Revising the history of number: how Ethnomathematics transforms perspectives on indigenous cultures

Resumo

Many accounts of the history of number rely on written evidence such as clay, stone, and wood engravings or paintings. However, some of the oldest cultural groups (between 5 000 and 30 000 years old) have had only recent contact with the rest of the world, namely between 80 and 140 years ago but these were oral cultures without written records. Finding out about their understanding of number has involved analysis of the types of counting but also how counting related to the rest of their cultural relationships. There is some surprising evidence of diversity of number systems, longevity of the systems, and the interplay with cultural practices that begs respect for Indigenous cultures. Brief summaries of this history of number in Papua New Guinea and Oceania and the diversity of systems is followed by how this new knowledge can inform school mathematics learning in any part of the world.

Keywords: History of number. Indigenous mathematics. Papua New Guinea. Melanesia. Pacific. Longevity of number systems.

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Referências

ADDISON, David; MATISOO-SMITH, Elizabeth. Rethinking Polynesians origins: a West-Polynesia Triple-I Model. Archaeology in Oceania, v. 45, n. 1, p. 1-12, 2010.

ALLEN, Jim. The pre-Austronesian settlement of Island Melanesia: implications for Lapita archaeology. Transactions of the American Philosophical Society, v. 86, n. 5, p. 11-27, 1996.

ASCHER, Marcia. Ethnomathematics: a multicultural view of mathematical ideas. New York: Chapman & Hall, 1994.

BENDER, Andrea; BELLER, Seighard. Cultural variation in numeration systems and their mapping onto the mental number line. Journal of Cross-Cultural Psychology, v. 42, n. 4, p. 579-597, 2011.

BENDER, Andrea; BELLER, Seighard. Numeral classifiers and counting systems in Polynesian and Micronesian languages: common roots and cultural adaptations. Oceanic Linguistics, v. 45, n. 2, p. 380-403, 2006.

BISHOP, Alan John. Mathematical enculturation: a cultural perspective on Mathematics Education. Dordrecht: Kluwer, 1988.

BISHOP, Alan John. Visualising and mathematics in a pre-technological culture. Educational Studies in Mathematics, v. 10, n. 2, p. 135-146, 1979.

BROUWER, Luitzen Egbertus Jan. Guidelines of intuitionistic mathematics. In: HEYTING, Arend. (Ed.). Philosophy and foundations of mathematics. Amsterdam: North Holland, 1975, p. 123-138.

CRAWFURD, John. On the numerals as evidence of the progress of civilization. Transactions of the Ethnological Society of London, v. 2, p. 84-111, 1863.

D’AMBROSIO, Ubiratan. The history of Mathematics and Ethnomathematics: how a native culture intervenes in the process of learning science. Impact of Science on Society, v. 40, n. 4, p. 369-378, 1990.

DIXON, Roland; KROEBER, A. L. Numerical systems of the languages of California. American Anthropologist, v. 9, p. 663-690, 1907.

DONOHUE, Mark. Complexities with restricted numeral systems. Linguistic Typology, v. 12, n. 3, p. 423-429, 2008.

EVANS, Nicholas. Two pus one makes thirteen: senary numerals in the Morehead-Maro region. Linguistic Typology, v. 13, n. 2, p. 321-335, 2009.

FISHER, John. Enriching students' learning through ethnomathematics in Kuruti elementary schools in Papua New Guinea. In: International Conference on Ethnomathematics, 3, 2006, Auckland. Proceedings ICEM-3: Cultural Connections and Mathematical Manipulations. Auckland: The University of Auckland, 2006, p. 1-17.

HARRISON, Sheldon; JACKSON, Frederick. Higher numerals in several Micronesian languages. In BENDER, Byron (Ed.). Studies in Micronesian Linguistics. Canberra: Pacific Linguistics: 1984, p. 61-79.

HOLZKNECHT, Susanne. The Markham languages of Papua New Guinea. Canberra: School of Pacific Research Studies, Australian National University, 1989.

JETT, Stephen. Diffusion versus independent development: the bases of controversy. In RILEY, Carroll; KELLEY, J. Charles; PENNINGTON, Campbell; RANDS, Robert (Ed.). Man Across the Sea: problems of pre-columbian contacts. Austin & London: University of Texas Press, 1971, p. 5-53.

KNIJNIK, Gelsa; WANDERER, Fernanda. Mathematics Education and differential inclusion: a study about two Brazilian time-space forms of life. ZDM Mathematics Education, v. 42, n. 3-4, p. 349-360, 2010.

LANCY, David. Indigenous mathematics systems: an introduction. Papua New Guinea Journal of Education, v. 14, p. 6-15, 1978.

LEAN, Glendon. Counting systems of Papua New Guinea and Oceania.1992. Thesis (Doctorate in Mathematics). Papua New Guinea University of Technology. Lae.

LYNCH, John. On the history of the Tanna numerals and number markers. Te Reo: Journal of the Linguistic Society of New Zealand, v. 20, p. 3-28, 1977.

MAY, Patricia; TUCKSON, Margaret. The traditional pottery of Papua New Guinea. rev. ed. Adelaide: Crawford House Publishing, 2000.

MIMICA, Jardin. Intimations of infinity: the mythopoeia (cultural meanings) of the Iqwaye counting and number systems. Oxford: Berg, 1988.

MUKE, Charly. Ethnomathematics: Mid-Wahgi counting practices in Papua New Guinea, 2000. Thesis (Masters in Mathematics Education). University of Waikato, Waikato.

OWENS, Kay. The work of Glendon Lean on the counting systems of Papua New Guinea and Oceania. Mathematics Education Research Journal, v. 13, n. 1, p. 47-71, 2001.

OWENS, Kay. Visuospatial reasoning: an ecocultural perspective for space, geometry and measurement education. New York: Springer, 2015.

OWENS, Kay; LEAN, Glendon, with PARAIDE, Patricia; MUKE, Charly. The history of number: perspective from Papua New Guinea and Oceania. New York: Springer, 2018.

OWENS, Kay; LEAN, Glendon; MUKE, Charly. 2-cycle systems including some digit-tally systems. In OWENS, Kay; LEAN, Glendon; PARAIDE, Patricia; MUKE, Charly. (Ed.). History of number: evidence from Papua New Guinea and Oceania. New York: Springer, 2018, p. 41-60.

PANTOFF, Michel. Father arithmetic: numeration and counting in New Britain. Ethnnology, v. 9, n. 4, p. 358-365, 1970.

PARAIDE, Patricia. Indigenous and western knowledge. In OWENS, Kay; LEAN, Glendon; PARAIDE, Patricia (Ed.). History of number: Evidence from Papua New Guinea and Oceania. New York: Springer, 2018, p. 223-242.

PARAIDE, Patricia; OWENS, Kay. Integration of Indigenous knowledge in formal learning environments. In OWENS, Kay; LEAN, Glendon; PARAIDE, Patricia; MUKE, Charly (Ed.). History of number: evidence from Papua New Guinea and Oceania. New York, NY: Springer, 2018, p. 243-269.

PARAIDE, Patricia; OWENS, Kay; CLARKSON, Philip; MUKE, Charly; OWENS, Chris. History of Mathematics Education in Papua New Guinea. New York: Springer (forthcoming).

PAWLEY, Andrew; GREEN, Roger. The Proto-Oceanic language community. In KIRK, Robert; SZATHMARY, EmOke. (Ed.). Out of Asia: peopling the Americas and the Pacific. Canberra: Australian National University, 1985, p. 161-184.

PUMUGE, Hilary. The counting system of the Pekai-Alue tribe of the Topopul village in Ialibu sub-district in the Southern Highlands District, Papua New Guinea. Science in New Guinea, v. 3, n. 1, p. 19-25, 1975.

RAGLAN, Lord B. How came civilization? London: Methuen and Company, 1939.

RINSVELD, Amandine Van; SCHILTZ, Christine; LANDERL, Karin; BRUNNER, Martin; UGEN, Sonja. Speaking two languages with different number naming systems: what implications for magnitude judgments in bilinguals at different stages of language acquisition? Cognitive Processing, v. 17, n. 3, p. 225-241, 2016.

ROSS, Malcolm. Proto Oceanic and the Austronesian languages of western Melanesia. Canberra: School of Pacific Research Studies, Australian National University, 1988.

ROSS, Malcolm; PAWLEY, Andrew; OSMOND, Meredith. The lexicon of Proto Oceanic: The culture and environment of ancestral Oceanic society. 2: The physical environment. Canberra, Australia: Pacific Linguistics, Research School of Pacific and Asian Studies ANU, 2003.

SALZMANN, Zdeněk. A method for analyzing numerical systems. Word, 6, p. 78-83, 1950.

SAXE, Geoffrey. A comparative analysis of the acquisition of numeration: studies from Papua New Guinea. The Quarterly Newsletter of the Laboratory for Comparative Human Cognition, v. 1, n. 3, p. 37-43, 1979.

SEIDENBERG, Abraham. The diffusion of counting practices. University of California Publications in Mathematics, v. 3, 1960.

SMITH, Geoffrey P. S. Morobe counting systems. In: Papers in New Guinea Linguistics. Series A, n. 76. Canberra: Pacific Linguistics, 1988, p. 1-132.

SMITH, Geoffrey P. S. Morobe counting systems: an investigation into the numerals of the Morobe Province, Papua New Guinea, 1984. Thesis (Masters in Language and Communication). Papua New Guinea University of Technology, Lae.

SMITH, Grafton Elliot. The diffusion of culture. London: Watts and Company, 1933.

SPRIGGS, Matthew. Archaeology and the Austronesian expansion: where are we now? Antiquity, v. 85, n. 328, p. 510-528, 2011.

STRATHERN, Andrew. Mathematics in the moka. Papua New Guinea Journal of Education, v. 13, n. 1, p. 16-20, 1977.

TRYON, Darrell (Ed.). Comparative Austronesian dictionary. Berlin: Mouton de Gruyter, 1995.

VAN DER WAERDEN, Bartel Leendert; FLEGG, Graham. Counting 1: primitive and more developed counting systems. Milton Keynes: Open University, 1975.

WILDER, Raymond. Evolution of mathematical concepts. London: Transworld, 1974.

WILLIAMS, Francis. Papuans of the Trans-Fly. Oxford: Clarendon Press, 1936.

WOLFERS, Edwards. The original counting systems of Papua and New Guinea. Arithmetic Teacher, v. 18, n. 1, p. 77-83, 1971.

WURM, Stephen. Papuan languages. In: MAY, Ronald James; NELSON, Hank (Ed.), Melanesia: Beyond diversity. Canberra: Research School of Pacific Studies, Australian National University, 1982, pp. 225-240.

WURM, Stephen; LAYCOCK, David; VOORHOEVE, Clemens; DUTTON, Thomas. Papuan linguistic prehistory, and past language migrations in the New Guinea area. New Guinea area languages and language study. Vol. 1: Papuan languages and the New Guinea linguistic scene, Pacific Linguistics v. C-38. Canberra: Research School of Pacific Studies Australian National University, 1975, p. 935-960.

ZASLAVSKY, Claudia. Africa counts: number and pattern in African culture. Boston: Prindle, Weber and Schmidt, 1973.

Publicado
2020-03-04
Seção
International Perspectives on Ethnomathematics: from research to practices