Ethnomathematics
In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture. Often associated with "cultures without written expression", it may also be defined as "the mathematics which is practised among identifiable cultural groups". It refers to a broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural mathematics education. The goal of ethnomathematics 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.
Development and meaning
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. Since D'Ambrosio put forth the term, there has been debate as to its precise definition.).The following is a sampling of some of the definitions of ethnomathematics proposed between 1985 and 2006:
- "The mathematics which is practiced among identifiable cultural groups such as national-tribe societies, labour groups, children of certain age brackets and professional classes".
- "The mathematics implicit in each practice".
- "The study of mathematical ideas of a non-literate culture".
- "The codification which allows a cultural group to describe, manage and understand reality".
- "Mathematics…is conceived as a cultural product which has developed as a result of various activities".
- "The study and presentation of mathematical ideas of traditional peoples".
- "Any form of cultural knowledge or social activity characteristic of a social group and/or cultural group that can be recognized by other groups such as Western anthropologists, but not necessarily by the group of origin, as mathematical knowledge or mathematical activity".
- "The mathematics of cultural practice".
- "The investigation of the traditions, practices and mathematical concepts of a subordinated social group".
- "I have been using the word ethnomathematics as modes, styles, and techniques of explanation, of understanding, and of coping with the natural and cultural environment in distinct cultural systems ".
- "What is the difference between ethnomathematics and the general practice of creating a mathematical model of a cultural phenomenon ? The essential issue is the relation between intentionality and epistemological status. A single drop of water issuing from a watering can, for example, can be modeled mathematically, but we would not attribute knowledge of that mathematics to the average gardener. Estimating the increase in seeds required for an increased garden plot, on the other hand, would qualify".
- "N.C. Ghosh included Ethnomathematics in the list of Folk Mathematics" Vide : Lokdarpan- a Journal of the Department of Folklore, Kalyani University and Rabindra Bharati Patrika- a Journal of Rabindra Bharati University, Kolkata, India. Lokashruti - a Journal of Govt. of West Bengal, India.
Areas
Numerals and naming systems
Numerals
Some of the systems for representing numbers in previous and present cultures are well known. Roman numerals use a few letters of the alphabet to represent numbers up to the thousands, but are not intended for arbitrarily large numbers and can only represent positive integers. Arabic numerals are a family of systems, originating in India and passing to medieval Islamic civilization, then to Europe, and now standard in global culture—and having undergone many curious changes with time and geography—can represent arbitrarily large numbers and have been adapted to negative numbers, fractions, and real numbers.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.
A completely different system is that of the quipu, which recorded numbers on knotted strings.
Ethnomathematicians are interested in the ways in which numeration systems grew up, as well as their similarities and differences and the reasons for them. The great variety in ways of representing numbers is especially intriguing.
Names for numbers
This means the ways in which number words are formed.English
For instance, in English, there are four different systems. The units words and ten are special. The next two are reduced forms of Anglo-Saxon "one left over" and "two left over". Multiples of ten from "twenty" to "ninety" are formed from the units words, one through nine, by a single pattern. Thirteen to nineteen are compounded from tens and units words in one way, and the non-multiples of ten from twenty-one to ninety-nine are compounded from tens and units words in a different way. Larger numbers are also formed on a base of ten and its powers. 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".. There were historical inconsistencies in the way the term "billion" was used between American English and British English. These have since been reconciled, and modern English speakers universally refer to 1,000,000,000 as 'one billion'.German
The German language and Dutch language counts similarly to English, but the unit is placed before the tens 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. It persists in some children's songs such as "."French
In the French language as used in France, one sees some differences. Soixante-dix is used for "seventy". The words "quatre-vingt" and "quatre-vingt-dix" are based on 20 instead of 10. Swiss French and Belgian French do not use these forms, preferring more standard Latinate forms: septante for 70, huitante for 80 and nonante for 90.Welsh
Counting in Welsh combines the vigesimal system with some other features. The following system is optional for cardinal numbers nowadays, but mandatory for ordinal numbers.| 14 | pedwar ar ddeg | four upon ten |
| 15 | pymtheg | five-ten |
| 16 | un ar bymtheg | one on five-ten |
| 20 | ugain | score |
| 37 | dau ar bymtheg ar hugain | two on five-ten on score |
| 57 | hanner cant a saith | half hundred and seven |
| 77 | dau ar bymtheg a thrigain | two on five-ten and three-score |
| 99 | cant namyn un | hundred less one |
Chinese
Number words in Chinese are assembled from the words for "one" through "nine" and words for powers of ten.For example, what is in English written out as "twelve thousand three hundred forty five" is "一万二千三百四十五" / "一萬二千三百四十五" whose characters translate to "one ten-thousand two thousand three hundred four ten five".
Mesopotamia
In ancient Mesopotamia, the base for constructing numbers was 60, with 10 used as an intermediate base for numbers below 60.West Africa
Many West African languages generally 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. The words for numbers below 20 are based on 5 and higher numbers combine the lower numbers with multiples and powers of 20.Finger counting
Many systems of finger counting have been, and still are, used in various parts of the world. Most are not as obvious as holding up a number of fingers. The position of fingers may be most important. One continuing use for finger counting is for people who speak different languages to communicate prices in the marketplace.In contrast to finger counting, the Yuki people keep count by using the four spaces between their fingers rather than the fingers themselves. This is known as an octal counting system.
The history of mathematics
This area of ethnomathematics mainly focuses on addressing Eurocentrism by countering the common belief that most worthwhile mathematics known and used today was developed in the Western world.The area stresses that "the history of mathematics has been oversimplified",
and seeks to explore the emergence of mathematics from various ages and civilizations throughout human history.