Far from being irrelevant or obscure, the ethnomathematicians are powerful within the US educational establishment, exercising a significant intellectual influence over the teaching of maths in state schools. Ethnomathematics: Challenging Eurocentrism in Mathematics Education is a recently published collection of essays that seeks to find in maths a mirror of America's racially and sexually diverse population. Starting from the premise that "geographically, Europe does not exist", the book seeks to elaborate a "culturally responsive pedagogy" which communicates the theory and practice of mathematics in terms of - among other disciplines - anthropology, cognitive psychology, feminism and African studies.
Never mind two plus two equals four, three is the square root of nine and other received Eurocentric banalities. By studying the geometry of sand drawings in Africa south of the Equator, quilt patterns in Africa north of the Equator and the accounting methods of the ancient Navajo Indians, you will soon lose your respect for the time- honoured authority of Euclid and Pythagoras. Indeed, the Ethnomathematics book includes a dismissive reference to the "so-called Pythagorean theorem".
The lesson is that maths, contrary to established opinion, is not an absolute science. The International Study Group on Ethnomathematics (ISGEm) advocates that the teaching in schools of "multicultural mathematics" should be based on the recognition "that learning mathematics is a unique process for each individual". It is nonsense to suggest that some are "good at maths" and some are not. All students can be good at maths, all can be "empowered", so long as they are taught in a culturally, historically and psychologically sensitive way.
The ISGEm is an affiliate of the US National Council of Teachers of Mathematics, the body which shapes the curriculum and determines the standards of maths education. A glance at some of the New Math, or Constructivist Math, ideas promoted by the council reveals just how wholeheartedly the ethnomathematicians' prescriptions have been absorbed.
The council's "position statement" repeatedly stresses the need for teachers to devise methods of instruction sensitive to the "cultural" background, heritage and learning styles of students. Later this year the council is due to publish a collection of essays under the title Changing the Faces of Mathematics, which will address itself to ethnomathematical, feminist and cross-cultural perspectives on: Gender, African Americans, Latinos and Latinas, American Indians, Asian Americans and Pacific Islanders. (Presumably because geographically they do not exist, Europeans do not feature in the list of chapter titles.)
The council has declared that a good primary maths class should "place less importance on paper-and-pencil calculations and more on numbers sense"; "place more emphasis on talking and writing about problem-solving than answers per se"; and, of course, "have a set of calculators that children can use".
More than three-quarters of US teachers have implemented the principles, but nowhere has its been embraced with more zeal than in California. The state's high priestess of New Math is Ruth Parker, an educational consultant who argues: "Mathematics as it is used in the real world is not about memorisation of theorems or rote procedures for getting right answers." The students' "thinking or approach must not be structured for them, so that they are not being led to 'the right way' of solving a problem."
Under this formula "conjecture" and "exploration" are prized above hard and fast solutions. Teachers are "co-learners" sharing the student's voyages of "self-discovery". A 12-year-old boy in Palo Alto said: "Everyone has a different way to solve things. I have learned how to become mathematically powerful."
Parents and recalcitrant teachers have denounced "fuzzy", "MTV" and "Mickey Mouse" maths. A website called Mathematically Correct has become the forum of organised resistance, positing such novel admonitions as "Honour the correct answer more than the guess" and "Give good grades only for good work."
Wayne Bishop, a professor of mathematics at California State University, has taken his own children out of the state school system for fear that their minds will be contaminated by what he considers to be a reckless laboratory experiment, using the children of California as guinea pigs. "There is no such thing as ethnomathematics," he said. "It is a way of avoiding mathematics while seeking to build some kind of cultural self- esteem. "
The Council of Teachers of Mathematics is reconsidering its loyalty to New Math after a scathing report last week from the American Federation of Teachers. It found that in every respect US maths students lagged far behind their counterparts in France, Germany and Japan.