Ethnomathematics Digital Library (EDL)

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Subject: Numbers and Computation>Arithmetic>Body parts used for counting

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Cognition, development and cultural practices
by Geoffrey Saxe (1999)
[http://www-gse.berkeley.edu/faculty/gsaxe/Documents/saxe_new_directions.pdf]
This paper looks at the interplay between cognitive development and culture change. This interplay is illustrated with information about economic exchange in the Oksapmin people of Papua New Guinea’s West Sepik Province. These people have a traditional body part counting system that begins with the thumb on one hand, enumerates 27 places around the upper periphery of the body, and ends on the little finger of the opposite hand. Changes in cultural practice resulted from the introduction of currency in the 1960s. The processes of microgenesis, ontogenesis, and sociogenesis are used for the analysis. Other terms: games, arithmetic, base-10 system, measurement, kina, computation, trade, money, global enumeration, quantity, fractions. (Includes 16 references)
Subject: Cultural Context>Cultural Perspectives on Mathematics>Standard versus Non-standard Mathematics,
Cultural Context>Influence of Culture on Learning Mathematics,
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Number Concepts>Natural Numbers>Counting
Geographical area: Papua New Guinea
Cultural group: Papua New Guinea Islander (Papuan)

Ethnomathematics snap shots
by John Kellermeier (2002)
[http://www.tacoma.ctc.edu/home/jkellerm/Ethnomath/index.htm]
This website has 12 short descriptions of the influence of mathematics on culturally relevant activities and products from around the world. These include women as the originators of mathematics, using such evidence as the lunar calendar, the Ishango Bone from Africa, and the Isturitz Baton from France; the Mesoamerican vigesimal (base twenty) number system; the Incan quipu as a counting tool; African counting words based on the human body; Mozambican methods of laying rectangles; global 3-in-a-row games; Native American petroglyphs; Amish quilts; symmetric strip decorations of the Inca and Maori; Inuit drawings; and Angolan sand drawings (sona). Geometrical themes include iteration, recursion, similtude, tiling, symmetry, repetition, reflection, and rotation. Other terms: menstruation, Paleolithic, pipe lagging, knitting, sock heel, angle, knot, cord. (Includes 22 references)
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design>Knitting,
Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design>Quilting,
Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design>Sona,
Applied Mathematics>Mathematics for Social Sciences>Games and Toys,
Cultural Context>Cultural Diversity>Women's Role in Mathematics,
Geometry and Topology>Plane Geometry>Patterns>Geometric Patterns,
Geometry and Topology>Plane Geometry>Patterns>Symmetry,
Geometry and Topology>Plane Geometry>Patterns>Tilings and Tessellations,
Geometry and Topology>Plane Geometry>Transformations>Reflection (Transformations),
Geometry and Topology>Plane Geometry>Transformations>Rotation (Transformations),
Geometry and Topology>Plane Geometry>Transformations>Translation (Transformations),
Geometry and Topology>Plane Geometry>Polygons,
Mathematical Tools and Devices>Khipu (Quipu),
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Number Concepts>Natural Numbers>Counting,
Numbers and Computation>Number Concepts>Natural Numbers>Number Systems (Natural),
Numbers and Computation>Number Concepts
Geographical area: Africa, Alaska (United States), Angola, Central America, Mozambique, New Zealand, South America, United States of America
Cultural group: African, Amish, Chokwe (Tchokwe) (Africa), Inca (Native American - South America), Inuit (Native American - North America), Maori, Mayan (Native American - Mexico and Central America), Mozambican, Native American (United States)

Have you seen (ISGEm Newsletter, Volume 12, Number 2, December 1997)
(1997)
[http://www.ethnomath.org/resources/ISGEm/093.htm]
This bibliography lists five works in ethnomathematics. A book chapter features the base five numeration system of the Gomileroi, an Australian Aboriginal people, and shows the language connection between number words and body parts. The other four articles by Ron Eglash cover recursion in ethnomathematics, ethnomathematics theory, Benjamin Banneker, and African influences in cybernetics. Other terms: heritage, Bamana sand divination.
Subject: Cultural Context>Cultural Perspectives on Mathematics,
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Number Concepts>Natural Numbers>Number Systems (Natural)
Geographical area: Africa, Australia
Cultural group: African, Australian Aborigine

Indigenous mathematics: a rich diversity
by Kay Owens (2001)
[http://www.aamt.edu.au/ICSIMAN/resources/papers/owens.pdf]
This paper examines the relevance and value of teaching Indigenous mathematics in the context of school mathematics, drawing a parallel between the impact of current nutritional knowledge on traditional food taboos. Different number cycle systems, body-part or digit tally systems, and counting and non-counting number systems in Papua New Guinea, Oceania, and Austronesia are described. The universality of measurement, the importance of spatial thinking in Indigenous mathematics, and the concept of time in Indigenous cultures are also discussed. Other terms: superordinals, diversity, base-10 system, operative pattern, linguistics, fractions, string, symmetry, volume, shared patterns, weaving, organization, balance, seasons, map, classification, activities, geometry, shape, rectangles, perimeter. (Includes 13 references)
Subject: Cultural Context>Influence of Culture on Learning Mathematics,
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Number Concepts>Natural Numbers>Counting
Geographical area: Australia, New Zealand, Oceania, Papua New Guinea
Cultural group: Australian, Australian Aborigine, Oceanian, Papua New Guinea Islander (Papuan)

Kapauku numeration: reckoning, racism, scholarship, and Melanesian counting systems
by Nancy Bowers (1977)
[http://www.ethnomath.org/resources/bowers1977.pdf]
This study details the numeration system of Kapauku, a Papuan ethnic group of Western New Guinea (West Irian), in a critical response to suggestions that the system may have originated from ancient Babylonia. The treatise refutes some points that were raised about a Kapauku-Babylonian connection (e.g., assertions that the Kapauku system is 60-based, that the Kapauku conceive of halves and thirds of 60, and that the Kapauku have been isolated from the outside world). References are also drawn from studies of numerals in New Guinea languages to underline local spheres of influence that can be found in body count systems, counting methods, and basic elements of numeration among various groups. (Includes 33 references)
Subject: Cultural Context>Cultural Perspectives on Mathematics>Euro-centrism,
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Number Concepts>Natural Numbers>Counting
Geographical area: Papua New Guinea
Cultural group: Papua New Guinea Islander (Papuan)

Making change in Oksapmin tradestores: a study of shifting practices of quantification under conditions of rapid shift towards a cash economy
by Geoffrey Saxe
[http://www-gse.berkeley.edu/faculty/gsaxe/Documents/saxe_esmonde.pdf]
This article describes the results of a study on how the mathematical practices of a native population in Sandaun Province, Papua New Guinea, is changing under the influence of Western education and currency. In pre-contact times, Oksapmin used a 27 body part count system. The study examined whether the mathematical language used for currency during transactions in stores was native language or Melanesian pidgin. Older adults who had not been educated tended to use native language terms, and younger adults and those who had used Western currency in other places tended to use pidgin. (Includes 16 references)
Subject: Instructional Issues>Mathematical Language,
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Measurement>Money
Geographical area: Papua New Guinea
Cultural group: Oksapmin (Papua New Guinea)

The Ayom pygmies' myth of origin and their method of counting
by Heinrich Aufenanger (1960)
[http://www.ethnomath.org/resources/aufenanger1960.pdf]
This report describes the “pygmies” from the “banks of the Asai river” and their body-part counting system similar to that of the Gende people of the Bismarck mountains. A list is provided of the body parts associated with most numbers up to 23 – the total of which can be repeatedly reached and expressed as 46, 69, and so on by counting the body parts again. For example, the counting of numbers begins with the fingers of the left hand laid on the bent little finger of the right hand for the number 1. Another list of terms for numbers 1 through 5 is for counting without the use of fingers. The counting of “many” things by twos is also explained, as well as the option for using two people to count. The Gainj-river pygmies’ counting system is covered as well.
Subject: Cultural Context>Cultural Awareness,
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Number Concepts>Natural Numbers>Counting
Geographical area: Papua New Guinea
Cultural group: Papua New Guinea Islander (Papuan)

The Polynesian numerals one, five, ten
by John Fraser (1902)
[http://www.ethnomath.org/resources/fraser1902.pdf]
Depending on the language, the base meaning for the word “hand” can point to different concepts (e.g., the number five, grasp, seize). In examining the probability that indigenous terms for “five” in Oceania and Asia revolve around a common derivative that relates to “holding”, this report stresses the first of several propositions that “the Polynesian word for ‘five’ is lima, which also means the ‘hand’;…” The study discusses how the word for “hand” in several languages (particularly the Aryan languages) shows that “the meaning of their base is to hold, to grasp,” and that this root of “ga” and “ka” may ultimately lead to the root of the Polynesian word for five - lima. Several comparative tables of words from Asia and the Pacific demonstrate the importance of this ancient root for the number five and its relationship to the concept of using a hand of five fingers to grasp.
Subject: Instructional Issues>Educational Research,
Numbers and Computation>Arithmetic>Body parts used for counting,
Numbers and Computation>Number Concepts>Natural Numbers>Counting
Geographical area: Oceania
Cultural group: Polynesian

The Ethnomathematics Digital Library is a component of the National Science, Technology, Engineering and Mathematics Education Digital Library (NSDL), funded by the National Science Foundation.