The Circulation of the HPM Tongxun and Its Relevance to the
Mathematics Teacher Community in Taiwan1
I. Introduction
The first issue of the HPM Tongxun (HPM Newsletter) was published
on October 5, 1998. Since then, about ten issues of the Newsletter have been
published for years to follow. Due to that fact that this was initiated to help
organize the HPM 2000 Taipei Conference, the title of the first nine issues
is called HPM Taipei Tongxun instead. As well known in the mathematics education
community, HPM, an international study group affiliated with the International
Commission on Mathematical Instruction (ICMI), was begun in the early 1970s
to explore relations between history and pedagogy of mathematics. Since the
International Congress on Mathematics Education (ICME), organized by the ICMI
every four years, takes place a couple of days before or after in some city,
the HPM satellite meeting will be held, as expected, in neighboring area. This
is to encourage participants, especially those from abroad, joining both of
the meetings.
When I attended the HPM 96 Braga Conference in 1996, a satellite meeting of
the ICME-8 (in Spain), I was invited to organize the satellite HPM meeting in
Taipei in 2000 just because the ICME-9 was decided to take place in Tokyo in
the same year. In order to help local colleagues to be familiar with the HPM
issues and in turn to encourage them to expose in the international academic
occasion, I began to publish the Newsletter and to circulate in the mathematics
education community. As suggests the title, the theme of the Newsletter is to
encourage mathematics teachers incorporating history into their classrooms.
However, proper attention is also paid to the history of mathematics per se
since historical literacy is indispensable for those who like to improve their
teaching in the perspective of the HPM.2 Nevertheless, the most important role
the Newsletter has been playing is to serve a forum for teachers who want to
share their teaching experiences including those not basically related with
the HPM. Moreover, since there is no official organization like mathematics
teachers association in Taiwan, the publication of the newsletter also provides
an avenue, which apparently allows them to join together in a "virtual"
community.
In this article, I will trace back the short history of the still young Newsletter
by serving a tour guide into the materials appeared in its issues. And see how
it plays a due role in promoting the activities in terms of the HPM and research
in the history of mathematics in the academic circle. On the other hand, a preliminary
study is undertaken in order to understand just how circulation of the Newsletter
can be relevant in the mathematics education community of Taiwan.
The front page of the first issue
5 October 1998
II. Theme of the HPM 2000 Taipei Conference3
The Conference, titled "History in Mathematics Education: Challenges for
a new millennium" (HME)", was held from August 9-14, 2000, in Taipei,
Taiwan. And it was hosted by Department of Mathematics at National Taiwan Normal
University (NTNU), with funding from the National Science Council (NSC) and
others. I, serving as the local organizer, was entrusted by the then chair of
the HPM, Prof. Jan van Maanen (University of Groningen) at the recommendation
of the late Prof. John Fauvel (1947-2001) in Braga, Portugal in 1996.
HME is one of the satellite meetings of ICME-9, the International Congress on
Mathematics Education being held in Japan from 30 July to 6 August 2000. The
HME meeting in Taiwan is affiliated to HPM, the International Study Group on
the Relations between the History and Pedagogy of Mathematics. It will follow
the examples set, every four years since 1988, for an HPM satellite to the International
Congress. Thus it follows the pattern whereby an HPM meeting was held in Florence
in 1988, next to Budapest’s ICME-6; in Toronto next to Quebec’s ICME-7
in 1992; and in Braga in 1996, following Sevilla’s ICME-8. The main purpose
of the Taipei HME is, therefore, to create a forum entirely for those concerned
about the issues of relating history and pedagogy of mathematics. During the
meeting, participants will be encouraged to explore and elaborate just how history
of mathematics could be integrated in the three key components of mathematics
education—teaching, learning, and curriculum—as well as in the education
and training of teachers themselves.
Taiwan, called "Formosa" by Portuguese sailors in recognition of its
outstanding beauty, has become used to both observing and sometimes participating
in the vigorous relations between the West and the East from the 16th century
onwards. Due to Taiwan’s special location and historical experience, the
Taipei HME is pleased to provide an opportunity, in the very beginning of the
new millennium, for participants from all over the world to meet and sit with
each other in friendship around the round table, share our knowledge of the
ways in which mathematical culture was transmitted from one place to another,
and share an understanding that we still have much to learn from one another.
The Taiwan HME is expected to attract some 300 delegates including 150 international
and 150 local participants: historians, mathematicians, and mathematics educators
as well as teachers around the island. At least 50 presentations concerning
local contexts will be encouraged in order to enrich the multicultural concerns
of HPM (local, that is to say, to wherever the presenter comes from). A dialogue
between West and East in terms of the experience of students and teachers in
their communities is, therefore, a strong focus that the local organizers would
like to share with all participants, especially the international ones.4
III. Editing and Publishing the Newsletter
The editor of the Newsletter is Ms. Hui-Yu Su, one of my former graduate students
and now teaching at a senior high school in Taipei City. Her editorial board
includes fourteen members who are qualified high school mathematics teachers.5
Almost of them are in-service teachers but now back to NTNU to join the doctoral
/ master program in the history of mathematics / HPM. As the publisher of the
Newsletter, I act as a role of supervisor. Toward the end of every month (except
in summer and winter vacations), Hui-Yu Su who is now still joining my seminar
on the history of mathematics / HPM weekly will talk to me just what can be
covered in the next issue. If there are not sufficiently many submitted articles
to be considered, I will suggest to the board members the appropriate topic
that they can contribute. In fact, it is an obligation for them to write relevant
articles for the Newsletter. Apparently due to the reason, special issues of
the Newsletter covers the topics like an annotation of the Suan Shu Shu (no
later than 186 B.C), a bamboo text on mathematics most recently discovered in
China, which is one of the team works of the board members.
The Newsletter is published ten issues for each year. In addition to its print
form, we also provide an electronic version on the website: http://www.math.ntnu.edu.tw/~horng.
It is published regularly on the fifth day of each month. Yet due to winter
and summer vacation in school schedule, February and March issues, August and
September issues of each volume will be put together to become only one issue
respectively. In addition, since its first issue was begun on October 5, 1998,
so the Volume I of it contains only three issues. Moreover, Volume 3 contains
only nine issues since we also merged June and July issues in order to save
energy for organizing the Conference. Up to now (April 2002), we have published
thirty-five issues in total, which covers as many as 556 (A4) pages. As to the
sponsor for the publication and circulation, part of the NSC funding for the
Conference went, as proposed, to meet the related payment. But that was affordable
only for the first 19 issues or so. Thereafter, I could only spare some pocket
money from the NSC sponsored research project to support the printing –
some five or six hundred copies for each issue.
The circulation of the Newsletter takes the advantage of the high school teacher
community, most of whose members are the NTNU alumni. As always happened in
the publication of periodicals, the Newsletter attracted great attention from
the community at its very beginning. Yet, the HPM is not anything like education
reform issue to which the teachers should pay attention. Therefore, the copies
circulated dropped quickly from three thousand to the now stabilized five hundred
despite that it is free for interested readers. To this small population of
readers, I should thank my former students who took my course on the history
of mathematics at their senior year and that offered them an opportunity to
know something about the HPM. On the other hand, we send some twenty copies
to colleagues (basically historians of Chinese mathematics or advocates of the
HPM) in Hong Kong, China and the USA, whose constant enthusiasm about the HPM
at least adds one piece of evidence to the "virtual" existence of
the international Chinese community of the HPM.
Apparently it is due to this international community, we are able to share not
only HPM contributions but also studies in the history of mathematics for its
own sake. For example, the aforementioned special issue on the Suan Shu Shu
attracts a lot of attention in the community. On the other hand, some other
special issues are also edited for topics like Islamic mathematics after the
911 tragedy in 2001. In this connection, authors of the related articles are
encouraged to share their multicultural concern in educational setting, exploring
in depth just how we can learn the legacy of Islamic mathematics from, for example,
the inheritance problems associated with the Koran law.
IV. Content of the HPM Tongxun
From the inception of the Newsletter, we have indeed a very clear goal to attain,
namely, promoting the HPM. However, what should and could be covered in it is
a kind of vague idea to us. For now, I can only report that the Newsletter is
very successful by an "amateur" standard. We feel easy and relaxed
for the time being but have a vision in the future.
By now articles appeared in the Newsletter concern the following themes:
o Circulating among local colleague problems and possibilities that are central
in the international HPM community. Take for example, messages from John Fauvel
and Jan van Maanen eds., History in Mathematics Education: An ICMI Study (2000).
o Creating a forum for local teachers / graduate students who like to know what
is the HPM all about.
Special issues are edited:
(1) Reflection on Helena Pycior’s "Biography in the Mathematics Classroom"
(Vol. 2(10));
(2) Critical discussion on the presentations for the Conference (Vol. 3(8/9),
3(10));
(3) Annotation of the former Han dynasty bamboo text of mathematics, the Suan
Shu Shu (Vol. 3(11));
(4) Book review on Chinese translations of popular mathematics publications
in Taiwan (Vol. 3(12), 4(1));
(5) Reflection on John Fauvel’s articles on HPM (Vol. 4(6), 4(7));
(6) Islamic mathematics (Vol. 4(11), 4(12));
(7) Annotation of the Suan Shu Shu again (Vol. 5 (2/3)).
Reports on research projects or sponsored seminar (granted by the NSC) related
with the HPM (Vol. 4(12), 5(2/3)).
Reflections on issues of mathematics education.
_ Worksheet / teaching project / "virtual" speech draft on HPM (Vol.
3(10), 4(8/9), 4(10))
_ Introduction of mathematics websites (Vol. 2(7), 2(8/9), 3(10), 4(1), 4(8/9)).
_ Examples of "proof without words" (Vol. 2(2/3), 2(4), 2(12)).
_ Multicultural Mathematics (Vol. 3(4), 3(6/7)).
_ Information about the newly arrived journals or books on the related issues
_ Articles on the History of (Chinese) Mathematics.
V. Feedback from the Readers
As Hui-Yu Su reports in Vol. 5(4) of the Newsletter, we collect one hundred
questionnaires, each of which include nine questions. For Question 1, the questionnaire
shows a population structure of the readers as follows: graduate students (7/100),
prospective high school teachers (70/100), and high school teachers (23/100).
Question 2 is about the subscription background. Among those who fill the questionnaire,
26 out of 100 are subscribers who receive free copy of the Newsletter through
email attached file or print form. For those who are not subscribers, they are
accessible to the Newsletter through the website, school library or their teachers’
recommendation. As to the reading frequency of the Newsletter (Question 3),
there are 21 out of 100 who never miss any issue. Among the other readers, 35
read the Newsletter only occasionally while the still other 44 come up to it
when they search for related references.
About what kinds of articles (if any) they think more interesting than others
(Question 4), their answers can be put into the following category: historical
(57), related to teaching (67), popular math reader recommendation (12), math
homepage recommendation (19).6 Such a response is also consonant with their
answer to the question: From what kinds of articles you think you can learn
more? (Question 6) In fact, to this question their answer-patterns are as follows:
historical (61), teaching (60), popular maths reader recommendation (12), and
maths website recommendation (13). However, almost the same proportion of answers
is given to the question: What kinds of articles you think more difficult to
read? (Question 5) In fact, for the last question, we have the following answers:
historical (55), teaching (24), popular math reader recommendation (19), math
homepage recommendation (6), none (1).
It deserves to note that articles on the history of mathematics are as most
needed as difficult for reading. This may well explain why the Newsletter proves
successful in providing a forum for high school mathematics teachers to learn
what is about the HPM. Apparently in doing so, they think that the history of
mathematics should always come first. In fact, a similar concern is also expressed
in their answer to Question 7: In what way you think reading of the Newsletter
can be beneficial? In addition to their choices of the answers as follows: teaching
(62), research (55), general education literacy (23) etc., they also write down
some more specific comments on how the reading of the Newsletter would do help
to their study or career development. For example, `some of them claim that
their attitude towards teaching has been changed quite a lot. Some others emphasise
that they get to know how to integrate history into their teaching. Still, they
also come to realize that mathematical knowledge has many aspects. And that
realization makes them feel closer to mathematics per se. In summary, they all
know how to improve their (future) teaching in terms of the HPM, if necessary.
Finally, Questions 8 & 9 are to ask for their suggestion on the coverage
and editing. As to what kinds of articles should be covered in the Newsletter
(Question 8), their response is as follows: historical research (14), teaching
related (55), popular science readers’ recommendation (14), website recommendation
(12) etc. In order to encourage the editorial board to hold on, the readers
like to see in the near future the Newsletter can be edited and printed in a
more attractive and fancy way. Meanwhile, they also hope that it become more
popular and more available to teacher’s seminar and workshop. For this
purpose, they even urge us to make the HPM study more pertain to teaching in
mathematics classroom. Consequently, it is expected that this would eventually
lead to a systematic study in the HPM and its incorporation with mathematical
teaching.
In her conclusion to this survey, Hui-Yu Su reminds that articles in this Newsletter
are supposed to serve examples demonstrating how resources related with HPM
can be reached out to wider readership. By getting familiar with the format
and discourse in the HPM, readers would eventually be able to share how the
HPM can be accessible to teachers who have passion and vision in teaching.
VI. The Future of the Newsletter
Compared with the international counterpart, History and Pedagogy of Mathematics
Newsletter, published three times a year, the ambition of the Newsletter is
as greater as its capacity and diversity in content. Despite it is served basically
for a small population of readers yet to be organized into an association or
society, the members of the editorial board takes this chance to have "fun"
in doing the HPM. And in this process, they get to know how to improve their
expertise both in the history of mathematics and the HPM. As a consequence,
they become now more confident in professional development as high school teachers.
For example, once they have a chance to join the seminar with historians of
mathematics and the experts of the HPM, says Jan van Maanen (the HPM chair of
the period 1996-2000) and Marjolein Kool, they feel very comfortable even though
their English speaking is not fluent.
Nevertheless, the board members and some intelligent readers deserve wider forum
to explore their professional expertise. As to be expected the Newsletter should
do more about their profession development. Indeed, we should make the priority
to encourage more teachers to join together and share their reflections on teaching,
whatever related to the HPM or not. Besides, the message of the Newsletter should
also make it clear that a learned society is needed in order for professional
historians of mathematics, the HPM experts, mathematics educators as well as
school mathematics teachers to join altogether. I hope, in the near future,
that we can organize the Taiwanese Society for the History of Mathematics. It
is a model copied from the British Society for the History of Mathematics, in
which John Fauvel (1947-2001), serving the chair of the HPM in the period 1992-1996,
endeavored to imprint his important steps. We the Taiwanese HPM members feel
regrettable to his untimely death but are pleased to keep alive his legacy of
the HPM and his first and also the last visit of Taiwan in the year of 2000.
Notes:
1. The early version of this article was presented to the Sino-Australian Symposium
2002 (Sydney, Peking, Hsinchu) "Public Understanding of STM and the Roles
of Science Studies in the 21st Century Asia, April 1-2, Tsing Hua University,
Hsinchu, Taiwan.
2. The only exception is Volume III which contains nine issues. As to the reason
why, see Section III of this article.
3. In memory of John Fauvel, I quote here the message from the Third Circular
of the Taipei HME which was modified at his suggestion.
4. Participants for the Conference were about 120, including 30 colleagues from
eighteen countries and area. See also John Fauvel’s "History in mathematics
education: challenges for a new millennium, Taipei, Taiwan, 9-14 August 2000",
History and Pedagogy of Mathematics Newsletter No. 44, November 2000.
5. Most of my graduate students who come back for further study in the history
of mathematics / HPM are in-service high school teachers or retain their teaching
posts temporarily (usually for two years).
6. It should be noted that answers for Questions 4-8 are not exclusive. In other
words, multiple answers can be chosen.
Wann-Sheng Horng
Taiwan
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