• Kay OwensEmail author


School mathematics tends to have developed from the major cultures of Asia, the Mediterranean and Europe. However, indigenous cultures in particular may have distinctly different systematic ways of referring to space and thinking mathematically about spatial activity. Their approaches are based on the close link between the environment and cultural activity. The affinity to place strengthens the efficient, abstract, mathematical system behind the reference and its connection to the real world of place and a holistic worldview. This paper sets out to present an overview of various approaches to aspects of space and geometry by drawing on linguistic and cultural literature, my collaborative research in Papua New Guinea, and from personal communications with indigenous colleagues in Australia and elsewhere. This diversity provides a challenge by which teachers can deconstruct their thinking about mathematics and subsequently to review the content of teaching and to be more responsive to the diversity of cultural backgrounds of students. To assist with recognising ecocultural mathematics on space and geometry, 4 principles are established and discussed on language structures, reference lines and points, measures of space and worldviews and interpretations of space as place.


ecocultural pedagogy ethnomathematics geometry mathematics education Papua New Guinea place-based education visuospatial reasoning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akerblom, K. (1968). Astronomy and navigation in Polynesia and Micronesia. Stockholm: Ethnogratiska Museet.Google Scholar
  2. Apple, M. (2004). Ideology and curriculum (3rd ed.). New York: Routledge Falmer.Google Scholar
  3. Atweh, B., Barton, A. C. & Borba, M. (Eds.). (2007). Internationalisation and globalisation in mathematics and science education. Dordrecht, the Netherlands: Springer.Google Scholar
  4. Barton, B. (2004). Mathematical discourses in different languages. In B. Clarke, D. Clarke, G. Emanuelsson, B. Johansson, D. Lambdin, F. Lester, A. Wallby & K. Wallby (Eds.), International perspective on learning and teaching mathematics (pp. 365–378). Gothenburg, Sweden: Göteborg University National Center for Mathematics Education.Google Scholar
  5. Barwell, R., Barton, B. & Setati, M. (2007). Multilingual issues in mathematics education: Introduction. Educational Studies in Mathematics, 64(2), 113–119.CrossRefGoogle Scholar
  6. Bishop, A. (1983). Space and geometry. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 176–204). New York: Academic Press.Google Scholar
  7. Bishop, A. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht, the Netherlands: Kluwer.CrossRefGoogle Scholar
  8. Bryan, E. H. (1938). Marshall Islands stick chart. Paradise of the Pacific, 50(7), 12–13.Google Scholar
  9. Bullivant, B. M. (1981). Race, ethnicity and curriculum. Melbourne, Australia: Macmillan.Google Scholar
  10. Cameron, J. (2003). Educating for place responsiveness: An Australian perspective on ethical practice. Ethics, Place and Environment, 6, 99–115.CrossRefGoogle Scholar
  11. Capell, A. (1969). A survey of New Guinea languages. Sydney, Australia: Sydney University Press.Google Scholar
  12. Clarkson, P. (1992). Language and mathematics: A comparison of bilingual and monolingual students of mathematics. Educational Studies in Mathematics, 23, 417–429.CrossRefGoogle Scholar
  13. Clements, K. (2008). Spatial abilities, mathematics, culture and the Papua New Guinea experience. In P. Clarkson & N. Presmeg (Eds.), Critical issues in mathematics education: Major contributions of Alan Bishop (pp. 97–106). Berlin, Germany: Springer.Google Scholar
  14. Codrington, R. H. (1885). The Melanesian languages. Oxford, UK: Clarendon Press.Google Scholar
  15. Davenport, W. H. (1960). Marshall Island navigational charts. Imago Mundi, 15, 19–26.Google Scholar
  16. Davis, W. (Writer). (2009). The Wayfinders - Why ancient wisdom matters in the modern world, Lecture 1, Season of the Brown Hyena, 2009 Massey Lectures. Toronto, Canada: The House of Anansi Press.Google Scholar
  17. Dehaene, S., Izard, V., Pica, P. & Spelke, E. (2006). Core knowledge of geometry in an Amazonian indigene group. Science, 311, 381–384.CrossRefGoogle Scholar
  18. Gammage, B. (1998). The sky travellers: Journeys in New Guinea 1938–1939. Melbourne: Miegunyah Press, Melbourne University Press.Google Scholar
  19. Furuto, L., & Furuto, D. (2010). Bridging policy and practice though ethnomathematcs voyaging in the Pacific. Paper presented at the Fourth International Conference on Ethnomathematics ICEm4, Towson University.Google Scholar
  20. Glen Lean Ethnomathematics Centre University of Goroka (last updated 2008), from
  21. González, N., Moll, L. & Amanti, C. (Eds.). (2005). Funds of knowledge: Theorizing practice in households, communities, and classrooms. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  22. Grant, S., & Rudder, J. (Eds.). (2010). A new Wiradjuri dictionary. Wagga Wagga, New South Wales, Australia: Restoration House.Google Scholar
  23. Gruenewald, D. (2008). The best of both worlds: A critical pedagogy of place. Environmental Education Research, 14(3), 308–324.Google Scholar
  24. Harris, P. (1989). Mathematics in a cultural context: Aboriginal perspectives on space, time and money. Geelong, Victoria, Australia: Deakin University Press.Google Scholar
  25. Hutchins, E. (1995). Cognition in the wild. Cambridge, MA: Massachusetts Institute of Technology.Google Scholar
  26. Jannok Nutti, Y. (2008). Sámi education in mathematics—a school development action research project. Journal of Australian Indigenous Issues, 12, 177–185.Google Scholar
  27. Johnston, E. (nd). Aboriginal art—Australian Aboriginal art, from
  28. Jones, J. (1974). Quantitative concepts, vernaculars, and education in Papua New Guinea. Education Research Unit Report 12, University of Papua New Guinea.Google Scholar
  29. Joseph, G. (2000). The crest of the peacock: The non-European roots of mathematics. Princeton, NJ: Princeton University Press.Google Scholar
  30. Lakoff, G. (1987). Women, fire, and dangerous things: What categories reveal about the mind. Chicago: University of Chicago Press.CrossRefGoogle Scholar
  31. Lean, G. (1992). Counting systems of Papua New Guinea and Oceania. Unpublished Ph.D. thesis, University of Technology, Lae, Papua New Guinea. Retrieved from
  32. Lean, G. & Clements, M. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267–299.CrossRefGoogle Scholar
  33. Lipka, J., & Adams, B. (2004). Culturally based math education as a way to improve Alaska native students’ math performance. Working Paper 20. Appalachian Collaborative Center for Learning (ED484849).Google Scholar
  34. Lewis, D. (1973). We, the Navigators. Honolulu: University Press of Hawaii.Google Scholar
  35. Margetts, A. (2004). Spatial deictics in Saliba. In G. Senft (Ed.), Deixis and demonstratives in Oceanic languages (Vol. 562, pp. 37–58). Canberra, Australia: Pacific Linguistics.Google Scholar
  36. Matang, R. (2003). The cultural context of mathematics learning and thinking in Papua New Guinea. In A. C. Maha & T. A. Flaherty (Eds.), Education for 21st century in Papua New Guinea and the South Pacific (pp. 161–168). Goroka, Papua New Guinea: University of Goroka.Google Scholar
  37. May, J. & Loeweke, E. (1981). Fasu namo me: Fasu lexicon and grammar. Ukurumpa, Papua New Guinea: SIL.Google Scholar
  38. Meaney, T., Trinick, T. & Fairhall, U. (2012). Collaborating to meet language challenges in Indigenous mathematics classrooms. Dordrecht, the Netherlands: Springer.CrossRefGoogle Scholar
  39. Mosel, U. (2004). Demonstratives in Samoan. In G. Senft (Ed.), Deixis and demonstratives in Oceanic languages (Vol. 562, pp. 141–174). Canberra, Australia: Pacific Linguistics.Google Scholar
  40. National Research Council Committee on Geography (2006). Learning to think spatially: GIS as a support system in the K–12 curriculum. Washington, DC: National Academies Press.Google Scholar
  41. Ness, D. & Farenga, S. (2007). Knowledge under construction: The importance of play in developing children’s spatial and geometric thinking. Lanham, MD: Rowan & Littlefield.Google Scholar
  42. Owens, C. (1980). Analysis of some chemistry curricula in Papua New Guinea. Master of Science, University of East Anglia, Norwich, UK.Google Scholar
  43. Owens, K. (1993). Spatial thinking processes employed by primary school students engaged in mathematical problem solving. Ph.D., Deakin University, Geelong, Victoria, Australia informit database.Google Scholar
  44. Owens, K. (2012a). Identity and ethnomathematics projects in Papua New Guinea. In D. Jaguthsing, L. P. Cheng & S. F. Ng (Eds.), Mathematics education: Expanding horizons. Proceedings of 35th annual conference of Mathematics Education Research Group of Australasia. Singapore, Singapore: MERGA.Google Scholar
  45. Owens, K. (2012b). Papua New Guinea indigenous knowledges about mathematical concepts. Journal of Mathematics and Culture (on-line), 6(1), 15–50.Google Scholar
  46. Owens, K. & Kaleva, W. (2008a). Case studies of mathematical thinking about area in Papua New Guinea. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano & A. Sepúlveda (Eds.), Annual conference of the International Group for the Psychology of Mathematics Education (PME) and North America chapter of PME, PME32—PMENAXXX, Vol. 4 (pp. 73–80). Morelia, Mexico: Organising Committee of PME32-PMENAXX.Google Scholar
  47. Owens, K., & Kaleva, W. (2008b). Indigenous Papua New Guinea knowledges related to volume and mass. Paper presented at the International Congress on Mathematics Education, Discussion Group 11 on The Role of Ethnomathematics in Mathematics Education, Monterrey, Mexico.Google Scholar
  48. Ozanne-Rivierre, F. (2004). Spatial deixis in Iaai. In G. Senft (Ed.), Deixis and demonstratives in Oceanic languages (Vol. 562, pp. 129–140). Canberra, Australia: Pacific Linguistics.Google Scholar
  49. Panoff, M. (1969). The notion of time among the Maenge people of New Britain. Ethnology, 8, 153–166.CrossRefGoogle Scholar
  50. Paredes-Canilao, N. (2006). Decolonising subjects from the discourse of difference. Journal of Multicultural Discourses, 1(1), 6–26.CrossRefGoogle Scholar
  51. Penn Museum (1997). Traditional navigation in the Western Pacific: A search for pattern. Retrieved 2006 from
  52. Pinxten, R., van Dooren, I. & Harvey, F. (1983). The anthropology of space: Explorations into the natural philosophy and semantics of the Navajo. Philadelphia, PA: University of Pennsylvania Press.Google Scholar
  53. Polynesian Voyaging Society (2003). Accessed 20 Oct 2009.
  54. Pumaye, H. (1978). The Kewa calendar. Papua New Guinea Journal of Education, Special Edition The Indigenous Mathematics Project, 14, 47–55.Google Scholar
  55. Salzmann, Z. (2006). Language, culture, and society: An introduction to linguistic anthropology (4th ed.). Boulder, CO: Westview Press.Google Scholar
  56. Senft, G. (Ed.). (1997). Referring to space: Studies in Austronesian and Papuan languages. Oxford, UK: Oxford University Press.Google Scholar
  57. Senft, G. (2004). Aspects of spatial deixis in Kilivila. In G. Senft (Ed.), Deixis and demonstratives in Oceanic languages (Vol. 562, pp. 59–80). Canberra, Australia: Pacific Linguists.Google Scholar
  58. 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, Papua New Guinea.Google Scholar
  59. Somerville, M. (2010). A place pedagogy for ‘global contemporaneity’. Educational Philosophy and Theory, 42(3). doi: 10.1111/j.1469-5812.2008.00423.x
  60. Spennemann, D. (1998). Essays on the Marshallese Past: Traditional Marshallese stickchart navigation. Accessed 2010.
  61. Tami, P. (2007). Linguistic structure of Alekano. Paper presented at the Papuan Linguists Conference, Madang, PNG.Google Scholar
  62. Thornton, M. B. & Watson-Verran, H. (1996). Living maths. Abbotsford, Victoria, Australia: Yirrkala Community School and Boulder Valley Films.Google Scholar
  63. Trninic, D., & Kim, H.-J. (2012). Abstract, concrete, and embodied: An embodied cognition perspective of mathematics education. Paper presented at the International Congress on Mathematics Education, Seoul, Korea.Google Scholar
  64. Tuan, Y.-F. (1977). Space and place: The perspective of experience. London: Edward Arnold.Google Scholar
  65. Tupper, I. (2007). Emphatic pronouns in Namia. Paper presented at the Papuan Linguists Association Conference, Madang, PNG.Google Scholar
  66. 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.Google Scholar
  67. Watson-Verran, H. & Turnbull, D. (1995). Science and other indigenous knowledge systems. In S. Jasanoff, G. Markle, J. C. Perersen & T. Pinch (Eds.), Handbook of science and technology studies (pp. 115–139). London: Sage.CrossRefGoogle Scholar
  68. Winduo, S. E. (2007). Decolonising the mind: The impact of the university on culture and identity in Papua New Guinea, 1971–1974. Contemporary Pacific, 19(1), 330–332.CrossRefGoogle Scholar
  69. Worsley, P. (1997). Knowledges: Culture, counterculture, subculture. New York: The New Press.Google Scholar
  70. Yunkaporta, T. & McGinty, S. (2009). Reclaiming Aboriginal knowledge at the cultural interface. The Australian Educational Researcher, 36(2), 55–72.CrossRefGoogle Scholar

Copyright information

© National Science Council, Taiwan 2013

Authors and Affiliations

  1. 1.Charles Sturt UniversityDubboAustralia

Personalised recommendations