420MATHEMATICS TEACHER
to your pupils are historical insights and mathe-
matical insights. (Furinghetti, 1997, p. 56)
I am convinced that, as Furinghetti indicates, a
good knowledge of the history of mathematics may
foster pedagogical creativity for integrating history
into mathematical activities.
IS INCLUDING THE HISTORY OF
MATHEMATICS IN MATHEMATICS
TEACHING EFFECTIVE?
A panel discussion, “On the Role of the History of
Mathematics in Mathematics Education,” at the
second International Conference on the Teaching of
Mathematics (ICTM-2), held on Crete in July 2002
addressed the role of the history of mathematics in
education. Following the panel’s reports, an Ameri-
can mathematics educator raised a critical ques-
tion: “Is there any evidence showing that including
the history of mathematics is effective in the teach-
ing of mathematics?” Answering this question is
difficult for anyone who advocates the importance
of including history in the mathematics curriculum.
We have to clarify one critical conception before
answering this question. Namely, what is meant by
“effective in the teaching of mathematics”? If it
means improving students’ performance on stan-
dardized examinations, my attitude would be
reserved. To my best knowledge, no empirical study
indicates that learning the history of mathematics
helps students perform better on traditional tests.
Although studying the history of mathematics may
improve students’ attitudes toward mathematics,
the linkage between attitude and achievement is
neither linear nor straightforward.
Yet if effectiveness means developing students’
views of thinking and further improving their
learning behavior, I am convinced that including the
history of mathematics in the curriculum can help.
After experiencing a problem-based course that
used a historical approach, many Taiwanese students
were likely to hold active views about mathematical
thinking and were able to demonstrate multiple
approaches to problems (Liu 2002). Particularly,
when learning about “peculiar” methods used by
ancient mathematicians, those students better
appreciated the role of imagination in problem solv-
ing, and some students were more willing to think
and try the problems. After seeing Archimedes’
derivation of the area of a circle, one of my students,
who had initially emphasized the deductive nature
of mathematics, reconsidered his view:
I consider imagination more important [than log-
ical thinking] because of Archimedes. I feel he is
so strange. He derived the volume of a sphere by
means of a lever. . . . How did he think of it?
Plus, he transformed a circle into a triangle. I
feel his imagination is quite strange.
That response is typical of those of students in
my class. Nevertheless, the empirical evidence
accumulated thus far is insufficient for us to con-
clude what history can or cannot do for teachers
and students. The International Study Group on
the Relations between History and Pedagogy of
Mathematics (HPM) is attempting to delineate a
role for the history of mathematics to play in school
teaching. With cooperation between researchers
and teachers, we hope that a clear picture of that
role can be drawn in the near future.
REFERENCES
Albers, Donald J., and Gerald L. Alexanderson. Math-
ematical People: Profiles and Interviews. Boston,
Mass.: Birkhäuser, 1985.
Arcavi, Abraham. “Two Benefits of Using History.” For
the Learning of Mathematics 11 (June 1991): 11.
Avital, Shmuel. “History of Mathematics Can Help
Improve Instruction and Learning.” In Learn from
the Masters, edited by Frank Swetz, John Fauvel,
Otto Bekken, Bengt Johansson, and Victor Katz, pp.
3–12. Washington, D.C.: Mathematical Association
of America, 1995.
Cajori, Florian. A History of Mathematical Notations.
Chicago, Ill.: Open Court Publishing Co., 1928.
Carlson, Marilyn P. “A Cross-Sectional Investigation
of the Development of the Function Concept.” In
Research in College Mathematics Education III, edit-
ed by Alan H. Schoenfeld, Jim Kaput, and Ed
Dubinsky, pp. 114–62. Washington, D.C.: Conference
Board of the Mathematical Sciences, 1998.
Cornu, Bernard. “Epistemological Obstacles in Histor-
ical Development.” In Advanced Mathematical Think-
ing, edited by David Tall, pp. 159–62. Dordrecht,
The Netherlands: Kluwer, 1991.
Dunham, William. Journey through Genius: The Great
Theorems of Mathematics. New York: Wiley, 1990.
Ernest, Paul. “The History of Mathematics in the
Classroom.” Mathematics in School 27 (September
1998): 25–32.
Fauvel, John. “Using History in Mathematics Educa-
tion.” For the Learning of Mathematics 11 (June
1991): 3–6.
Furinghetti, Fulvia. “History of Mathematics, Mathe-
matics Education, School Practice: Case Studies in
Linking Different Domains.” For the Learning of
Mathematics 17 (February 1997): 55–61.
International Conference on the Teaching of Mathe-
matics (ICTM-2). “On the Role of the History of
Mathematics in Mathematics Education.” Panel dis-
cussion at ICTM-2, Crete, July 2002.
Katz, Victor. “Some Ideas on the Use of History in the
Teaching of Mathematics. For the Learning of Math-
ematics 17 (February 1997): 62–63.
Kline, Morris. Mathematical Thought from Ancient to
Modern Times. New York: Oxford University Press,
1972.
———. Mathematics: The Loss of Certainty. New York:
Oxford University Press, 1980.
Lakatos, Imre. Proofs and Refutations: The Logic of
Mathematical Discovery. New York. Cambridge Uni-
versity Press, 1976.
Students
better
appreciated
the role of
imagination
in problem
solving