Louis Proyect lnp3 at
Sun Feb 23 08:23:01 MST 2003

NY Times Magazine, Feb. 23, 2003

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.)


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