Our friend Julio poses a difficult but meaningful task in
soliciting our views in the context of the framework of his four
questions. To answer these questions in any degree of details would
amount to writing a paper on the relation between history of
mathematics and mathematics education. As for myself I do not yet feel
prepared to take on this task. However, since Julio is so kind as to
send me his question, even though I am currently off the Historia-
Matematica-list (owing to my own incapacity to cope with the bulk of
incoming emails each day despite the benefit I would have derived
from subscribing to the list), I should respond to these questions,
if only in a sketchy way.
> 1. What would be, in your opinion, the pros and cons of integrating
> history of mathematics in teaching mathematics at
> undergraduate/secondary level?
We have heard a lot on the "pros", so here I only concentrate on
the "cons". In a plenary address given in April of 1998 at the ICMI
Study Working Conference on the role of history of mathematics in
mathematics teaching (held at Luminy, France) I made up a list of
"cons" by playing the devil's advocate. Let me reproduce the list
below.
** "I have no time for it in class!"
** "This is not mathematics!"
** "How can you set questions on it in a test?"
** "It can't improve the student's grade."
** "Students don't like it."
** "Students regard it as history and they don't like history class."
** "Students regard it just as boring as the subject mathematics
itself."
** "Students do not have enough general knowledge on culture to
appreciate it."
** "Progress in mathematics is to make difficult problems routine, so
why bother to look back?"
** "There is a lack of resource material on it."
** "There is a lack of teacher training in it."
** "I am not a professional historian of mathematics. How can I be
sure that it actually happened that way?"
** "What really happened can be rather tortuous. Telling it as it was
can confuse rather than enlighten."
** "Does it really help to read original texts, which can be a
difficult task?"
** "Is it liable to breed chauvinism and parochial nationalism?"
I hope to elaborate on each point in a paper I am supposed to
write up (twenty months ago!) For now I will just say something more
general. I once read the book "The Teaching of Science" by F.R.
Jevons(1969). He says, "Any history is not necessarily better than
none. ... Rarely based on first-hand historical study, they sometimes
amount merely to the dropping of a few illustrious names; or they may
take the form of anecdotes chosen --- all too often --- more for
romantic appeal than for accuracy. Such gestures tend to be ignored by
beginners and to irritate those who know." He also says, "It reflects
the fact that history of science can be just as dull, stale and
unprofitable as any other subject. ... The course that scampers
through from the Greeks to Darwin, giving just the main events and
dates, is of little more value to a student than learning the dates of
the kings of England." The same caveat can be applied to history of
mathematics. History of mathematics is not to be seen as a panacea to
all pedagogical issues in mathematics education. History of
mathematics is just one of the many means which may help under certain
circumstances, besides its own intrinsic value.
> 2. Which subjects should be integrated, and why?
My rule of thumb is : integrate wherever fitting. For a more
detailed discussion and in-class examples, please consult my article
"The ABCD of using history of mathematics in the (undergraduate)
classroom" published in the BULLETIN OF THE HONG KONG MATHEMATICAL
SOCIETY, vol.1 (1997), 143-154. The journal is quite a local journal,
not readily available in most libraries. Worse yet, it became defunct
after a short life span of two years. Thanks to the kind and generous
help from Professors Reinhard Laubenbacher and David Pengelley of the
New Mexico State University, the full article (with correction) is
available on their homepage on history of mathematics (at
http://www.math.nmsu.edu/~history ).
> 3. Taking (3c) into account, which topics should be taught
> (considered)?
This is a project dear to my heart, but I do not yet have much
experience with it. Next year I am going to offer a course for
students not majoring in science-oriented areas, bearing the course
title "Mathematics: Our Cultural Heritage". I have a lot yet to
learn. Maybe a year from now I can have more to say about this
question.
> 4. How should the math community 'behave' so that societies be prone
> to include (the history of) mathematics (bits, at least) in their
> *cultural* (non-utilitarian!) baggage?
I do not really know how best to proceed. For myself I just try
to keep an open mind and try to get interested in different areas of
intellectual and cultural endeavour. Mathematics is important, but not
the sole subject worth studying. It is the harmony of mathematics with
other intellectual and cultural pursuit that makes it important. I
like to learn more about this point, especially in civilizations other
than the Western world in which the ancient Greek civilization (with
its strong emphasis on mathematics) plays a significant role. Thus,
history is again a key to this question, and we are back to square
one!
I am eager to listen to what others have to say on these four
questions. Please cc your reply to the list to me at my email address
(<<mathsiu@hkucc.hku.hk>>) as I am currently off the list.
Thank you and have a good day!
Man Keung
SIU Man-Keung
Department of Mathematics
University of Hong Kong
Hong Kong SAR
China