Preventing mathematical illiteracy in our culture

Preventing mathematical illiteracy in our culture

By Mochtar Buchori

JAKARTA (JP): During my visit to Simon Fraser University in
Vancouver last February I met an Indonesian graduate student who
was pursuing a masters in Mathematics Education.

She told me she was more interested in the "education part",
rather than the "mathematics part" of the program. The reason
was, she said, because she did not want to become a
mathematician. She complained she was required to take a course
on the History of Mathematics. "Why must I take that course? I am
not going to be a mathematician," she said.

This statement puzzled me. I am neither a mathematician nor a
historian. As a matter a fact, I am almost illiterate in
mathematics and only semiliterate in history. But based on my
decades of experience in teaching and learning, I am convinced
that knowledge about the history of whatever we happen to teach
and learn is very important. It not only enriches our knowledge,
but also enhances our intellectuality.

In addition to this belief, I happened to read about two years
ago an article about the development of mathematics throughout
the ages. This article also analyzes changes in the relationship
between mathematics and several branches of the humanities,
including poetry, music and philosophy.

In spite of my very limited knowledge about mathematics, this
article increased my understanding about the significance of
mathematics in shaping the capability of a nation to make
disciplined inquiries into the problems it faces. If I understood
this article, being familiar with mathematics helps us avoid
"sloppy thinking".

Based on these two insights, I gave this graduate student the
following advice: "You must be grateful that you have this
wonderful opportunity to enrich and deepen your knowledge of
mathematics. Anyone who aspires to be a good teacher of
mathematics must to some extent be a mathematician. Where in
Indonesia could you take a course on the history of mathematics?
So do your best to overcome your apprehensions and you will
greatly enjoy the experience and benefit greatly from it."

I wish I could have given her better advice, but that was all
I could say at the time since I forgot the finer details of that
beautiful article. I felt she was not entirely persuaded by my
advice.

Upon returning home, I immediately reread the article, this
time reading it very carefully. I wanted to understand every bit
of the argument so I could give better advice the next time I
faced a similar situation. But more importantly, I wanted to use
the insights I gained from this article to help our mathematics
teachers see the lager purpose of their labor. I want them to
realize that by teaching mathematics in a systematic way they
help the nation create a new and healthy habit; putting rigorous
logic and exactitude behind every argument and discourse.

The article I have in mind has a strange title, Mathematics as
the Stepchild of Contemporary Culture. It was written by Norman
Levitt, a professor in the Department of Mathematics at Rutgers
University, and appears in The Flight from Science and Reason,
published by the New York Academy of Sciences in 1996.

Professor Levitt argues that mathematics occupies an
ambivalent place in our contemporary world of ideas. It is both
resented and admired. This is not a healthy situation. This
ambivalence has created ignorance about and indifference and even
hostility toward mathematics. And when mathematical illiteracy
becomes institutionalized it will, in the long run, lead us into
"blind alleys" which will cause us to ignore things we cannot
afford to ignore.

Ignorance about and indifference toward mathematics, says
Levitt, has caused the "general culture's ties with reality to
fray" because a minimum of mathematical skills is vital to
understanding the important scientific explanations of the
complex realities of life.

As an example, Levitt says that to understand serious academic
works in economics and demography, mathematics is an
indispensable intellectual tool. It is of course possible to
grasp the essence of such articles without going through and
understanding the mathematical parts, but understanding the
mathematics of such articles certainly results in better
understanding.

According to Levitt, the gulf between mathematics and
humanistic culture is something new in Western intellectual life.
That is if one adopts a long-term view of Western culture. The
historical links between mathematical competence and the "general
ability to think deeply and effectively" go back at least as far
as the ancient Athenians. For nearly two millennia the
intellectuality of the learned class was acquired through the
study of grammar, rhetoric, logic, geometry, arithmetic, music
and astronomy.

John Dunstable, the 15th century English composer was famed
throughout Europe as a mathematician simply because "in the high
culture of his day, musical composition or ars combinatoria, was
a branch of mathematics".

According to Paul Hillier, a modern student of Dunstable's
music, the task of a composer could be described as "reflecting
the ordered perfection of the universe in musical structures that
obey the same numerical principles".

It is on the basis of this scholarly tradition that Voltaire
was quoted as saying that "a great mathematician has at least as
much imagination as a great poet". And Bertrand Russell, in The
Study of Mathematics, wrote: "Mathematics possesses not only
truth, but supreme beauty -- a beauty cold and austere, like that
of sculpture, without appeal to any part of our weaker nature,
sublimely pure and capable of a stern perfection such as only the
greatest art can show."

Against such a background of intellectual history,
mathematical ability was a vital component of the typical
scholar's intellectual arsenal well into the 18th century.
Notwithstanding such history, however, the 19th century witnessed
a growing disjunction between what was regarded as general
scholarly competence and the particular talent for doing and
understanding mathematics.

According to Levitt, there were three main reasons for this
split. First, the arrival of the Romantic style in art and
thought created a wedge between humanistic and scientific
thought. Second, the growing difficulty, both conceptually and
technically, of mathematics itself, as embodied in calculus and
mathematical physics, which are harder to understand than basic
geometry and elementary algebra. And third, the emergence of a
professional class of technocrats and an educational system
designed to nurture them.

Mathematics was increasingly perceived as belonging
exclusively to schools of engineering and lost its long-standing
association with the worlds of classical learning and systematic
philosophy.

The damage caused by this split in human culture was the
subject of a lecture delivered by Lord C.P. Snow to an audience
at Cambridge University, and later published in his famous work
The Two Cultures and the Scientific Revolution.

In this context, Professor Levitt argues that an intellectual
will loose a great deal by being mathematically illiterate.
Mathematical illiteracy will exclude one from a decent
comprehension of vast realms of experience. Training in
systematic, rigorous deductive thinking, experiencing the process
and the results of such thinking, is an aspect of intellectual
development which, if we neglect it, will lead us toward
"intellectual slovenliness".

Even a modest mathematical education, if done honestly and
thoroughly, will breed a "certain salutary impatience, a distaste
for intellectual flatulence, for otiose pseudotheorizing, for
argument by browbeating".

Do we have this illness in our culture? And what do we have to
do to prevent future generations from suffering such cultural
illness? This is a question that I hope our mathematics teachers
will become aware of and think seriously about. I hope that by
the time our friend at Simon Fraser University finishes her
studies and comes home, she will realize what a blessing it was
for her to have had the opportunity to study a little bit about
the history of mathematics.

The writer is an observer of social and cultural affairs.