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.