Preventing mathematical illiteracy in our culture<\/p>\n
By Mochtar Buchori<\/p>\n
JAKARTA (JP): During my visit to Simon Fraser University in
\nVancouver last February I met an Indonesian graduate student who
\nwas pursuing a masters in Mathematics Education.<\/p>\n
She told me she was more interested in the "education part",
\nrather than the "mathematics part" of the program. The reason
\nwas, she said, because she did not want to become a
\nmathematician. She complained she was required to take a course
\non the History of Mathematics. "Why must I take that course? I am
\nnot going to be a mathematician," she said.<\/p>\n
This statement puzzled me. I am neither a mathematician nor a
\nhistorian. As a matter a fact, I am almost illiterate in
\nmathematics and only semiliterate in history. But based on my
\ndecades of experience in teaching and learning, I am convinced
\nthat knowledge about the history of whatever we happen to teach
\nand learn is very important. It not only enriches our knowledge,
\nbut also enhances our intellectuality.<\/p>\n
In addition to this belief, I happened to read about two years
\nago an article about the development of mathematics throughout
\nthe ages. This article also analyzes changes in the relationship
\nbetween mathematics and several branches of the humanities,
\nincluding poetry, music and philosophy.<\/p>\n
In spite of my very limited knowledge about mathematics, this
\narticle increased my understanding about the significance of
\nmathematics in shaping the capability of a nation to make
\ndisciplined inquiries into the problems it faces. If I understood
\nthis article, being familiar with mathematics helps us avoid
\n"sloppy thinking".<\/p>\n
Based on these two insights, I gave this graduate student the
\nfollowing advice: "You must be grateful that you have this
\nwonderful opportunity to enrich and deepen your knowledge of
\nmathematics. Anyone who aspires to be a good teacher of
\nmathematics must to some extent be a mathematician. Where in
\nIndonesia could you take a course on the history of mathematics?
\nSo do your best to overcome your apprehensions and you will
\ngreatly enjoy the experience and benefit greatly from it."<\/p>\n
I wish I could have given her better advice, but that was all
\nI could say at the time since I forgot the finer details of that
\nbeautiful article. I felt she was not entirely persuaded by my
\nadvice.<\/p>\n
Upon returning home, I immediately reread the article, this
\ntime reading it very carefully. I wanted to understand every bit
\nof the argument so I could give better advice the next time I
\nfaced a similar situation. But more importantly, I wanted to use
\nthe insights I gained from this article to help our mathematics
\nteachers see the lager purpose of their labor. I want them to
\nrealize that by teaching mathematics in a systematic way they
\nhelp the nation create a new and healthy habit; putting rigorous
\nlogic and exactitude behind every argument and discourse.<\/p>\n
The article I have in mind has a strange title, Mathematics as
\nthe Stepchild of Contemporary Culture. It was written by Norman
\nLevitt, a professor in the Department of Mathematics at Rutgers
\nUniversity, and appears in The Flight from Science and Reason,
\npublished by the New York Academy of Sciences in 1996.<\/p>\n
Professor Levitt argues that mathematics occupies an
\nambivalent place in our contemporary world of ideas. It is both
\nresented and admired. This is not a healthy situation. This
\nambivalence has created ignorance about and indifference and even
\nhostility toward mathematics. And when mathematical illiteracy
\nbecomes institutionalized it will, in the long run, lead us into
\n"blind alleys" which will cause us to ignore things we cannot
\nafford to ignore.<\/p>\n
Ignorance about and indifference toward mathematics, says
\nLevitt, has caused the "general culture's ties with reality to
\nfray" because a minimum of mathematical skills is vital to
\nunderstanding the important scientific explanations of the
\ncomplex realities of life.<\/p>\n
As an example, Levitt says that to understand serious academic
\nworks in economics and demography, mathematics is an
\nindispensable intellectual tool. It is of course possible to
\ngrasp the essence of such articles without going through and
\nunderstanding the mathematical parts, but understanding the
\nmathematics of such articles certainly results in better
\nunderstanding.<\/p>\n
According to Levitt, the gulf between mathematics and
\nhumanistic culture is something new in Western intellectual life.
\nThat is if one adopts a long-term view of Western culture. The
\nhistorical links between mathematical competence and the "general
\nability to think deeply and effectively" go back at least as far
\nas the ancient Athenians. For nearly two millennia the
\nintellectuality of the learned class was acquired through the
\nstudy of grammar, rhetoric, logic, geometry, arithmetic, music
\nand astronomy.<\/p>\n
John Dunstable, the 15th century English composer was famed
\nthroughout Europe as a mathematician simply because "in the high
\nculture of his day, musical composition or ars combinatoria, was
\na branch of mathematics".<\/p>\n
According to Paul Hillier, a modern student of Dunstable's
\nmusic, the task of a composer could be described as "reflecting
\nthe ordered perfection of the universe in musical structures that
\nobey the same numerical principles".<\/p>\n
It is on the basis of this scholarly tradition that Voltaire
\nwas quoted as saying that "a great mathematician has at least as
\nmuch imagination as a great poet". And Bertrand Russell, in The
\nStudy of Mathematics, wrote: "Mathematics possesses not only
\ntruth, but supreme beauty -- a beauty cold and austere, like that
\nof sculpture, without appeal to any part of our weaker nature,
\nsublimely pure and capable of a stern perfection such as only the
\ngreatest art can show."<\/p>\n
Against such a background of intellectual history,
\nmathematical ability was a vital component of the typical
\nscholar's intellectual arsenal well into the 18th century.
\nNotwithstanding such history, however, the 19th century witnessed
\na growing disjunction between what was regarded as general
\nscholarly competence and the particular talent for doing and
\nunderstanding mathematics.<\/p>\n
According to Levitt, there were three main reasons for this
\nsplit. First, the arrival of the Romantic style in art and
\nthought created a wedge between humanistic and scientific
\nthought. Second, the growing difficulty, both conceptually and
\ntechnically, of mathematics itself, as embodied in calculus and
\nmathematical physics, which are harder to understand than basic
\ngeometry and elementary algebra. And third, the emergence of a
\nprofessional class of technocrats and an educational system
\ndesigned to nurture them.<\/p>\n
Mathematics was increasingly perceived as belonging
\nexclusively to schools of engineering and lost its long-standing
\nassociation with the worlds of classical learning and systematic
\nphilosophy.<\/p>\n
The damage caused by this split in human culture was the
\nsubject of a lecture delivered by Lord C.P. Snow to an audience
\nat Cambridge University, and later published in his famous work
\nThe Two Cultures and the Scientific Revolution.<\/p>\n
In this context, Professor Levitt argues that an intellectual
\nwill loose a great deal by being mathematically illiterate.
\nMathematical illiteracy will exclude one from a decent
\ncomprehension of vast realms of experience. Training in
\nsystematic, rigorous deductive thinking, experiencing the process
\nand the results of such thinking, is an aspect of intellectual
\ndevelopment which, if we neglect it, will lead us toward
\n"intellectual slovenliness".<\/p>\n
Even a modest mathematical education, if done honestly and
\nthoroughly, will breed a "certain salutary impatience, a distaste
\nfor intellectual flatulence, for otiose pseudotheorizing, for
\nargument by browbeating".<\/p>\n
Do we have this illness in our culture? And what do we have to
\ndo to prevent future generations from suffering such cultural
\nillness? This is a question that I hope our mathematics teachers
\nwill become aware of and think seriously about. I hope that by
\nthe time our friend at Simon Fraser University finishes her
\nstudies and comes home, she will realize what a blessing it was
\nfor her to have had the opportunity to study a little bit about
\nthe history of mathematics.<\/p>\n
The writer is an observer of social and cultural affairs.<\/p>", "url": "https:\/\/jawawa.id\/newsitem\/preventing-mathematical-illiteracy-in-our-culture-1447893297", "image": "" }, "sponsor": "Okusi Associates", "sponsor_url": "https:\/\/okusiassociates.com" }