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In
mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although re ...
, ethnomathematics is the study of the relationship between
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
and
culture Culture () is an umbrella term which encompasses the social behavior, institutions, and norms found in human societies, as well as the knowledge, beliefs, arts, laws, customs, capabilities, and habits of the individuals in these groups ...
. 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.


The development and meaning of "ethnomathematics"

The term "ethnomathematics" was introduced by the Brazilian educator and mathematician
Ubiratan D'Ambrosio Ubiratan D'Ambrosio (December 8, 1932 – May 12, 2021) was a Brazilian mathematics educator and historian of mathematics. Life D'Ambrosio was born in São Paulo, and earned his doctorate from the University of São Paulo in 1963. He retired as ...
in 1977 during a presentation for the
American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is an American international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific respons ...
. Since D'Ambrosio put forth the term, people - D'Ambrosio included - have struggled with its meaning ("An etymological abuse leads me to use the words, respectively, ''ethno'' and ''mathema'' for their categories of analysis and ''tics'' from (from techne)".). 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
anthropologist An anthropologist is a person engaged in the practice of anthropology. Anthropology is the study of aspects of humans within past and present societies. Social anthropology, cultural anthropology and philosophical anthropology study the norms an ...
s, 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 (''tics'') of explanation, of understanding, and of coping with the natural and cultural environment (''mathema'') in distinct cultural systems (''ethnos'')". *"What is the difference between ethnomathematics and the general practice of creating a mathematical model of a cultural phenomenon (e.g., the "mathematical anthropology" of Paul Kay
971 Year 971 ( CMLXXI) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Battle of Dorostolon: A Byzantine expeditionary army (possibly 30–40,000 men ...
and others)? The essential issue is the relation between intentionality and
epistemological Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Episte ...
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 Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, ...
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 Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers such a ...
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 In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every re ...
. Less well known systems include some that are written and can be read today, such as the
Hebrew Hebrew (; ; ) is a Northwest Semitic language of the Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, the Jews and Samaritans. It was largely preserved ...
and
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
method of using the letters of the
alphabet An alphabet is a standardized set of basic written graphemes (called letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a syllab ...
, in order, for digits 1–9, tens 10–90, and hundreds 100–900. A completely different system is that of the
quipu ''Quipu'' (also spelled ''khipu'') are recording devices fashioned from strings historically used by a number of cultures in the region of Andean South America. A ''quipu'' usually consisted of cotton or camelid fiber strings. The Inca peop ...
, 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 English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ...
, there are four different systems. The units words (one to nine) and ten are special. The next two are reduced forms of
Anglo-Saxon The Anglo-Saxons were a cultural group who inhabited England in the Early Middle Ages. They traced their origins to settlers who came to Britain from mainland Europe in the 5th century. However, the ethnogenesis of the Anglo-Saxons happened wit ...
"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 100 or one hundred (Roman numeral: C) is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to des ...
" 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 Score or scorer may refer to: *Test score, the result of an exam or test Business * Score Digital, now part of Bauer Radio * Score Entertainment, a former American trading card design and manufacturing company * Score Media, a former Canadian ...
", "
dozen A dozen (commonly abbreviated doz or dz) is a grouping of twelve. The dozen may be one of the earliest primitive integer groupings, perhaps because there are approximately a dozen cycles of the Moon, or months, in a cycle of the Sun, or year ...
", and "gross". (Larger number words like "
million One million (1,000,000), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian ''millione'' (''milione'' in modern Italian), from ''mille'', "thousand", plus the a ...
" are not part of the original English system; they are scholarly creations based ultimately on Latin.). 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 German ( ) is a West Germanic language mainly spoken in Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, Liechtenstein, and the Italian province of South Tyrol. It is also a ...
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 A nursery rhyme is a traditional poem or song for children in Britain and many other countries, but usage of the term dates only from the late 18th/early 19th century. The term Mother Goose rhymes is interchangeable with nursery rhymes. From ...
" 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
One and Twenty
"


=French

= In the
French language French ( or ) is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Gallo-Romance, the Latin spoken in Gaul, and more specifically in N ...
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 Belgian French (french: français de Belgique) is the variety of French spoken mainly among the French Community of Belgium, alongside related Oïl languages of the region such as Walloon, Picard, Champenois, and Lorrain (Gaumais). The Frenc ...
do not use these forms, preferring more standard
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
ate forms: ''septante'' for 70, ''huitante'' (formerly ''octante'') for 80 and ''nonante'' for 90.


=Welsh

= Counting in Welsh combines the vigesimal system (counting in twenties) with some other features. The following system is optional for cardinal numbers nowadays, but mandatory for ordinal numbers.


=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" (simplified) / "一萬二千三百四十五" (traditional) whose characters translate to "one ten-thousand two thousand three hundred four ten five".


=Mesopotamia

= In ancient
Mesopotamia Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the ...
, the base for constructing numbers was 60, with 10 used as an intermediate base for numbers below 60.


=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 African languages is badly oversimplified; better information and references can be found in Zaslavsky (1973).


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 The Yuki (also known as Yukiah) are an indigenous people of California, whose traditional territory is around Round Valley, Mendocino County. Today they are enrolled members of the Round Valley Indian Tribes of the Round Valley Reservation. Bef ...
(indigenous Americans from
Northern California Northern California (colloquially known as NorCal) is a geographic and cultural region that generally comprises the northern portion of the U.S. state of California. Spanning the state's northernmost 48 counties, its main population centers incl ...
) keep count by using the four spaces between their fingers rather than the fingers themselves. This is known as an
octal The octal numeral system, or oct for short, is the radix, base-8 number system, and uses the Numerical digit, digits 0 to 7. This is to say that 10octal represents eight and 100octal represents sixty-four. However, English, like most languages, ...
(base-8) counting system.


The history of mathematics

This area of ethnomathematics mainly focuses on addressing
Eurocentrism Eurocentrism (also Eurocentricity or Western-centrism) is a worldview that is centered on Western civilization or a biased view that favors it over non-Western civilizations. The exact scope of Eurocentrism varies from the entire Western worl ...
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.


Some examples and major contributors

D'Ambrosio's 1980 review of the evolution of mathematics, his 1985 appeal to include ethnomathematics in the history of mathematics and his 2002 paper about the historiographical approaches to non-Western mathematics are excellent examples. Additionally, Frankenstein and Powell's 1989 attempt to redefine mathematics from a non-eurocentric viewpoint and Anderson's 1990 concepts of world mathematics are strong contributions to this area. Detailed examinations of the history of the mathematical developments of non-European civilizations, such as the mathematics of ancient Japan, Iraq,
Egypt Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a List of transcontinental countries, transcontinental country spanning the North Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via a land bridg ...
, and of Islamic, Hebrew, and Incan civilizations, have also been presented.


The philosophy and cultural nature of mathematics

The core of any debate about the cultural nature of mathematics will ultimately lead to an examination of the nature of mathematics itself. 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 Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
, an externalist, and
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
, an internalist. On the one hand, Internalists such as Bishop, Stigler and Baranes, believe mathematics to be a cultural product. On the other hand, externalists, like Barrow, Chevallard and Penrose, see mathematics as culture-free, and tend to be major critics of ethnomathematics. With disputes about the nature of mathematics, come questions about the nature of ethnomathematics, and the question of whether ethnomathematics is part of mathematics or not. Barton, who has offered the core of research about ethnomathematics and philosophy, asks whether "ethnomathematics is a precursor, parallel body of knowledge or precolonized body of knowledge" to mathematics and if it is even possible for us to identify all types of mathematics based on a Western-epistemological foundation.


Political math

The contributions in this area try to illuminate how mathematics has affected the nonacademic areas of society. One of the most controversial and provocative political components of ethnomathematics is its racial implications. Ethnomathematicians purport that the prefix "ethno" should not be taken as relating to race, but rather, the cultural traditions of groups of people. However, in places like
South Africa South Africa, officially the Republic of South Africa (RSA), is the southernmost country in Africa. It is bounded to the south by of coastline that stretch along the South Atlantic and Indian Oceans; to the north by the neighbouring coun ...
concepts of culture, ethnicity and race are not only intertwined but carry strong, divisive negative connotations. So, although it may be made explicit that ethnomathematics is not a "racist doctrine" it is vulnerable to association with racism. Another major facet of this area addresses the relationship between gender and mathematics. 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.


Some examples and major contributors

Gerdes' writings about how mathematics can be used in the school systems of
Mozambique Mozambique (), officially the Republic of Mozambique ( pt, Moçambique or , ; ny, Mozambiki; sw, Msumbiji; ts, Muzambhiki), is a country located in southeastern Africa bordered by the Indian Ocean to the east, Tanzania to the north, Malawi ...
and South Africa, and D'Ambrosio's 1990 discussion of the role mathematics plays in building a democratic and just society are examples of the impact mathematics can have on developing the identity of a society. In 1990, Bishop also writes about the powerful and dominating influence of Western mathematics. More specific examples of the political impact of mathematics are seen in Knijik's 1993 study of how
Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area ...
ian sugar cane farmers could be politically and economically armed with mathematics knowledge, and Osmond's analysis of an employer's perceived value of mathematics (2000).


The mathematics of different cultures

The focus of this area is to introduce the mathematical ideas of people who have generally been excluded from discussions of formal, academic mathematics. The research of the mathematics of these cultures indicates two, slightly contradictory viewpoints. The first supports the objectivity of mathematics and that it is something discovered not constructed. 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. This can be used to argue that these mathematical concepts are being discovered rather than created. However, others emphasize that the usefulness of mathematics is what tends to conceal its cultural constructs. Naturally, it is not surprising that extremely practical concepts such as numbers and counting have arisen in all cultures. 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). One of the challenges faced by researchers in this area is the fact that they are limited by their own mathematical and cultural frameworks. The discussions of the mathematical ideas of other cultures recast these into a Western framework in order to identify and understand them. This raises the questions of how many mathematical ideas evade notice simply because they lack similar Western mathematical counterparts, and of how to draw the line classifying mathematical from non-mathematical ideas.


Some examples and major contributors

The majority of research in this area has been about the intuitive mathematical thinking of small-scale, traditional, indigenous cultures, including
Aboriginal Australians Aboriginal Australians are the various Indigenous peoples of the Australian mainland and many of its islands, such as Tasmania, Fraser Island, Hinchinbrook Island, the Tiwi Islands, and Groote Eylandt, but excluding the Torres Strait ...
, the indigenous people of
Liberia Liberia (), officially the Republic of Liberia, is a country on the West African coast. It is bordered by Sierra Leone to Liberia–Sierra Leone border, its northwest, Guinea to Guinea–Liberia border, its north, Ivory Coast to Ivory Coast� ...
, Native Americans in North America,
Pacific Islander Pacific Islanders, Pasifika, Pasefika, or rarely Pacificers are the peoples of the Pacific Islands. As an ethnic/ racial term, it is used to describe the original peoples—inhabitants and diasporas—of any of the three major subregions of O ...
s, Brazilian construction foremen, and various tribes in
Africa Africa is the world's second-largest and second-most populous continent, after Asia in both cases. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 6% of Earth's total surface area ...
.


Games of skill

An enormous variety of games that can be analyzed mathematically have been played around the world and through history. The interest of the ethnomathematician usually centers on the ways in which the game represents informal mathematical thought as part of ordinary society, but sometimes has extended to mathematical analyses of games. It does not include the careful analysis of good play—but it may include the social or mathematical aspects of such analysis. A mathematical game that is well known in European culture is
tic-tac-toe Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. ...
(noughts-and-crosses). This is a geometrical game played on a 3-by-3 square; the goal is to form a straight line of three of the same symbol. There are many broadly similar games from all parts of
England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe ...
, to name only one country where they are found. Another kind of
geometrical Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
game involves objects that move or jump over each other within a specific shape (a "board"). There may be captures. 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 Nine men's Morris is a strategy board game for two players dating at least to the Roman Empire. The game is also known as nine-man morris, mill, mills, the mill game, merels, merrills, merelles, marelles, morelles, and ninepenny marl in English. ...
; 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 mathematical game found in West Africa is to draw a certain figure by a line that never ends until it closes the figure by reaching the starting point (in mathematical terminology, this is a Eulerian path on a graph). Children use sticks to draw these in the dirt or sand, and of course the game can be played with pen and paper. The games of checkers,
chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...
, oware (and other
mancala The mancala games are a family of two-player turn-based strategy board games played with small stones, beans, or seeds and rows of holes or pits in the earth, a board or other playing surface. The objective is usually to capture all or some ...
games), and Go may also be viewed as subjects for ethnomathematics.


Mathematics in folk art

One way mathematics appears in art is through symmetries. Woven designs in cloth or carpets (to name two) commonly have some kind of symmetrical arrangement. A rectangular carpet often has rectangular symmetry in the overall pattern. 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 Weaving is a method of textile production in which two distinct sets of yarns or threads are interlaced at right angles to form a fabric or cloth. Other methods are knitting, crocheting, felting, and braiding or plaiting. The longitudinal ...
patterns. Several types of patterns discovered by ethnomathematical communities are related to technologies; see Berczi (2002) about illustrated mathematical study of patterns and symmetry in Eurasia. Following the analysis of Indonesian folk weaving patterns and
Batak Batak is a collective term used to identify a number of closely related Austronesian ethnic groups predominantly found in North Sumatra, Indonesia, who speak Batak languages. The term is used to include the Karo, Pakpak, Simalungun, Tob ...
traditional architectural ornaments, the geometry of Indonesian traditional motifs of
batik Batik is an Indonesian technique of wax-resist dyeing applied to the whole cloth. This technique originated from the island of Java, Indonesia. Batik is made either by drawing dots and lines of the resist with a spouted tool called a ''ca ...
is analyzed by
Hokky Situngkir Hokky Situngkir (born February 7, 1978) is an Indonesian scientist who researches complexity theory at Surya University. He is the founder of the Bandung Fe Institute, a research institute for social complexity research. His academic activities ...
that eventually made a new genre of
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...
batik designs as generative art; see Situngkir and Surya (2007) for implementations.


Mathematics education

Ethnomathematics and mathematics education addresses first, how cultural values can affect teaching, learning and curriculum, and second, how mathematics education can then affect the political and social dynamics of a culture. One of the stances taken by many educators is that it is crucial to acknowledge the cultural context of mathematics students by teaching culturally based mathematics that students can relate to. Can teaching math through cultural relevance and personal experiences help the learners know more about reality, culture, society and themselves? Robert (2006) Another approach suggested by mathematics educators is exposing students to the mathematics of a variety of different cultural contexts, often referred to as multicultural math. This can be used both to increase the social awareness of students and offer alternative methods of approaching conventional mathematics operations, like
multiplication Multiplication (often denoted by the Multiplication sign, cross symbol , by the mid-line #Notation and terminology, dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four Elementary arithmetic, elementary Op ...
(Andrew, 2005).


Examples

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 African art describes the modern and historical paintings, sculptures, installations, and other visual culture from native or indigenous Africans and the African continent. The definition may also include the art of the African diasporas, such ...
and games, Malloy (1997) about African American students and Flores (1997), who developed instructional strategies for
Hispanic The term ''Hispanic'' ( es, hispano) refers to people, cultures, or countries related to Spain, the Spanish language, or Hispanidad. The term commonly applies to countries with a cultural and historical link to Spain and to viceroyalties for ...
students.


Criticism

Some critics claim that
mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although re ...
unduly emphasizes ethnomathematics in order to promote
multiculturalism The term multiculturalism has a range of meanings within the contexts of sociology, political philosophy, and colloquial use. In sociology and in everyday usage, it is a synonym for " ethnic pluralism", with the two terms often used interchang ...
while spending too little time on core mathematical content, and that this often results in
pseudoscience Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claim ...
being taught.
Richard Askey Richard Allen Askey (4 June 1933 – 9 October 2019) was an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials (introduced by him in 1984 together with James A. Wilson) are on the t ...
examined ''Focus on Algebra'' (an
Addison-Wesley Addison-Wesley is an American publisher of textbooks and computer literature. It is an imprint of Pearson PLC, a global publishing and education company. In addition to publishing books, Addison-Wesley also distributes its technical titles throug ...
textbook criticized in an op-ed by Marianne M. Jennings) and among other shortcomings found it guilty of repeating debunked claims about Dogon astronomy. More recently, curriculum changes proposed by the Seattle school district drew criticism to ethnomathematics. 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?" and "Who gets to say if an answer is right?"


See also

* Anti-racist mathematics *
Cultural imperialism Cultural imperialism (sometimes referred to as cultural colonialism) comprises the cultural dimensions of imperialism. The word "imperialism" often describes practices in which a social entity engages culture (including language, traditions, ...
*
Culturally relevant teaching Culturally relevant teaching or responsive teaching is a pedagogy grounded in teachers' practice of cultural competence, or skill at teaching in a cross-cultural or multicultural setting.Diller, J., & Moule, J. (2005). Cultural competence: A prime ...
*
Critical pedagogy Critical pedagogy is a philosophy of education and social movement that developed and applied concepts from critical theory and related traditions to the field of education and the study of culture. It insists that issues of social justice and de ...
* Ethnocomputing * Informal mathematics *
Multiculturalism The term multiculturalism has a range of meanings within the contexts of sociology, political philosophy, and colloquial use. In sociology and in everyday usage, it is a synonym for " ethnic pluralism", with the two terms often used interchang ...
*''
Pedagogy of the Oppressed ''Pedagogy of the Oppressed'' ( pt, Pedagogia do Oprimido) is a book by Brazilian educator Paulo Freire, written in Portuguese between 1967–68, but published first in Spanish in 1968. An English translation was published in 1970, with the Por ...
'' *
Postmodernity Postmodernity (post-modernity or the postmodern condition) is the economic or cultural state or condition of society which is said to exist ''after'' modernity. Some schools of thought hold that modernity ended in the late 20th century – in the ...
*
Pseudoscience Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claim ...
* Social progressivism * Teaching for social justice * Mathematics and arts


References


Further reading

*Ascher, Marcia (1991). ''Ethnomathematics: A Multicultural View of Mathematical Ideas'' Pacific Grove, Calif.: Brooks/Cole. *D'Ambrosio. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5, 44–8. *D'Ambrosio. (1997). "Foreword", ''Ethnomathematics'', p.xv and xx. . *D'Ambrosio. (1999). Literacy, Matheracy, and Technoracy: A Trivium for Today. ''Mathematical Thinking and Learning 1''(2), 131–153. *Berczi, Sz. (2000): Katachi U Symmetry in the Ornamental Art of the Last Thousands Years of Eurasia. ''FORMA'', 15/1. 11–28. Tokyo *Closs, M. P. (ed.) (1986). ''Native American Mathematics.'' Austin, TX: University of Texas Press. *Crowe, Donald W. (1973). Geometric symmetries in African art. Section 5, Part II, in Zaslavsky (1973). *Eglash, Ron (1999). ''African Fractals: Modern Computing and Indigenous Design.'' New Brunswick, New Jersey, and London: Rutgers University Press. , paperback *Eglash, R., Bennett, A., O'Donnell, C., Jennings, S., and Cintorino, M. "Culturally Situated Design Tools: Ethnocomputing from Field Site to Classroom." ''American Anthropologist'', Vol. 108, No. 2. (2006), pp. 347–362. *Goetzfridt, Nicholas J. (2008) Pacific Ethnomathematics: A Bibliographic Study. Honolulu: University of Hawai'i Press. . * Harrison, K. David. (2007) When Languages Die: The Extinction of the World's Languages and the Erosion of Human Knowledge. New York and London: Oxford University Press. *Joseph, George Gheverghese (2000). ''The Crest of the Peacock: Non-European Roots of Mathematics.'' 2nd. ed. London: Penguin Books. * Menninger, Karl (1934), ''Zahlwort und Ziffer''. Revised edition (1958). Göttingen: Vandenhoeck and Ruprecht. *Menninger, Karl (1969), ''Number Words and Number Symbols''. Cambridge, Massachusetts: The M.I.T. Press. *Luitel, Bal Chandra and Taylor, Peter. (2007). The shanai, the pseudosphere and other imaginings: Envisioning culturally contextualised mathematics education. Cultural Studies of Science Education 2(3). *Powell, Arthur B., and Marilyn Frankenstein (eds.) (1997). ''Ethnomathematics: Challenging Eurocentrism in Mathematics Education'', p. 7. Albany, NY: State University of New York Press. * Situngkir, H., Surya Y. (2007). ''Fisika Batik (The Physics of Batik)''. Gramedia Pustaka Utama. * Zaslavsky, Claudia (1973). ''Africa Counts: Number and Pattern in African Culture.'' Third revised ed., 1999. Chicago: Lawrence Hill Books. *Zaslavsky, Claudia (1980). ''Count On Your Fingers African Style.'' New York: Thomas Y. Crowell. Revised with new illustrations, New York: Black Butterfly Books.


External links


Ethnomathematics Digital Library.
Pacific Resources for Education and Learning. This is a Web collection of source and resource materials.
Journal of Mathematics and Culture
This is NASGEm's refereed journal on ethnomathematics.
The Journal of Humanistic Mathematics
The focus of submitted papers should be on the aesthetic, cultural, historical, literary, pedagogical, philosophical, psychological, and sociological aspects of doing, learning, and teaching mathematics. {{Authority control Mathematics and culture Mathematics education Ethnology Traditional knowledge Critical pedagogy