ETHNO MATHEMATICS

Every country has its own culture. There is a different culture between Indonesia and Malaysia, also between Indonesia and Japan. There’s also different culture between one province and another province in Indonesia. It is because Indonesia is a country with thousands of islands spanning out from the West (Aceh, Sumatra) to the East (Merauke, Irian Jaya). It is located between two oceans, the Pacific and Indian, and two continents, Asia and Australia. The population would be about 350 million residents. In fact by 2011, the population had grown to 375 million. Those different cultures we usually called as ethnology.

Mathematics learning process is also different between one country and another country. It depends on the culture of the country. For example, in Europe we can use mathematics problem based on four seasons. But we can’t do this in Indonesia, since Indonesia only has two seasons. This difference usually called as ethno mathematics. Ethno mathematics consists of the culture of mathematics, mathematical culture, the uncultured of mathematics, and also the context of mathematics.

In mathematics education, ethno mathematics is the study of the relationship between mathematics and culture (D'Ambrosio, 1999, 146). Often associated with "cultures without written expression" (D'Ambrosio, 1997, may paraphrases Ascher 1986), it may also be defined as "'the mathematics which is practiced among identifiable cultural groups'" (Powell and Frankenstein, 1997 quoting D'Ambrosio). It refers to a broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural mathematics education. The goal of ethno mathematics is to contribute both to the understanding of culture and the understanding of mathematics, and mainly to lead to an appreciation of the connections between the two. ⁽¹⁾

Ethno mathematics comes from the philosophy of mathematics that affected to the paradigm of mathematics. This paradigm then developed into two kinds of theories. The first theory is about history, psychology, anthropology, and sociology. The second theorem is about mathematics. Then this two theories combined together become ethno mathematics that developed into mathematical context (formal mathematics, model of mathematics, model concrete, and the concrete of mathematics. Ethno mathematics also be in ice berg theorem.

The final project of studying ethno mathematics is a small research in mathematics learning process that’s affected by the culture of a country. This research based on a theory. Then from the theory we can uncover the culture phenomena, so we get the data and develop it into a construction of research and we can make a new theory. This research must contain of the unity, concept, method, scope, relationship, structure, subject, characteristics, value, and timeline.

The example of ethno mathematics around the world is on numerals. These are some explanation of the numerals in some countries: ⁽¹⁾

1.      English

For instance, in English, there are four different systems. The units words (one to nine) and ten are special. The next two are reduced forms of Anglo-Saxon "one left over" and "two left over" (i.e., after counting to ten). Multiples of ten from "twenty" to "ninety" are formed from the units words, one through nine, by a single pattern. Thirteen to nineteen, and in a slightly different way twenty-one through ninety-nine (excluding the tens words), are compounded from tens and units words. Larger numbers are also formed on a base of ten and its powers ("hundred" and "thousand"). One may suspect this is based on an ancient tradition of finger counting. Residues of ancient counting by 20s and 12s are the words "score", "dozen", and "gross". (Larger number words like "million" are not part of the original English system; they are scholarly creations based ultimately on Latin).

2.      German

The German language counts similarly to English, but the unit is placed first in numbers over 20. For example, "26" is "sechsundzwanzig", literally "six and twenty". This system was formerly common in English, as seen in an artifact from the English nursery rhyme "Sing a Song of Sixpence": Sing a song of sixpence, / a pocket full of rye. / Four and twenty blackbirds, / baked in a pie.

3.      French

In the French language as used in France, one sees some differences. Soixante-dix (literally, "sixty-ten") is used for "seventy". The words "quatre-vingt" (literally, "four-twenty", or 80) and "quatre-vingt-dix" (literally, "four-twenty ten" 90) are based on 20 ("vingt") instead of 10. Swiss French and Belgian French do not use these forms, preferring more standard Latinate forms: octante for 80 and nonante for 90.

4.      Mesopotamia

In ancient Mesopotamia the base for constructing numbers was 60, with 10 used as an intermediate base for numbers below 60.

5.      West Africa

Many West African languages base their number words on a combination of 5 and 20, derived from thinking of a complete hand or a complete set of digits comprising both fingers and toes. In fact, in some languages, the words for 5 and 20 refer to these body parts (e.g., a word for 20 that means "man complete"). The words for numbers below 20 are based on 5 and higher numbers combine the lower numbers with multiples and powers of 20. Of course, this description of hundreds of languages is badly oversimplified; better information and references can be found in Zaslavsky (1973).

From the example above, it’s very clear that the culture of a region or a country affected to mathematics itself. But, since mathematics also different for each province in Indonesia, so there are some issue about ethno mathematics in Indonesia :

1.      The role of mathematics in Yogyakarta palace

2.      The role of mathematics in Javanese culture

3.      The role of mathematics in ‘wayang’ culture

4.      The role of mathematics in Borobudur and Prambanan building

5.      The role of mathematics on the counting of someone death

6.      The role of mathematics in fengshui

7.      The role of mathematics in Javanese calendar

8.      The relation of mathematics and forecasting

9.      Irrational mathematics

10.  The relation of mathematics and horoscope

11.  The role of mathematics on Javanese ‘primbon’.