Ethnomathematics ... or niggers in space ?
Anonymous
nobody at remailer.privacy.at
Sun Feb 23 21:40:10 PST 2003
http://www.nytimes.com/2003/02/23/magazine/23CRASH.html?ex=1047027608&ei=1&en=b5465666bfebf361
Ethnomathematics
February 23, 2003 By DIRK OLIN
Mathematics is one academic subject that would seem to reside in a world
of universality, protected from competing opinions by the objectivity of
its laws. But the real universal law is that everything is relative,
even in math. The release last month of a new math curriculum for New
York City schools by Mayor Michael R. Bloomberg has elicited something
just short of vituperation. Back-to-basics advocates denounce as ''fuzzy
math'' its inclusion of so-called constructivist teaching techniques.
Critics complain that those approaches encourage self-discovery and
collaborative problem-solving at the expense of proved practices like
memorization, repetition and mastery of algorithm.
It's all the latest in a century of American math wars. The previous
generation can remember the struggle over ''new math'' during the 1950's
and 60's. (''Hooray for new math,/New-hoo-hoo math!'' Tom Lehrer sang.
''It won't do you a bit of good to review math./It's so simple,/So very
simple./That only a child can do it!'') Battles flared even earlier in
the century over ''progressive'' agendas for math education of the type
pushed by John Dewey.
How tame those struggles seem, however, when compared to the rising
vanguard of self-described ethnomathematicians. For some, the new
discipline just means studying the anthropology of various measurement
methods; they merely want to supplement the accepted canon -- from
Pythagoras to Euclid to Newton -- with mind-expanding explorations of
mathematical ideas from other cultures. For others, however,
ethnomathematics is an effort to supplant the tyranny of Western
mathematical standards.
The Postulates
Ethnomathematics has a few parents, but most observers trace its formal
birth to a speech given by the Brazilian mathematician Ubiratan
D'Ambrosio in the mid-1980's. Now an emeritus professor of math at the
State University of Campinas outside S-o Paulo, he explained his
thinking a couple of years ago to The Chronicle of Higher Education:
''Mathematics is absolutely integrated with Western civilization, which
conquered and dominated the entire world. The only possibility of
building up a planetary civilization depends on restoring the dignity of
the losers.'' Robert N. Proctor, who teaches the history of science at
Pennsylvania State University, says he wants to counter the notion
''that the West is the be all and end all'' when it comes to
mathematical studies. ''After all,'' he adds, ''all math is ethnomath --
not just African kinship numerics or Peruvian bead counting, but also
the C.I.A.'s number-crunching cryptology and Reaganomics.''
To redress their pedagogical grievances, these ethnomathematicians want
math curriculums that place greater emphasis on the systems of previous
civilizations and certain traditional cultures. Studies of state
civilizations might focus on Chinese or Arabic math concepts. One study,
for example, has shown how the Chinese Chu Shih-chieh triangle
anticipated by more than three centuries the highly similar arrangement
of numerals by Pascal that holds sway in many Western teachings of
probability theory.
In her seminal books ''Ethnomathematics'' and ''Mathematics Elsewhere,''
Marcia Ascher, emerita professor of mathematics at Ithaca College,
chronicles the astonishingly complex data-storage systems embedded in
quipu, bundles of cotton cord knotted by Incans according to a
sophisticated base-10 numeration system. At a more quotidian level, Ron
Eglash of Rensselaer Polytechnic Institute has written and taught
extensively about the nuances of fractals, or repeating patterns, that
can be found in certain African craft work. (Eglash stresses a
distinction between simple-minded multicultural math -- ''which merely
replaces Dick and Jane counting marbles with Tatuk and Esteban counting
coconuts'' -- and what he calls the ''deep design themes'' that
represent mature, developed mathematical systems too often ignored in
the study of many societies.)
What Its Critics Fear
Some of this is just fine, says David Klein, a professor of mathematics
with California State University at Northridge. Klein (a self-described
liberal who insists on separating his academic critique from any
connection to a conservative political agenda) says the danger lies in
allowing such precepts to crowd out fundaments on which modernity is
based. He argues that the statistically lower achievements of some
female and minority math students have resulted in an overreaction that
doesn't serve their interests. ''The practical effect,'' Klein says,
''has been watered-down math books that overemphasize inductive
reasoning (like continuing visual patterns), because this is supposed to
be good for women and minorities, and de-emphasizing deductive reasoning
and mathematical proofs, which is the heart of mathematics, because that
supposedly favors white males.
''But mathematics is a worldwide monoculture. Look at the chalkboards in
math departments at universities all around the world -- in Africa,
Asia, Europe, Latin America. You will see the same symbols everywhere
you go on this planet, except perhaps in colleges of education where
fads reign supreme.'' Klein says he does spend some class time
discussing the math of Mayans, Egyptians and other early civilizations.
''But ancient techniques and early discoveries in math will not take
students very far who want to do something in the modern world with
mathematics,'' he says.
Will It Pass?
Some proponents argue that whatever the freestanding authenticity of the
cross-discipline, it is useful as a carrot to attract indifferent
students. Philip Straffin, who has been teaching the popular ''Cultural
Approaches to Mathematics'' at Beloit College for about 10 years, says
that the lectures lure a mix of teachers in training and art students:
''Every time we give this course, there are twice as many students who
want to take it as we have room for.'' As long as such developments
complement and enhance rather than take time from and substitute for
other mathematics learning, Judith Grabiner, who teaches at Pitzer
College, says they are a plus. ''I don't want people teaching students
that Mohammed ibn Musa al-Khwarizmi gave a systematic treatment of
quadratic equations in the 10th century instead of learning how to solve
quadratic equations,'' she says. ''But that's a false choice. Putting
the math in its cultural context helps teach the mathematics and makes
it more meaningful to students, since it has a human context.''
Indeed, those who think this threatens to spawn a brave new world of
mathematical correctness might search their memories to recall if they
didn't have a fourth- or fifth-grade teacher who brought an abacus to
class.
Calculating Cultural Impact
>From 'Ethnomathematics: A Multicultural View of Mathematical Ideas,' by
Marcia Ascher
For mathematics, however, there has been a long philosophical debate on
the reality of the objects it studies. Is a square something that has
external reality or is it something only in our minds? . . . The
relationship between the length of the hypotenuse and lengths of the
sides of a right triangle is an eternal truth, but that does not mean
that any other culture need share the categories triangle, right
triangle, hypotenuse. . . . A critical issue is that, as it stands, much
of mathematics education depends upon assumptions of Western culture and
carries with it Western values. Those with other traditions are, as a
result, often turned away by the subject or unsuccessful in learning it.
And, for them, the process of learning mathematics, particularly when
unsuccessful -- but even when successful -- can be personally
debilitating as it detracts from and conflicts with their own cultural
traditions. . . . [In] the United States, the concern has been
stimulated by the realization that our educational approaches have yet
to come to grips with the fact that we ourselves are a multicultural
society.''
Dirk Olin is national editor at The American Lawyer.
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