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Topic: [HM] International HPM 2000 meeting
Replies: 2   Last Post: Aug 31, 2000 5:49 PM

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J.G.Fauvel (John Fauvel)

Posts: 25
Registered: 12/3/04
Re: [HM] International HPM 2000 meeting
Posted: Aug 31, 2000 5:49 PM
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Dear Colleagues,

Obedient as ever to Julio's wishes, I enclose my impressions of the HPM
Meeting in Taipei two weeks ago. Best wishes John

History in mathematics education: challenges for a new millennium,
Taipei, Taiwan, 9-14 August 2000

Every four years a meeting is organised somewhere near the location of that
year's ICME (International Congress on Mathematics Education), preferably in
a different country, on the relations between history and pedagogy of
mathematics (HPM). In 1996 the HPM meeting took place in Braga, Portugal (a
valuable book of papers from that conference has recently appeared, edited
by Victor Katz: Using history to teach mathematics: an international
perspective, Washington: MAA 2000). This year the ICME was in Japan, and
the HPM meeting was held in Taiwan, at the National Taiwan Normal
University, Taipei, where there was a tremendously warm welcome for foreign
delegates (from nineteen countries and all continents) from Taiwanese
students and teachers.

The general pattern of each day was to lead off with a plenary lecture,
followed by a mid-morning break involving cake, fruit and various teas; then
some talks in parallel sessions, followed by lunch. The afternoon sessions
were again interspersed with fruit, cakes, juices and teas, and the evenings
were sometimes free for delegates to wander the nearby night markets and
sometimes occupied with conference dinners and karaoke. Two of the
conference dinners, all consisting of an apparently endless selection of
wonderful and delicious courses, were prepared and served by students at the
catering college which was one of the sponsors of the HPM meeting. The
karaoke aspect of such evenings were no less impressive: unlike western
karaoke which is a solitary singer stumbling nervously through a dreary
song, Taiwanese karaoke is a social event in which anyone volunteered
receives immediate backing, vocal and calisthenic, from audience and waiters
alike; every song an opportunity for imaginative social supportiveness.

The conference expeditions took place on two afternoons, one to climb a
volcano in a typhoon before a communal hot springs bath, the other to visit
the greatest assemblage of Chinese art in the world, the Imperial collection
once housed in the Forbidden City, Beijing, and now held in Taipei's
National Palace Museum.

These varied and well-judged social events formed an admirable context
within which the academic content of the HPM meeting could flourish. The
five plenary lectures, given by Marjolein Kool (The Netherlands), Park
Seong-Rae (Korea), Christopher Cullen (UK), Karine Chemla (France) and
Masami Isoda (Japan), provided a range of background studies against which
various themes of the conference could be played out in symposia, workshops,
round tables and panels. The two-volume proceedings issued in advance,
edited by Wann-Sheng Horng and Fou-Lai Lin, provided an invaluable aid for
delegates to study (before, during or afterwards) papers whose verbal
delivery might be in an unfamiliar language. And of course the publication
of a full range of papers in advance makes it possible to become informed
about the clashing sessions one could not attend. Looking through the
papers in the proceedings might provide interesting evidence for cultural
nuances in the modern HPM research world: papers written by Japanese or
Taiwanese researchers tend towards looking more "scientific" in the sense of
having fuller statistical backup, while occidental researchers tend to
report on their work in a more purely verbal way. (But this observation may
reflect a host of other factors such as what kind of researchers from
different countries were able to attend, as well as what kind of reports are
easier to write in English.)

There was the usual rich mixture of contributions which is one of the
strengths of HPM meetings: papers unveiling new historical research, and
overviews of historical themes to inform teachers and others of recent
developments in historical understanding, as well as papers in educational
research and describing ways of incorporating history in the mathematics
classroom. In the opening plenary address, Marjolein Kool (Netherlands)
struck exactly the right tone by showing how problems from sixteenth-century
Dutch arithmetic books could enthral and stimulate today's pupils, and in
her classroom had done so: the moral being not that Taiwanese teachers
should use old Dutch problems particularly, but that old texts introduce
students to issues such as different problem-solving strategies, the
humanity of mathematics, its universality (as similar problems are found in
many lands and cultures), and above all generate an enthusiasm which not all
mathematics education achieves.

Eastern mathematics, and issues around the meeting of eastern and western
mathematics, played of course a welcome and major role in the programme.
The second plenary lecture was Park Seong-Rae's masterly survey of the
introduction of western mathematics to China, Japan and Korea. It was a
revelation to many delegates that the history of modern (western-influenced)
mathematics in Korea is pretty much a phenomenon of the past half century.
Among the many other studies in eastern mathematics it is worth drawing
attention to papers by Wann-Sheng Horng (Taiwan) on pedagogical aspects of a
nineteenth-century Korean mathematical text; Shigeru Jochi (Japan) on the
influence of the Jiu Zhang Suan Shu on Japanese mathematics (the conclusion
seems to be that its influence was rather limited); Yan-Chyuan Lin (Taiwan)
on a fifth-century Chinese computational canon; Osamu Kota (Japan) on the
history of calculus education in Japan; and Naomichi Makinae (Japan) on
post-1945 mathematics education in Japan.

The most impressive dimension of this HPM (of a meeting with many impressive
dimensions) was the reports from Taiwanese teachers about how they have
incorporated history of mathematics in their teaching. Yu-Yi Lin,
mathematics teacher at the catering college whose students prepared the
conference dinners, shared the way she uses history to help students
overcome "math anxiety", arousing their motivation with the bold claim "Let
students find the meaning of life through mathematics history". Yen Fu Ming
described using a range of historic proofs of Pythagoras' theorem, from
several cultures, to enable Junior High School students to construct the
knowledge for themselves and begin to feel themselves to be mathematicians.
Hui-Yu Su reported on using the so-called Pascal's triangle in high school
mathematics lessons, for students to learn actively about connections
between different mathematical concepts.

These schoolroom activities were doubtless the result of work in previous
years in the Normal University and other Taiwanese teacher training
institutions, for Taiwanese teacher trainers, too, turn out to incorporate
history of mathematics in a variety of ways. Ya-Hui Hsaio and Ching-Kuch
Chang described using history to help in-service teachers invigorate and
motivate mathematical underachievers. Feng-Jui Hsieh discussed how the
beliefs of teachers themselves can be broadened and enriched, in the
particular case of perceptions of negative numbers, through history. In
short, the foreign delegates were welcomed to an island which has already
made great strides in relating history to pedagogy of mathematics.

Here are just a few more of the memorable sessions which struck me. (Those
attending other sessions will have their own list, of course.) Li Yu Fu's
fascinating explanation of the Bunun calendar which formed the conference
logo: the Bunun people of central Taiwan are among the so-called
"aboriginal", that is, pre-Chinese, inhabitants of the island. Karine
Chemla and Christopher Cullen enjoying a robust interchange over the deep
historiographical question of whether the same word 'proof' can be used to
describe both what ancient Greek and ancient Chinese mathematicians did. In
a remarkable tour-de-force of technological as well as intellectual
sophistication, Masami Isoda's plenary lecture on using technology in
teaching mathematics with history incorporating images, on his computer,
from the conference itself, photographed a few hours earlier. The Botswana
delegate Luckson Kaino's account of the challenges facing mathematics
education in sub-Saharan Africa in the years ahead. Coralie Daniel's
Maori-inspired Fibonacci scarves. Greisy Winicki-Landman's fine worksheets
on the history of quadratic equations to enable pre-service Israeli teachers
to explore different teaching sequences. The Platonic solids (or rather
hollows, being Chinese lanterns and the like) constructed from Coca-Cola
cans, old milk cartons and other symbols of western capitalism by the pupils
of Chun-Chih Peng. And Fr�©d�©rick Metin's talk on seventeenth century
fortification proved so popular that he was asked by the Taiwanese students
to repeat it.

There were two Round Tables at the conference, on values in mathematics
education and on issues of transmission between and meeting of cultures. In
the bad old days (at other conferences in other disciplines) a "round table"
used to mean a number of speakers successively reading their pre-prepared
texts at the audience until the time ran out, a thoroughly dispiriting event
for all concerned. The round tables at HPM Taipei were quite different,
full of rich interest and leading to stimulating and genuine discussion.
The values session, chaired by Alan Bishop (Australia) was to introduce the
Australian-Taiwanese team who are working on a three-year project enticingly
called VAMP (Values in Mathematics Education). The cultural transmission
session -- "Culture meets culture: where next?" -- sought with the help of
an international and multicultural panel, chaired by John Fauvel (UK), to
explore how to take forward into one's home community the insights and
experiences of a conference such as this, with the aid of those who have
studied and observed other meetings of cultures in history and elsewhere.

The contribution made by Taiwanese teachers and students to the conference
marked an important consolidation of a trend already noticeable in earlier
HPM meetings, in the strength of the home team. The Taiwanese
school-teachers at the conference were already informed and enthusiastic
about HPM issues, having been trained at the Normal University in Taipei,
and the students were currently studying there, often for master's degrees,
under the guidance of Wann-Sheng Horng and his colleagues. So there was
already a strong base for fruitful interaction with the visiting teachers,
historians and educators, and a sense that the activities and approaches
stimulated by the HPM meeting could and would continue afterwards. Thus the
efforts put in beforehand over several years, by the conference organisers,
in their role as teachers at the Normal University, ensured that the HPM
meeting was part of the ongoing development of HPM studies in Taiwan as well
as benefiting HPM activities world-wide.

In developing HPM activities further in the region, the hope was expressed
for holding a series of regular future conferences, somewhat after the
fashion of the European Summer University, which could bring together
students and teachers from many East Asian countries, notably Japan, Taiwan
and Hong Kong.

A comparison
I began this report by stressing the group dynamics and social context of
the meeting for a reason, in order to bring out the strength of HPM culture
as it is developing. For the sake of contrast, consider what apparently
happens among our colleagues in science education. Last year's Fifth
International Congress on History and Philosophy of Science in Science
Teaching, a science version of HPM held in Italy in September 1999, was
reviewed in the BSHS Education newsletter (no 30, February 2000, pp. 6-10)
by a number of British participants at the conference. In a surprisingly
critical set of reports, Clive Sutton drew attention to the lack of
discussion ("discussion (in the sense of a real engagement between people
with different perspectives) did not occur") while Peter Ellis drew
attention to the distance of the whole proceedings from classroom reality:

"what was sad about the conference was the lack of reports about actual
experiences in the classroom and strategies for introducing and using
historical material. It was sad that some of the few school teachers who
did speak were criticised for trivial errors or generalisations by their
more authoritative academic counterparts. [. . .] Unless the group can be
more appealing to science teachers and science teacher trainers it does not
seem to be fulfilling its function of promoting the history and philosophy
of science in science teaching."

(I suspect the writer half had in mind to describe the academics as
"authoritarian" before substituting the less charged word "authoritative"!)
And Elspeth Crawford, another conference delegate, commented sardonically on
the relation between the congress's activities and its title, 'Science as
Culture', and the conference culture itself, in forthright terms:

"I am not sure if the title did anything other than allow people to come and
talk about what they were going to talk about anyway. There was no attempt
that I heard to address the issue of science as culture, so I still do not
know what it means to refer to science in this way. [. . .] Once again, I
find my report of a conference finishing with a plea that those who organise
conferences pay attention to the group dynamics and the culture set up
within the conference itself. We need far more time spent working at
particular topics and issues, in genuine discussion, and a much greater
emphasis on how to enable teachers within the systems which employ them."

The authoritarian image of the history and pedagogy of science congress
emerging from these authoritative reflections could not be further in every
respect from the tradition of HPM meetings, not least in its latest splendid
manifestation in Taiwan. The success of the Taipei meeting was due
especially to the enormous care of Wann-Sheng Horng and his colleagues to
meet Elspeth Crawford's last point, in effect, paying attention to the group
dynamics and conference culture. Everything that could be done was done to
foster an inclusive atmosphere in which people from different cultures,
traditions, and locations within the educational world could all participate
and contribute their insights to furthering the relations between history
and pedagogy of mathematics. Everyone knew, and cared, that what this
meeting was ultimately about was what would happen in classrooms, and took
on board the absolute responsibility to support teachers and learners at the
front line, in countries across the world.

John Fauvel

> Date: Wed, 30 Aug 2000 11:38:37 -0300
> From: Julio Gonzalez Cabillon <>
> Subject: [HM] International HPM 2000 meeting
> Dear Colleagues,
> ( For those who have just got back from the International HPM 2000
> meeting, in Taiwan )... I would appreciate whether you could share
> with us (at least, a snapshot of) your impressions (a brief report
> would be OK) on these talks ...

. . .
> Best wishes and many thanks,
> Julio Gonzalez Cabillon

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