Counting by “elevens” and why nine and two make twenty: The material roots of Polynesian numbers (original) (raw)
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Analytical data for EU project 785793
The bibliography lists the resources used to characterize counting practices in Polynesia and map their geographic distribution. The data were analyzed in: Overmann, Karenleigh A. (2020). The curious idea that Māori once counted by elevens, and the insights it still holds for cross-cultural numerical research, Journal of the Polynesian Society. Overmann, Karenleigh A. (2020). Counting by “elevens” and why nine and two make twenty: The material roots of Polynesian numbers. Journal of Mathematics and Culture. Forthcoming. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793.
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This critical literature review explores the use of ethnomathematics and Indigenous languages in the teaching of mathematics in Polynesian language regions of the Cook Islands, French Polynesia, Hawai'i and Samoa. Across all regions, concerns have been raised, to various degrees, about the loss of language and culture. Although there have been some initiatives to maintain and revive Indigenous languages and ethnomathematical practices, none have been sustained in the long term and few have been thoroughly evaluated. Although many ethnomathematical practices have been documented, the complicated nature of changing educational policy restricts possibilities for using Indigenous culture and language as a basis for mathematics teaching in these regions.
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Number systems constitute one of the major domains in which language has been invoked as a source of variation in thought or cognition. The notion that the features of a language's numeral system index cognitive complexity in mathematics has been pervasive in anthropological linguistics, from nineteenth century unilinear evolutionists to contemporary neo-Whorfians. In particular, the extreme case of languages with small numerical vocabularies have attracted enormous scholarly interest, but other features for which representational effects on cognition are claimed include systemic irregularity and the presence of multiple parallel numeral systems (numeral classifiers and object-specific counting). Quite independently but relatedly, the comparison of graphic numerical notations has inferred cognitive advantages directly from notation, such as the idea that the Roman numerals limited Western mathematical progress. The question of cognitive effects of language is interwoven with issues of social complexity; in place of a pure relativistic language-thought relationship, the discussion has been, and continues to be framed through a triad of language structure-cognition-social structure. Recognizing the enormous cross-cultural variation in lexical numerals and numerical notations, how can we best evaluate the extent to which, and more importantly, the processes by which, they affect numerical cognition? An activity-based explanatory model in which materiality, discourse, and practice mutually engage to constitute knowledge systems allows us to move past the presumption that language structure has direct cognitive effects, without denying that there are linguistic patterns of real interest for future inquiry into numerical cognition.
Eastern Polynesian: The linguistic evidence revisited
Oceanic Linguistics, 2014
For the past fifty years, historical linguistics and archaeology have provided seemingly mutually corroboratory evidence for the settlement of east Polynesia. However, more recent findings in archaeology have shifted this relationship out of balance, calling previous conclusions into question. This paper first reviews the generally accepted archaeological and linguistic theories of east Polynesia's settlement, then describes the recent archaeological findings, highlighting the areas where the evidence from the two disciplines is now discordant. In sections four and five, I examine the linguistic data from Eastern Polynesian languages and propose a new, contact-based model for the region. The new linguistic model ultimately demonstrates that the settlement of east Polynesia and the development of the Eastern Polynesian languages occurred in one major period of dispersal with subsequent spheres of contact among central Polynesian communities, producing the pattern of cultural and linguistic traits we see today.
Advances In Polynesian Prehistory: A Review and Assessment of the Past Decade (19932004)
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The pace of archaeological research in Polynesia has intensified in recent years, resulting in more than 500 new literature citations over the past decade. Fieldwork has continued in such previously well-studied archipelagoes as Tonga and Samoa in Western Polynesia, and Hawai‘i and New Zealand in Eastern Polynesia, but has also expanded into previously neglected islands including Niue, the Equatorial Islands, the Austral Islands, and Mangareva. The emergence of Ancestral Polynesian Culture out of its Eastern Lapita predecessor is increasingly well understood, and the chronology of Polynesian dispersal and expansion into Eastern Polynesia has engaged several researchers. Aside from these fundamental issues of origins and chronology, major research themes over the past decade include: (1) defining the nature, extent, and timing of long distance interaction spheres, particularly in Eastern Polynesia; (2) the impacts of human colonization and settlement on island ecosystems; (3) variation in Polynesian economic systems and their transformations over time; and (4) sociopolitical change, especially as viewed through the lens of household or microscale archaeology. Also noteworthy is the rapidly evolving nature of interactions between archaeologists and Native communities, a critical aspect of archaeological practice in the region