The work of Glendon Lean on the counting systems of Papua New Guinea and Oceania
- Kay Owens
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Glendon Lean collated data on nearly 900 counting systems of Papua New Guinea, Oceania, and Irian Jaya (West Papua). Lean’s data came from a questionnaire completed by students and talks with village elders. He read old documents written in English, German, and Dutch. He made comparisons between older and new accounts of the counting systems and compared neighbouring counting systems from both Austronesian and non-Austronesian languages. His work drew attention to the rich diversity of the systems and suggested that systems based on body parts and cyclic systems developed spontaneously. Digit tally systems were also relatively common. Lean’s thesis on spontaneous developments of these ancient cultures challenged traditional theories describing the spread of number systems from Middle East cultures.
- Biersack, A. (1982). The logic of misplaced concreteness: Paiela body-counting and the nature of primitive mind.American Anthropologist, 84, 811–829. CrossRef
- Bowers, N., & Lepi, P. (1975). Kaugel valley systems of reckoning.Journal of the Polynesian Sodety, 84, 309–324.
- Butterworth, B. (1999).The mathematical brain. London: Macmillan.
- Clarkson, P. (1996). NESB migrant students studying mathematics: Vietnamese and Italian students in Melbourne. In L. Puig & A. Gutiérrez (Eds.),Proceedings of the 20th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 225–232). Valencia, Spain: Program Committee.
- Deakin, M. (1995, July).The origins of our number-words. Invited address presented at 39th annual conference of the Australian Mathematical Society, Hobart.
- Drabbe, P. (1949). Bfjzonderheden uit de talen van Frederik-Hendrik-Eiland: Kimaghama, Ndom en Riantana [Special features of the number systems on Frederik Hendrik Island: Kimaghama, Ndom and Riantana].Bijdragen tot de Taal-, Land- en Volkenkunde, 105, 1–24.
- Franklin, K. (1971). A grammar of Kewa.New Guinea, 3–16.
- Franklin, K., & Franklin, J. (1962). The Kewa counting systems.Journal of the Polynesian Society, 71, 188–191.
- Galis, K. (1960). Telsystemen in Nederlands-New-Guinea [Counting systems in Duth New-Guinea].Nieuiv-Guinea Studien, 4(2), 131–150.
- Gerdes, P. (1999).Geometry from Africa: Mathematical and educational explorations. Washington, DC: Mathematical Association of America.
- Ifrah, G. (1998).The universal history of numbers: From prehistory to the invention of computers (D. Bellow, E. Harding, S. Wood, & I. Monk, Trans.). London, England: Harvill Press.
- Lancy, D. (1978). Indigenous mathematics systems: Introduction.Papua New Guinea Journal of Education, 14, 6–15.
- Lean, G. (1988).Counting systems of Papua New Guinea (Vols. 1-17). Lae, PNG: Papua New Guinea University of Technology.
- Lean, G. (1990). Numeration in the cultures of Oceania. Paper presented at the international research seminar on Mathematics and Science Education: The Cultural Context, Deakin University, Geelong, VIC.
- Lean, G. (1991).Counting systems of Papua Neiv Guinea: Vol. 9, Enga, Western, and Simbu Provinces; Vol. 10, Southern Highlands Province; Vol. 13, Sandaun (West Sepik) Province; Vol. 14, East Sepik; Vol. 15, Madang Province (2nd ed.). Lae, PNG: Department of Mathematics and Statistics, Papua New Guinea University of Technology.
- Lean, G. (1992).Counting systems of Papua New Guinea and Oceania. Unpublished PhD thesis, Papua New Guinea University of Technology, Lae, PNG.
- Pumuge, H. (1975). The counting system of the Pekai-Alue tribe of the Topopul village in the Ialibu sub-district, Papua New Guinea.Science in New Guinea, 3(1), 19–25.
- Ray, S. (1926).A comparative study of the Melanesian island languages. Cambridge, England: Cambridge University Press.
- Ross, M. D. (1988). Proto-Oceanic and the Austronesian languages of Western Melanesia.Pacific Linguistics, C-98.
- Salzmann, Z. (1950). A method for analyzing numerical systems.Word, 6, 78–83.
- Saxe, G. (1981). Body parts as numerals: A developmental analysis of numeration among the Oksapmin in Papua New Guinea.Child Development, 52, 306–316. CrossRef
- Seidenberg, A. (1960). The diffusion of counting practices.University of California Publications in Mathematics, 3 (Whole No.).
- Seidenberg, A. (1962). The ritual origin of counting.Archive for the History of the Exact Sciences, 2 (3), 1–40. CrossRef
- Smith; G. (1984).Morobe counting systems: An investigation into the numerals of the Morobe Province, Papua New Guinea. Unpublished M. Phil thesis, Papua New Guinea University of Technology, Lae, PNG.
- Smith, G. (1988). Morobe counting systems.Papers in New Guinea Linguistics, A-76 (pp. 1–132). Canberra: Pacific Linguistics.
- Strathern, A. (1977). Mathematics in the Moka.Papua New Guinea Journal of Education, 13(1), 16–20.
- Wassmann, J., & Dasen, P. (1994) Yupno number system and counting.Journal of Cross-Cultural Psychology, 25, 78–94. CrossRef
- Wurm, S. (1982).Papuan languages of Oceania. Tübingen, Germany: Gunter Narr Verlag.
- Wurm, S., & Hattori, S. (Eds.). (1981).Language atlas: Pacific area, Part 1. Canberra: Australian Academy of the Humanities.
- Zepp, R. (Ed) (1993).Ethnomathemntical lessons for Papua New Guinea high schools. Goroka. PNG: Department of Mathematics Education, University of Papua NewGuinea.
- The work of Glendon Lean on the counting systems of Papua New Guinea and Oceania
Mathematics Education Research Journal
Volume 13, Issue 1 , pp 47-71
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- Springer Netherlands
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- Kay Owens (1)
- Author Affiliations
- 1. Faculty of Education, University of Western Sydney, P. O. Box 555, 2560, Campbelltown, NSW