Revisando la historia de los números: cómo las Etnomatemáticas transforma las perspectivas sobre las culturas indígenas

Palabras clave: Historia de los Números, Matemáticas indígenas, Papua Nueva Guinea, Melanesia, Pacifico, Longevidad de sistemas numéricos

Resumen

Muchos relatos de la historia de los números se basan en pruebas escritas como grabados o pinturas de arcilla, piedra y madera. Sin embargo, algunos de los grupos culturales más antiguos (entre 5 000 y 30 000 años) solo han tenido contacto reciente con el resto del mundo, es decir, hace entre 80 y 140 años, pero se trataba de culturas orales sin registros escritos. Conocer su comprensión del número ha implicado el análisis de los tipos de conteo, pero también cómo el conteo se relaciona con el resto de sus relaciones culturales. Hay alguna evidencia sorprendente de la diversidad de sistemas numéricos, la longevidad de los sistemas y la interacción con prácticas culturales que exigen respeto por las culturas indígenas. Breves resúmenes de esta historia del número en Papua Nueva Guinea y Oceanía y la diversidad de sistemas es seguida por cómo este nuevo conocimiento puede informar el aprendizaje matemático escolar en cualquier parte del mundo.

Descargas

La descarga de datos todavía no está disponible.

Citas

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
Cómo citar
OWENS, K.; MUKE, C. Revisando la historia de los números: cómo las Etnomatemáticas transforma las perspectivas sobre las culturas indígenas. Revemop, v. 2, p. e202007, 4 mar. 2020.
Sección
Perspectivas internacionales de la Etnomatemáticas: de la investigación a la prá