History of Number

Owens, Kay; Lean, Glen; Paraide, Patricia; Muke, Charly

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

Cited by 20 publications

(9 citation statements)

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“…Fingers, toes, and other body parts seem to have played a central role in the emergence of number words (Owens et al 2018). The origins of these systems can be seen as quite similar to the origins of tallying techniques based on pegs, sticks or notches, discussed in the previous section.…”

Section: Four and Beyond: Tallies With Body Partsmentioning

confidence: 70%

Enculturation and the historical origins of number words and concepts

Santos

2021

Synthese

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In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical.

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Section: Four and Beyond: Tallies With Body Partsmentioning

confidence: 70%

Enculturation and the historical origins of number words and concepts

Santos

2021

Synthese

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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%

“…However, some cultures have imposed constraints on the category of items that their number words can be applied to (Seidenberg, 1962), suggesting that the generalizability and abstraction that our culture finds in number—and encodes into features like an innate successor function—does not generalize well to other human groups. Such diversity is particularly evident in Papua New Guinea (Wolfers, 1971), where variations likely developed through a combination of innovation and diffusion, moderated by cultural constraints on necessity and interest in enumeration (Owens & Lean, 2018). For example, Ponam Islanders have an extensive decimal count system with terms upwards of 9,000, yet strikingly, not everything would be counted with this system.…”

Section: Forms Of Number Representation Are Diverse Across Culturesmentioning

confidence: 99%

“…Saxe (2014) has shown how the introduction of monetary exchange drives the creation of new forms of number representation and arithmetical abilities, but exchange itself does not necessarily imply number usage. For some groups the exact number of gifts given in a ceremonial exchange is important (e.g., the Ekagi or the Melpa; Owens & Lean, 2018, pp. 132–133), whereas for others, it is the visual quality of the presentation that takes precedence, with exact number playing little to no role (e.g., the Adzera, Dani, or Loboda; Owens & Lean, 2018, pp.…”

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%

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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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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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History of Number

Cited by 20 publications

References 0 publications

Enculturation and the historical origins of number words and concepts

Enculturation and the historical origins of number words and concepts

The cultural origins of symbolic number.

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

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