The term "ethnomathematics" was introduced by Brazilian educator and mathematician Ubiratan D'Ambrosio in 1977 during a presentation for the American Association for the Advancement of Science.
Less well known systems include some that are written and can be read today, such as the Hebrew and Greek method of using the letters of the alphabet, in order, for digits 1–9, tens 10–90, and hundreds 100–900.
(Larger number words like "million" are not part of the original English system; they are scholarly creations based ultimately on Latin.).
[21] One continuing use for finger counting is for people who speak different languages to communicate prices in the marketplace.
One of the oldest and most controversial topics in this area is whether mathematics is internal or external, tracing back to the arguments of Plato, an externalist, and Aristotle, an internalist.
On the other hand, externalists, like Barrow, Chevallard and Penrose, see mathematics as culture-free, and tend to be major critics of ethnomathematics.
Ethnomathematicians purport that the prefix "ethno" should not be taken as relating to race, but rather, the cultural traditions of groups of people.
[30] However, in places like South Africa concepts of culture, ethnicity and race are not only intertwined but carry strong, divisive negative connotations.
This looks at topics such as discrepancies between male and female math performance in educations and career-orientation, societal causes, women's contributions to mathematics research and development, etc.
The studies reveal that all cultures have basic counting, sorting and deciphering methods, and that these have arisen independently in different places around the world.
The universality of these concepts, however, seems harder to sustain as more and more research reveals practices which are typically mathematical, such as counting, ordering, sorting, measuring and weighing, done in radically different ways (see Section 2.1: Numerals and Naming Systems).
The discussions of the mathematical ideas of other cultures recast these into a Western framework in order to identify and understand them.
The majority of research in this area has been about the intuitive mathematical thinking of small-scale, traditional, indigenous cultures, including Aboriginal Australians,[31] the indigenous people of Liberia,[32] Native Americans in North America,[33] Pacific Islanders,[34] Brazilian construction foremen,[35] and various tribes in Africa.
Another kind of geometrical game involves objects that move or jump over each other within a specific shape (a "board").
The goal may be to eliminate the opponent's pieces, or simply to form a certain configuration, e.g., to arrange the objects according to a rule.
One such game is nine men's morris; it has innumerable relatives where the board or setup or moves may vary, sometimes drastically.
This kind of game is well suited to play out of doors with stones on the dirt, though now it may use plastic pieces on a paper or wooden board.
A woven cloth may exhibit one of the seventeen kinds of plane symmetry groups; see Crowe (2004) for an illustrated mathematical study of African weaving patterns.
Following the analysis of Indonesian folk weaving patterns[38] and Batak traditional architectural ornaments,[39] the geometry of Indonesian traditional motifs of batik is analyzed by Hokky Situngkir that eventually made a new genre of fractal batik designs as generative art; see Situngkir and Surya (2007) for implementations.
This can be used both to increase the social awareness of students and offer alternative methods of approaching conventional mathematics operations, like multiplication (Andrew, 2005).
Various mathematics educators have explored ways of bringing together culture and mathematics in the classroom, such as: Barber and Estrin (1995) and Bradley (1984) on Native American education, Gerdes (1988b and 2001) with suggestions for using African art and games, Malloy (1997) about African American students and Flores (1997), who developed instructional strategies for Hispanic students.
[citation needed] Richard Askey examined[40] Focus on Algebra (an Addison-Wesley textbook criticized in an op-ed by Marianne M. Jennings[41]) and among other shortcomings found it guilty of repeating debunked claims about Dogon astronomy.
Some people judged the proposed changes, which involved a framework for blending math and ethnic studies, for incorporating questions like "How important is it to be right?"