Daejeon, Korea, October 16-17, 2009
http://www.ksme.info, ksme_ser_d at yahoo.co.kr

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

TIME 2009  - Third National Workshop & Conference
  "Technology and Innovation in Math Education"
IIT Bombay, India, December 4-7, 2009
Prof. Inder K. Rana Prof. Inder K. Rana, Convener (ikrana at iitb.ac.in)

"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/

Thirteenth Conference on Research in Undergraduate Mathematics Education
Marriott Raleigh City Center - Raleigh, North 
Carolina, USA, February 25-28, 2010
http://rume.org/crume2010/

International Consortium for Research in Science 
and Mathematics Education - 2010 Consultation
BlueBay Los Angeles Locos Hotel, La Manzanilla, Mexico, March 9-12, 2010
http://ehe.osu.edu/groups/icrsme/

5th International Conference on Origami in Science, Mathematics and Education
Singapore Management University, Singapore, July 13-17, 2010
org: Eileen Tan (origamiwolf at gmail.com), Patsy 
Wang-Iverson (pwangiverson at gmail.com)

ESU-6 - 6th EUROPEAN SUMMER UNIVERSITY ON THE 
HISTORY AND EPISTEMOLOGY IN MATHEMATICS EDUCATION
Vienna, Austria, July 19-23, 2010
http://www.algebra.tuwien.ac.at/kronfellner/esu6/

EARCOME5 - The Fifth East Asia Regional Conference on Mathematics Education
Tokyo, Japan, August 18-22, 2010
http://www.earcome5.jp/

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7. ICMI encounters: Hassler Whitney, Laurence C. 
Young and Dirk J. Struik: Personal recollections.

I owe much of my academic life to my professors 
in the High School and in the college and, later, 
to my graduate advisor and research mentors. I 
never had a formal preparation in neither 
Mathematics Education nor in the History of 
Mathematics. After my graduation, in 1954, I 
taught for a few years in Elementary and High 
School. I owe much of my style of teaching to my 
father, who was a Math Teacher. Out of my 
practice in classroom I reflected about the 
meaning and purpose of Mathematics Education and 
published a few papers, which later proved to be 
influential. But I soon devoted my attention to 
research in Pure Mathematics and engaged in a 
doctoral program, completed in 1963. My research 
area was Calculus of Variations and Area Theory. 
Immediately after my doctorate, I went to the USA 
as a post-doctoral fellow, to continue my 
research. Due to political circumstances, I 
decided to stay in the USA and taught 
undergraduate and graduate courses. In 1972 I 
decided to return to Brazil, to become the 
Director of the Institute of Mathematics, 
Statistics and Computer Science/IMECC of a new 
university, the State University of 
Campinas/UNICAMP, which had been created in 1968.

In this short note, I will comment on my personal 
experiences after my return to Brazil, focusing 
on Hassler Whitney (1907-1989), Laurence Chisholm 
Young (1905-2000) and Dirk Jan Struik 
(1894-2000).  I owe much of my attitudes and 
views on Mathematics Education and the History of 
Mathematics to these distinguished 
mathematicians, who became my very close friends.

The work of Hassler Whitney, particularly his 
book on Geometric Integration Theory, where he 
gives a theoretical basis for Stokes' theorem 
with singularities on the boundary, was basic for 
my research. My doctoral thesis, on Calculus of 
Variations and Measure Theory, was based on the 
generalized surfaces introduced, in the fifties, 
by Ennio De Giorgi and Laurence C. Young, both 
internationally recognized for their works on 
measure theory and the calculus of variations.

Although the focus of the Institute in Campinas 
was research in Pure and Applied Mathematics, I 
soon realized how fundamental it was for our 
country to develop also the area of Mathematics 
Education. We had enough funding to invite 
foreign mathematicians as visiting professors and 
I used these funds to invite Hassler Whitney and 
Laurence C. Young, two basic references in my 
doctoral research. Whitney came to Campinas for 
the first time in 1976 and returned for a number 
of years, for one-month visits. Young came in 
1978 and later returned.

When I invited Hassler Whitney for the first 
time, he very kindly thanked the invitation, but, 
to my surprise, he said that he was not doing 
research in mathematics anymore and that his 
interest was only Mathematics Education. Since I 
was willing to get started some projects in 
Mathematics Education at UNICAMP, I promptly 
confirmed the invitation.

At the Institute we were all excited to have such 
a distinguished mathematician with us. He was 
always prompt to engage in conversation with the 
faculty and he agreed to give a memorable 
mathematical lecture on the "Four Colors 
Problem", which we, fortunately, taped.
But he was more interested in our projects on 
Mathematics Education. It was an opportunity for 
him to apply his theories of education in a 
different cultural environment. His proposals for 
education were supported by the humanistic and 
phenomenological approach to psychology of Carl 
Rogers (1902-1987), who was his friend. 
Essentially, Whitney believed that all 
individuals exist in a continually changing world 
of experience of which they are the centre. His 
ideas about mathematics education were 
synthesized in a booklet published as Elementary 
Mathematics Activities. Part A. in the series of 
Trial Materials 1976, of Institute for Advance 
Studies, in Princeton. He always referred to it 
as Part A. This was a basic manual for me and for 
our projects.
Our objective was to develop curricula for 
elementary and secondary schools based in a sort 
of experimental mathematics. Influenced by 
Eliakim Moore's Presidential Address to the AMS, 
1902, we were developing a series of instruments 
to favor mathematics experiences. Whitney 
writings encouraged us. He clearly wrote
  "The child's need is to live and grow in his own 
way. Story problems become part of oneself when 
acted out; in this way, they become real, and in 
particular, numerical relations appear naturally.
The child's natural approach is to experiment and 
explore. Carrying this out, he finds courage to 
try many things; some work out in funny ways 
(which we prefer to call wrong), others come out 
right. Intrigued, he plays with the funny things, 
changes them, sees what happens, and makes them 
come out right also. He is beginning to act like 
a research worker."(Part A, p.3)

Problem solving was the focus of much interest in 
Brazil, maybe as a sort of reaction to the 
dominance of the so-called Modern Mathematics 
Movement, in the previous decade. As an 
alternative to formal problems, frequently 
hindered by lack of motivation, we favored story 
problems. In a very inspiring writing, Hassler 
Whitney says in the same book:

"How does one solve story problems? First of all, 
replace 'solve it' by 'play around with it'. Half 
the difficulty is now over. Make it concrete: act 
out the story. Have courage to try the story in 
different ways, getting used to its various 
features. When things turn out wrong, be 
interested in how they are wrong, and try 
changes; act out the story again. Now if you ask 
what was wanted, you may be ready to see or 
quickly find the answer. It is really basically 
as simple as that. Courage to play with and try 
different things is the key note."(Part A, p. 41)

Hassler Whitney behavior goes much beyond the 
great mathematician and educator he was. Hass, as 
he wanted to be called, was very kind and gentle. 
In his first visit to Brazil, in 1976, I went to 
receive him at the airport. It was a surprise, 
Simply dressed, with a backpack, a small piece of 
luggage and a violin case. We reserved a suite in 
the best hotel of Campinas. Next day, we went to 
pick him up and he asked to go to another hotel, 
near the train station.  He had decided to walk 
in downtown and found this low category hotel. 
We, surprised, complied to his wish. Every year, 
on his returns to Campinas, he would go to the 
same hotel. He asked for us to pick him up in the 
early afternoon. In the morning he would juggle 
and he became well known in the neighborhood, 
which was downtown, dense with popular commerce. 
We were surprised.
I frequently invited him to have dinner in our 
home. His meals were frugal. But he would always 
bring his violin to play with my son Alexandre, 
then 13 years old. Beatriz, then 16 years old, 
played flute. Together they would spend some 
hours playing. He was so patient with them. Also, 
many colleagues in the faculty would look for 
Hass, as a sort of psychoanalyst, to talk about 
personal problems. Hass, patiently, listened to 
them and gave advise. Hassler Whitney, besides 
the recognized distinguished mathematician, was 
an inspired mathematics educator and a remarkable 
human being.

In a completely different strand, Laurence C. 
Young was also very influential in my personal 
development and a great benefit for our 
Institute. He was active in mathematics and 
always prompt to discuss the research of our 
young functional analysts, an area of much 
interest in our department of mathematics. He 
offered very interesting courses.

Young was indirectly influential in our projects 
of curriculum development for elementary 
geometry. He told us about the concerns of his 
parents, Grace Chisholm Young and William Henry 
Young, both very distinguished mathematicians, 
with the mathematics education of children. He 
suggested to us the book Beginner's Book of 
Geometry, which his parents published in 1905, 
which starts with paper folding and leads to 
theorems. We readily acquired this important 
approach to experimental geometry. I personally 
owe much to this book.

I particularly benefited from the fact that 
besides being active in pure mathematics, Young 
was finishing his book on the History of 
Mathematics, based on his vast literary culture 
and personal recalls. The book, Mathematicians 
and their time, was finished in Campinas and 
published by North-Holland in 1981. I learned 
much from Young on literature and the classics, 
and I developed my approach to historiography by 
trying to recognize how mathematics and 
mathematicians were influenced by the material 
and intellectual atmosphere of their time and the 
World scenario. Mathematics is like a flower, 
among many others, in a garden. They all grow in 
symbiosis. Probably, this was the moment I 
started to develop my ideas on the dynamics of 
cultural encounters.

My interest in history developed much earlier. 
Indeed, historical background, based on 
"academic" primary sources, was fundamental for 
my research on the Calculus of Variations and 
Measure Theory of generalized varieties. But 
years later, when I taught in Africa, I began to 
question the hegemony of the "official" History 
of Mathematics and also of Mathematics Education. 
Later, teaching in several countries of Latin 
America and in rural areas and urban periphery in 
major cities, I became even more uncomfortable 
with the traditional approach, to both History of 
Mathematics and Mathematics Education. It was 
clear that what we call Mathematics emerged in 
the Mediterranean basin and spread to the entire 
World after the "discoveries" and the colonial 
process.

I had read Dirk J. Struik's A Concise History of 
Mathematics and A Source Book in Mathematics, 
1200-1800. Both became basic references to look 
for a broader approach to the History of Science 
and Mathematics and the colonial scenario. I knew 
of Struik's political posture and I was impressed 
by his historiographical approach to the colonial 
period, as seen in Yankee Science in the Making. 
I also found The Birth of the Communist Manifesto 
very elucidative. The interest I developed about 
the colonial period and the political overtones 
of the expansion of Western mathematics to the 
entire World attracted me to Struik.

In 1984, I boldly wrote to him, with an 
invitation to visit Campinas. He replied saying 
he had never been in South America and would very 
much like to accept the invitation. But he could 
not travel alone. His wife had to come with him. 
Since he was ninety years old, we found it 
natural that his wife should care for him when 
they were travelling. Since his wife had a degree 
in Mathematics, we managed to send a ticket also 
for her. When they arrived, a big surprise. 
Although Mrs. Struik was younger than him, it was 
he who had to care for her. She was fragile, 
losing her memory. He was surprisingly vigorous. 
She depended on him for permanent care. Dirk, as 
he liked to be called, was a great company. 
Always caring much for his wife, they liked to 
visit the countryside and enjoyed Brazilian food 
and drinks.

Conversations with Dirk were rewarding. I was 
much influenced about his deep and comprehensive 
views of World politics, particularly of the role 
of Science and Mathematics and education in it. I 
was structuring the Program Ethnomathematics and 
Struik was much influential in the development of 
my ideas. His remarks on the colonial process of 
developing Mathematics in Latin America and in 
the short lived Dutch attempt of establishing a 
colony in Brazil were precious. He gave several 
lectures and wrote a remarkable paper for the 
Revista da Sociedade Brasileira de História da 
Ciência.

It was a great emotion for me when, while driving 
him to the airport, he said he never thought that 
at his age he would make such a strong new 
friendship.  Indeed, we became close friends. I 
visited the Struiks a couple of times in their 
old home near Boston. When he was awarded the 
Kenneth O, May Medal, in 1989, in Hamburg, I was 
there to greet him. Later, I flew from Brazil 
specially to address the Symposium organized in 
Providence to commemorate his 100th birthday. A 
few years later, during the AMS/MAA Joint Annual 
meeting in Baltimore, in 1998, my colleagues and 
friends organized a Seminar honoring my 65th 
birthday. Dirk was the main speaker. When I 
thanked him for having travelled to Baltimore 
specially for this occasion, he replied "I had to 
be here. You came from Brazil for my 100th 
birthday party. And I will come to your 100th 
birthday". Although my friendship with Dirk 
Struik came later in my life, he was a remarkable 
influence.

I consider Hassler Whitney, Laurence C. Young and 
Dik J, Struik not only academic mentors, but 
above all exemplary human beings which inspire my 
behavior.

Ubiratan D'Ambrosio, ubi at usp.br

------------------------------------------------------------------------

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