Rewriting the History of Number from Papua New Guinea and Oceania Evidence

Owens, Kay; Lean, Glen

doi:10.1007/978-3-319-45483-2_13

Cited by 12 publications

(16 citation statements)

References 24 publications

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“…We can find literally hundreds of different counting systems, using different symbols or no symbols, objects and materials varying with the cycles, or bases, used to deal with large numbers. Even in single countries like Papua New Guinea, a land of four million people but 800+ languages, there is a myriad of counting systems (Owens et al 2018). The symbolic and religious properties of geometric figures are of more interest in some societies than others, as are the predictive powers of certain numerological practices, myths and ideologies around their symbolic importance.…”

Section: Introductionmentioning

confidence: 99%

The Role of Value Alignment in Levels of Engagement of Mathematics Learning

Kalogeropoulos

Clarkson

2019

ICME-13 Monographs

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Low levels of student engagement in mathematics education has been a growing concern in the Australian context and internationally. In this chapter, we will explore how value alignment strategies (Scaffolding, Balancing, Intervention and Refuge) could be used to rework conflict, resentment and disengagement of students in the mathematics classroom. When students are encouraged to discuss their individual thoughts and opinions, ideas and approaches, students' values and identities become more apparent. We also begin to explore the notion of identity as an extension to the completed work on value alignment strategies. We propose a possibility that value alignment strategies could be the catalyst in many more students proclaiming that 'mathematics is my most valuable subject!' Keywords Values • Value alignment strategies • Student engagement • Student disengagement • Mathematical identity

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Section: Introductionmentioning

confidence: 99%

The Role of Value Alignment in Levels of Engagement of Mathematics Learning

Kalogeropoulos

Clarkson

2019

ICME-13 Monographs

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“…The attention to differences in whole number approaches is increasing. It is worthwhile to mention at least the book by Owens (2015), with a chapter on visuospatial reasoning with numbers, and the book by Owens et al (2017) on the history of number in Papua New Guinea and Oceania that details number systems other than base 10 systems.…”

Section: Discussionmentioning

confidence: 99%

Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic

Bartolini

Sun

2018

New ICMI Study Series

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Il ne s'agit pas là de philosophie comparée, par mise en parallèle des conceptions; mais d'un dialogue philosophique, où chaque pensée, à la rencontre de l'autre, s'interroge sur son impensé ('This is not about comparative philosophy, about paralleling different conceptions, but about a philosophical dialogue in which every thought, when coming towards the other, questions itself about its own unthought' (Jullien 2006, p. vi)) 他山之石,可以攻玉 (tā shān zhī shí, kěyǐ gōng yù) ('The stone from another mountain can be used to polish one's own jade' (Xiao Ya, Shijing: He Ming, 1000 A. C.)

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“…Verbally these systems can be compared with modulus systems, although they may function like base counting systems when totals are able to be carried, either mentally or with additional bodies (Wolfers, 1971). An abundance of multibase systems have also been studied in Papua New Guinea and Oceania (Owens, 2001;Owens & Lean, 2018), for instance the common 2-5-20 cycle, where counting proceeds: 1, 2, 2 + 1, 2 + 2, 5 (often one "hand"), 5 + 1, 5 + 2, 5 + 2 + 1, 5 + 2 + 2, 5 + 5, and so on, up to a new base of 20 (often one "man"). Even systems of finger counting show a great deal of diversity (Bender & Beller, 2012), as do numerical notation systems (Chrisomalis, 2009b).…”

Section: Forms Of Number Representation Are Diverse Across Culturesmentioning

confidence: 99%

“…The cultural history of mathematics shows that, large, exact, symbolic number is cognitively difficult for humans to create, the product of a long cross-cultural history (Chrisomalis, 2009b;Damerow, 2015;Ifrah, 2000;Joseph, 1987) and that modern conceptions of number are far from universal across human groups. The picture that emerges instead from the ethnographic literature reveals a diversity of culturally contingent approaches to problems of quantity, which are constructed according to local needs, perceptions, practices, and history (Beller et al, 2018;Crossley, 2007;Dixon & Kroeber, 1907;Hymes, 1955;Owens & Lean, 2018;Robson, 2008;Wolfers, 1971). We consider each of (i)-(vi) in turn.…”

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confidence: 99%

The cultural origins of symbolic number.

O’Shaughnessy¹,

Gibson²,

Piantadosi³

2022

Psychological Review

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In order to explain the unacceptability of certain long-distance dependencies --termed syntactic islands by Ross (1967) --syntacticians proposed constraints on long-distance dependencies which are universal and purely syntactic and thus not dependent on the meaning of the construction (Chomsky 1977(Chomsky , 2006. This predicts that these constraints should hold across constructions and languages. In this paper, we investigate the "subject island" constraint across constructions in English and French, a constraint that blocks extraction out of subjects. In particular, we compare extraction out of nominal subjects with extraction out of nominal objects, in relative clauses and wh-questions, using similar materials across constructions and languages. Contrary to the syntactic accounts, we find that unacceptable extractions from subjects involve (a) extraction in wh-questions (in both languages); or (b) preposition stranding (in English). But the extraction of a whole prepositional phrase from subjects in a relative clause, in both languages, is as good or better than a similar extraction from objects. Following Erteschik-Shir (1973) and Kuno (1987) among others, we propose a theory that takes into account the discourse status of the extracted element in the construction at hand: the extracted element is a focus (corresponding to new information) in wh-questions, but not in relative clauses. The focus status conflicts with the non-focal status of a subject (usually given or discourse-old). These results suggest that most previous discussions of islands may rely on the wrong premise that all extraction types behave alike. Once different extraction types are recognized as different constructions (

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Rewriting the History of Number from Papua New Guinea and Oceania Evidence

Cited by 12 publications

References 24 publications

The Role of Value Alignment in Levels of Engagement of Mathematics Learning

The Role of Value Alignment in Levels of Engagement of Mathematics Learning

Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic

The cultural origins of symbolic number.

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