Abstract
During the late 1990s, the Papua New Guinean Department of Education introduced a new elementary school mathematics curriculum that utilised the country’s rich and diverse cultural traditions. The resulting changes saw patterns, one of a family of practices related to the decorative arts, take on a prominent role as a tool for understanding number, space, time, measurement, all of which form the basis of mathematics. Drawing primarily on the author’s own anthropological fieldwork, this chapter examines the culture of pattern in community life in order to understand its selection as a cultural resource for mathematics learning. It will demonstrate that while pattern is not spoken about, people are nevertheless especially adept at engaging with it. Since Papua New Guinea is full of patterns, and pattern plays such a robust role in the mathematics curriculum, the chapter demonstrates how pattern can be understood as an expression of the mathematical mind at work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The Yupno cord, kirugu, could be compared to the Inca knotted cord, quipu, a focus of study in the field of ethnomathematics by Ascher and Ascher (1981) and Urton (2003). Both cord devices use mnemonic devices tied into the main thread to schematise and give order to cultural knowledge. They both play important roles in encoding and transmitting cultural memories.
- 2.
- 3.
One interesting exception—although not in the field of anthropology—is Schiralli’s work on the meaning of pattern (Schiralli 2007). Drawing on the work of anthropologist Bateson and art historian Gombrich, Schiralli argues that because of pattern’s ubiquity and its significance in various disciplines, it merits further attention within mathematics, one that returns to the roots of the subject. He does so by examining the relation between pattern and number in the school of Pythagoras.
- 4.
Goetzfridt (2008) has compiled a bibliography of Pacific ethnomathematics.
- 5.
A figure-ground relationship is a design where the figure defines the ground and the ground defines the figure; the two elements are inseparable. It forces the viewer to shift from one element to the other, but not both simultaneously. The face/vase illusion is an example of this.
- 6.
See Were (2003) for a more in-depth analysis of the relation between the various motifs.
- 7.
Affinal relations are based upon marriage e.g. son-in-law.
References
Ascher, M. (2002). Mathematics elsewhere: An exploration of ideas across cultures. Princeton: Princeton University Press.
Ascher, M. & Ascher, R. (1981). Code of the quipu: A study in media, mathematics, and culture. Ann Arbor: University of Michigan Press.
Barton, B., Fairhall, U., & Trinick, T. (1998). Tikanga reo tātai: Issues in the development of a Māori mathematics register. For the Learning of Mathematics, 18(1), 3–9.
Barton, B. (2008). The language of mathematics: Telling mathematical tales. New York: Springer.
Bell, F. L. S. (1935). Geometrical art. Man, 35, 16.
Borofsky, R. (1987). Making history: Pukapukan and anthropological constructions of knowledge. Cambridge: Cambridge University Press.
Crump, T. (1990). The anthropology of numbers. Cambridge: Cambridge University Press.
D’Ambrosio, U. (1989). On ethnomathematics. Philosophia Mathematica, 2–4(1), 3–14.
Deacon, A. & Wedgwood, C. (1934). Geometrical drawings from Malekula and other islands of the New Hebrides. Journal of the Royal Anthropological Institute of Great Britain and Ireland, 64, 129–175.
Department of Education (1998). Elementary scope and sequence. Waigani, Papua New Guinea: Department of Education.
Department of Education (2006). Good beginnings in mathematics with patterns: Elementary patterns resource book. Waigani, Papua New Guinea: Department of Education.
Eglash, R. (1999). African fractals: Modern computing and indigenous design. New Brunswick: Rutgers University Press.
Gardner, H. (1985). Frames of mind: The theory of multiple intelligences. New York: Basic Books.
Goetzfridt, N. (2008). Pacific ethnomathematics: A bibliographic study. Honolulu: University of Hawaii Press.
Kuechler, S. (1987). Malangan: Art and memory in a Melanesian society. Man, 22(2), 238–255.
Kuechler, S. (1999). Binding in the Pacific: Between loops and knots. Oceania, 69(3), 145–156.
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press.
Mimica, J. (1988). Intimations of infinity: The mythopoeia of the Iqwaye counting system and number. Oxford: Berg.
Rose, M. (2004). The mind at work: Valuing the intelligence of the American worker. New York: Viking.
Schiralli, M. (2007). The meaning of pattern. In N. Sinclair (Ed.), Mathematics and the aesthetic: New approaches to an ancient affinity (pp. 234–279). New York: Springer Books.
Stafford, B. (1999). Visual analogy: Consciousness as the art of connecting. Cambridge: The MIT Press.
Toren, C. (1990). Making sense of hierarchy: Cognition as social process in Fiji. LSE Monograph on Social Anthropology: Vol. 61. London and Atlantic Highlands: Athlone Press.
Urton, G. (2003). Signs of the Inka khipu: Binary coding in the Andean knotted-string records. Austin: University of Texas Press.
Vagi, O. & Green, R. (2004). The challenges in developing a mathematics curriculum for training elementary teachers in Papua New Guinea. Early Child Development and Care, 174(4), 313–319.
Washburn, D. & Crowe, D. (1988). Symmetries of culture: Theory and practice of plane pattern analysis. Seattle: University of Washington Press.
Wassmann, J. (1991). The song to the flying fox. Boroko, Papua New Guinea: National Research Institute.
Were, G. (2003). Objects of learning: An anthropological approach to mathematics learning. Journal of Material Culture, 8(1), 25–44.
Were, G. (2010) Lines that connect: Rethinking pattern and mind in the Pacific. Honolulu: University of Hawaii Press.
Zaslavsky, C. (1973). Africa counts: Number and pattern in African culture. Boston: Prindle, Weber & Schmidt.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Were, G. (2012). From the Known to the Unknown: Pattern, Mathematics and Learning in Papua New Guinea. In: Forgasz, H., Rivera, F. (eds) Towards Equity in Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27702-3_38
Download citation
DOI: https://doi.org/10.1007/978-3-642-27702-3_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27701-6
Online ISBN: 978-3-642-27702-3
eBook Packages: Humanities, Social Sciences and LawEducation (R0)