[ICMI-News] ICMI News 11: August 2009
J Carvalho e Silva
jaimecs at mat.uc.pt
Fri Sep 4 08:44:08 CEST 2009
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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