Abstract
This multidisciplinary study draws on archaeological information, linguistics, and an understanding of mathematics. A summary of the background archaeology for New Guinea and Oceania provides some evidence of the longevity of these cultures and the archaeological evidence for the spread of languages in New Guinea and Oceania. The diversity of language groups is a result of movement, colonisation, influence and innovation over time. The overview presented in this chapter permits the reader to link the pursuing discussion in a time and place. The chapter finishes with an overview of the book that sets out the diversity of counting system cycles, where they are established, and how they may have developed.
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Notes
- 1.
PREL, Pacific Resources in Education and Learning in Hawaii included this project in a USA National Science Foundation grant.
- 2.
This study was funded by a Charles Sturt University Competitive Grant.
References
Adam, N. A. (2010). Mutual interrogation: A methodological process in ethnomathematical research. Procedia, Social and Behavioral Sciences, 8, 700–707.
Addison, D. J., & Matisoo-Smith, E. (2010). Rethinking Polynesians origins: A West-Polynesia Triple-I Model. Archaeology in Oceania, 45(1), 1–12.
Allen, J. (1984). In search of the Lapita homeland. Journal of Pacific History, 19(3–4), 186–201.
Allen, J. (1996). The pre-Austronesian settlement of Island Melanesia: Implications for Lapita archaeology. Transactions of the American Philosophical Society, 86(5), 11–27. doi:10.2307/1006618.
Ascher, M. (1994). Ethnomathematics: A multicultural view of mathematical ideas. New York, NY: Chapman & Hall.
Ascher, M. (2002). Mathematics elsewhere: An exploration of ideas across cultures. Princeton, NJ: Princeton University Press.
Berry, J., & Dasen, P. (1974). Culture and cognition: Readings in cross-cultural psychology. London, UK: Methuen.
Boyer, C., & Merzbach, U. (1989). A history of mathematics (2nd ed.). New York, NY: Wiley.
Bulmer, S. (1975). Settlement and economy in prehistoric Papua New Guinea: A review of the archaeological evidence. Journal de la Société des Océanistes, 31, 7–75.
Butler, M., & Dean, B. (Writers). (2013). First footprints (4 episodes). Australia: ABC Broadcasting.
Capell, A. (1969). A survey of New Guinea languages. Sydney, Australia: Sydney University Press.
Carrier, A. (1981). Counting and calculation on Ponam Island. Journal of the Polynesian Society, 90(4), 465–479.
Clark, G. (2003). Shards of meaning: Archaeology and the Melanesia-Polynesia divide. The Journal of Pacific History, 38(2), 197–215. doi:10.1080/0022334032000120530.
Closs, M. (Ed.). (1986). Native American mathematics. Austin, TX: University of Texas Press.
Cole, M., Gay, J., Glick, J., & Sharp, D. (1971). The cultural context of learning and thinking. London, UK: Methuen.
Cooke, R. L. (2011). The history of mathematics: A brief course (2nd ed.). New York, NY: Wiley.
D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity (M. Borba, Trans.). Rotterdam, The Netherlands: Sense Publishers.
Dantzig, T. (1954). Number: The language of science (4th ed.). New York, NY: Macmillan.
Dasen, P., & de Ribaupierre, A. (1987). Neo-Piagetian theories: Cross-cultural and differential perspectives. International Journal of Psychology, 22(5/6), 793–832.
Davidson, J. M. (1977). Western Polynesia and Fiji: Prehistoric contact, diffusion and differentiation in adjacent archipelagos. World Archaeology, 9, 82–94.
Dempwolff, O. (1938). Vergleichende des Austronesischen Wortschatzes. Austronesischen Wörterverzeichnis (Vol. 3). Berlin, Germany: Dietrich Reimer.
Dutton, T. (Ed.). (1982). The Hiri in history, Pacific Research Monograph No. 8. Canberra, Australia: Australian National University Press.
Dwyer, P., & Minnegal, M. (2016). Counting systems of the Strickland-Bosavi languages, Papua New Guinea. Language and Linguistics in Melanesia, 34(1), 1–36.
Eglash, R. (1999). African fractals. New Brunswick, NJ: Rutgers University Press.
Eglash, R. (2010). From ethnomathematics to ethnocomputing. Paper presented at the Fourth International Conference on Ethnomathematics ICEm4, Towson.
Ernest, P. (1996). The nature of mathematics and teaching. Philosophy of Mathematics Education, 9, 40–45.
Ernest, P. (2012). What is our first philosophy in mathematics education? For the Learning of Mathematics, 32(3), 8–14.
Fisher, J. (~2010). Enriching students’ learning through ethnomathematics in Kuruti elementary schools in Papua New Guinea. Lae, Papua New Guinea: ResearchGate.
Flegg, G. (1984). Numbers: Their history and meaning. New Orleans, LA: Pelican Books.
Flegg, G. (1989). Numbers through the ages. London, UK: Macmillan and the Open University.
Frobenius, L. (1900). Die Mathematik der Oceanier, (Allgemein-verständliche Naturwissenschaftliche Abhandlungen, Heft 23). Berlin, Germany: F. Dümmler.
Gay, J., & Cole, M. (1967). The new mathematics and an old culture. New York, NY: Holt, Rinehart and Winston.
Gerdes, P. (1999). Geometry from Africa: Mathematical and educational explorations. Washington, DC: The Mathematical Association of America.
GLEC. (2008). Glen Lean Ethnomathematics Centre. Retrieved from http://www.uog.ac/glec/
Goetzfridt, N. (2008). Pacific ethnomathematics: A bibliographic study. Honolulu, HI: Japanese Cultural Centre and University of Hawaii Press.
Goetzfridt, N. (2012). Pacific ethnomathematics: The richness of environment and practice. Journal of Mathematics and Culture, International Conference on Ethnomathematics, 4(Focus Issue), 223–252.
Green, R. (2003). The Lapita horizon and traditons: Signature for one set of oceanic migrations. In C. Sand (Ed.), Pacific archaeology: Assessments and prospects. Proceedings of the First International Conference for the 50th Anniversary of the First Lapita Conference (Vol. 15). Noumea, New Caledonia: Les Cahiers de L’Archelogie en Nouvelle-Caledonie, New Caledonia Museum.
Harding, T. (1967). Voyagers of the Vitiaz Strait: A study of a New Guinea trade system. Seattle, WA: University of Washington Press.
Hughes, I. (1977). New Guinea stone age trade: Terra Australis 3. Canberra, Australia: Australian National University.
Hurford, J. (1987). Language and number: The emergence of a cognitive system. Oxford, UK: Basil Blackwell.
Ifrah, G. (1987). From one to zero: A universal history of numbers. Harmondsworth, UK: Penguin.
Izard, V., Pica, P., Spelke, E., & Dehaene, S. (2011). Flexible intuitions of Euclidean geometry in an Amazonian indigene group. Proceedings of the National Academy of Sciences of the United States of America, 108(24), 9782–9787. doi:10.1073/pnas.1016686108.
Joseph, G. (2000). The crest of the peacock: The non-European roots of mathematics. Princeton, NJ: Princeton University Press.
Keck, V. (Ed.). (1998). Common worlds and single lives: Constituting knowledge in Pacific societies. London, UK: Berg.
Kennedy, J. (1983). On the prehistory of western Melanesia. Australian Archaeology, 16, 115–122.
Kettenis, F. (1978). Traditional food classification and counting systems of Kilenge, West New Britain. Papua New Guinea Journal of Education, 14, 28–43.
Lancy, D. (1983). Cross-cultural studies in cognition and mathematics. New York, NY: Academic.
Lave, J. (1988). Cognition in practice. Cambridge, MA: Harvard University Press.
Lean, G. (1992). Counting systems of Papua New Guinea and Oceania (Unpublished PhD thesis). PNG University of Technology, Lae, Papua New Guinea.
Lynch, J., & Tryon, D. (1985). Central-Eastern Oceanic: A subgrouping hypothesis. Austronesian linguistics at the 15th Pacific Science Congress (C-88). Canberra, Australia: Pacific Linguistics, ANU.
Malinowski, B. (1920). Kula: The circulating exchange of valuables in the archipelagoes of eastern New Guinea. MAN, 20, 97–105.
Malinowski, B. (1922). Argonauts of the Western Pacific. London, UK: Routledge and Kegan Paul.
Matang, R., & Owens, K. (2006). Rich transitions from Indigenous counting systems to English arithmetic strategies: Implications for mathematics education in Papua New Guinea. In F. Favilli (Ed.), Ethnomathematics and mathematics education, Proceedings of the 10th International Congress on Mathematical Education Discussion Group 15 Ethnomathematics. Pisa, Italy: Tipografia Editrice Pisana.
Matang, R., & Owens, K. (2014). The role of Indigenous traditional counting systems in children’s development of numerical cognition: Results from a study in Papua New Guinea. Mathematics Education Research Journal, 26(3), 531–553. doi:10.1007/s13394-013-0115-2.
Mimica, J. (1988). Intimations of infinity: The mythopoeia (cultural meanings) of the Iqwaye counting and number systems. Oxford, UK: Berg Publishers.
Muke, C. (2000). Ethnomathematics: Mid-Wahgi counting practices in Papua New Guinea (Unpublished MEd thesis). University of Waikato, Waikato, New Zealand.
O’Connell, J., & Allen, J. (2004). Dating the colonization of Sahul (Pleistocene Australia-New Guinea): A review of recent research. Journal of Archaeological Science, 31(6), 835–853. doi: 10.1016/j.jas.2003.11.005.
Owens, K. (2001). The work of Glendon Lean on the counting systems of Papua New Guinea and Oceania. Mathematics Education Research Journal, 13(1), 47–71.
Owens, K. (2010, July). Changing our view on space: Place mathematics as a human endeavour. Paper presented at the annual conference of the Mathematics Education Research Group of Australasia, Perth.
Owens, K. (2014). The impact of a teacher education culture-based project on identity as a mathematics learner. Asia-Pacific Journal of Teacher Education, 42(2), 186–207. doi:10.1080/1359866X.2014.892568.
Owens, K. (2015). Visuospatial reasoning: An ecocultural perspective for space, geometry and measurement education. New York, NY: Springer.
Owens, K., & Kaleva, W. (2008). Indigenous Papua New Guinea knowledges related to volume and mass. Paper presented at the International Congress on Mathematics Education ICME 11, Discussion Group 11 on The Role of Ethnomathematics in Mathematics Education, Monterray, Mexico. http://dg.icme11.org/document/get/311
Paraide, P. (2010). Integrating Indigenous and Western mathematical knowledge in PNG early schooling (PhD thesis). Deakin University, Geelong, Victoria, Australia.
Pawley, A. (1981). Melanesian diversity and Polynesian homogeneity: A unified explanation for language. In K. Hollyman & A. Pawley (Eds.), Studies in Pacific languages and cultures in honour of Bruce Biggs (pp. 269–309). Auckland, NZ: Linguistic Society of New Zealand.
Pawley, A., & Ross, M. (2006). The prehistory of Oceanic languages: Current view. In P. Bellwood, J. Fox, & D. Tyron (Eds.), The Austronesians: Historic and cultural perspectives. Canberra, Australia: Pacific Linguistics, Australian National University.
Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499–503.
Pickles, A. (2013). The pattern changes changes: Gambling value in highland Papua New Guinea. PhD thesis, University of St Andrews, UK. Retrieved from https://research-repository.st-andrews.ac.uk/bitstream/10023/3389/6/AnthonyPicklesPhDThesis.pdf
Rosa, M., & Orey, D. (2012). Ethnomodeling: A pedagogical action for uncovering ethnomathematical practices. International Congress on Mathematics Education. Retrieved from http://www.icme12.org/upload/UpFile2/TSG/1799.pdf
Ross, M. (1988). Proto Oceanic and the Austronesian languages of western Melanesia. Canberra, Australia: Pacific Linguistics, C-98.
Ross, M. (1989). Early Oceanic linguistic prehistory. A reassessment. Journal of Pacific History, 24(2), 135–149.
Salzmann, Z. (1950). A method for analyzing numerical systems. Word, 6, 78–83.
Saxe, G. (1979). A comparative analysis of the acquisition of numeration: Studies from Papua New Guinea. The Quarterly Newsletter of the Laboratory for Comparative Human Cognition, 1(3), 37–43.
Saxe, G. (1981a). Body parts as numerals: A developmental analysis of numeration among the Oksapmin in Papua New Guinea. Child Development, 52, 306–316.
Saxe, G. (1981b) Numerical reasoning. Oksapmin: Development and change. Educational Research Unit Occasional Paper 7. Port Moresby, PNG: University of Papua New Guinea.
Saxe, G. (1981c). When fourth can precede second: A developmental analysis of an indigenous numeration system among Ponam Islanders in Papua New Guinea. Journal of Cross-Cultural Psychology, 12(1), 37–50.
Saxe, G. (1982). Developing forms of arithmetical thought among the Oksapmin of Papua New Guinea. Developmental Psychology, 18(4), 583–594.
Saxe, G. (1985). The effects of schooling on arithmetical understandings: Studies with Oksapmin children in Papua New Guinea. Journal of Educational Psychology, 77(5), 503–513.
Saxe, G. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale, NJ: L. Erlbaum Associates.
Saxe, G. (2012). Cultural development of mathematical ideas: Papua New Guinea studies. New York, NY: Cambridge University Press.
Saxe, G., & Esmonde, I. (2005). Studying cognition in flux: A historical treatment of fu in the shifting structure of Oksapmin mathematics. Mind, Culture, and Activity, 12(3), 171–225.
Seidenberg, A. (1960). The diffusion of counting practices. University of California Publications in Mathematics, 3, 215–300.
Sheppard, P., Walter, R., & Roga, K. (2010). Friends, relatives and enemies: The archaeology and history of interaction among Austronesian and non-Austronesian speakers in the western Solomons. In J. Bowden, N. Himmelmann, & K. Ross (Eds.), A journey through Austronesian and Papuan linguistic and cultural space: Papers in honour of Andrew Pawley (Vol. 615, pp. 95–112). Canberra, Australia: Pacific Linguistics, ANU.
SIL. (nd). Ethnologue: Languages of the world. Retrieved from http://www.ethnologue.com/
Smith, G. (1978). Counting and classification on Kiwai Island. Papua New Guinea Journal of Education, Special Edition the Indigenous Mathematics Project, 14, 53–68.
Smith, G. (1981). Traditional mathematics in Morobe (Working Paper no. 21). Lae, PNG: Papua New Guinea University of Technology.
Smith, G. (1984). Morobe counting systems: An investigation into the numerals of the Morobe Province, Papua New Guinea (MPhil). Papua New Guinea University of Technology, Lae, PNG.
Spriggs, M. (1984). The Lapita cultural complex. Journal of Pacific History, 19(3–4), 202–223.
Spriggs, M. (2006). The Lapita culture and Austronesian prehistory in Oceania. In P. Bellwood, J. Fox, & D. Tyron (Eds.), The Austronesians: The historical and comparative perspectives (pp. 119–142). Canberra, Australia: Australian National University.
Spriggs, M. (2010). “I was so much older then, I’m younger than that now”: Why the dates keep changing for the spread of Austronesian languages. In J. Bowden, N. Himmelmann, & K. Ross (Eds.), A journey through Austronesian and Papuan linguistic and cultural space: Papers in honour of Andrew Pawley (Vol. 615, pp. 113–140). Canberra, Australia: Pacific Linguistics, Australian National University.
Spriggs, M. (2011). Archaeology and the Austronesian expansion: Where are we now? Antiquity, 85(328), 510–528.
Struik, D. (1987). A concise history of mathematics. New York, NY: Dover Publications.
Tryon, D. (1982). Austronesian languages. In R. May & H. Nelson (Eds.), Melanesia: Beyond diversity (pp. 241–248). Canberra, Australia: Research School of Pacific Studies, Australian National University.
Tryon, D. (1984). The peopling of the Pacific: A linguistic appraisal. Journal of Pacific History, 19(3–4), 147–159.
Tryon, D. (2006). Proto-Austronesian and the major subgroups of Austronesian. In P. Bellwood, J. Fox, & D. Tryon (Eds.), The Austronesians: Historical and comparative perspectives (pp. 19–42). Canberra, Australia: ANU Press.
Tryon, D., & Hackman, B. (1983). Solomon Islands languages: An internal classification. Canberra, Australia: Pacific Linguistics, C-72.
Van der Waerden, B., & Flegg, G. (1975a). Counting 1: Primitive and more developed counting systems. Milton Keynes, UK: Open University.
Van der Waerden, B., & Flegg, G. (1975b). Counting 2: Decimal counting words, tallies and knots. Milton Keynes, UK: Open University.
Voorhoeve, C. (1987). Worming one’s way through New Guinea: The chase of the peripatetic pronouns. A world of language: Papers presented to Professor S.A. Wurm on his 65th birthday (C-100) (pp. 709–727). Canberra, Australia: Pacific Linguistics.
Wassmann, J. (1997). Finding the right path. The route knowledge of the Yupno of Papua New Guinea. In G. Senft (Ed.), Referring to space: Studies in Austronesian and Papuan languages. Oxford, UK: Oxford University Press.
Wassmann, J., & Dasen, P. (1994). Yupno number system and counting. Journal of Cross-Cultural Psychology, 25, 78–94.
White, J., O’Connell, J., & Koettig, M. (1982). A prehistory of Australia, New Guinea and Sahul. Sydney, Australia: Academic Press.
Wurm, S. (1982a). Papuan languages. In R. May & H. Nelson (Eds.), Melanesia: Beyond diversity (pp. 225–240). Canberra, Australia: Research School of Pacific Studies, Australian National University.
Wurm, S. (1982b). Papuan languages of Oceania. Tübingen, Germany: Gunter Narr Verlag.
Wurm, S., & Hattori, S. (Eds.). (1981). Language atlas of the Pacific area. Part 1: New Guinea area, Oceania, Australia. Canberra, Australia: Australian Academy of the Humanities.
Wurm, S., Laycock, D., Voorhoeve, C., & Dutton, T. (1975). Papuan linguistic prehistory, and past language migrations in the New Guinea area. In S. A. Wurm (Ed.), New Guinea area languages and language study, Vol. 1: Papuan languages and the New Guinea linguistic scene (Pacific Linguistics, C-38, pp. 935–960). Canberra, Australia: Australian National University.
Zaslavsky, C. (1973). Africa counts: Number and pattern in African culture. Boston, MA: Prindle, Weber & Schmidt.
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Owens, K., Lean, G. (2018). An Overview of the Studies, Papua New Guinea, Oceania, Languages and Migrations. In: History of Number. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-45483-2_1
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