Body-Part Tally Systems

Owens, Kay; Lean, Glen

doi:10.1007/978-3-319-45483-2_4

Cited by 3 publications

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“…This is important because it suggests that humans could, in principle, represent and reason about exact equality without verbal labels. Given this, although counting provides an especially powerful tool for representing number, other, non-symbolic, procedures that draw on one-to-one correspondence might also be used to establish equality, including tallies (e.g., Owens & Lean, 2018), tit-for-tat procedures (Sheldon, 1999;Silk, 2003), or simply pairing off individuals from two sets until none remain. The existence of such practices raises the possibility that humans who do not have a symbolic system for expressing exact numbers might nevertheless recognize that number can be represented exactly.…”

Section: Introductionmentioning

confidence: 99%

Counting and the ontogenetic origins of exact equality

et al. 2022

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Section: Introductionmentioning

confidence: 99%

Counting and the ontogenetic origins of exact equality

et al. 2022

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Indigenous Mathematics: From Mainstream Misconceptions to Educational Enrichment

Xu,

Ball

2024

Can. J. Sci. Math. Techn. Educ.

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The old canard that Indigenous and First Nations peoples had, or have, only rudimentary mathematical skills has been curiously persistent, against widespread published evidence over the past century and a half. In Australia, attempts to include Indigenous mathematical knowledge in curriculums have encountered strong resistance. After more than 12 years of advocacy and development by expert Indigenous advisers, content elaborations on Indigenous mathematics were included in the 2022 release of the Australian school curriculum. This hard-won achievement is welcomed widely, but experience also tells us to expect some resistance from sectors of the education communities who maintain and gatekeep an exclusively British-European or Western provenance of mathematics. In this article, we employ an exemplary approach to counter such narratives by summarising and replying to five published critiques of Indigenous mathematics, which typify widely held and propagated misconceptions. We seek to forestall potential pushback constructively, and address concerns regarding the legitimacy and pedagogical value of Indigenous mathematics, by countering with evidence claims in these critiques that Australian First Nations peoples historically had no autonomously developed mathematical knowledge. In doing so, we seek to stimulate more diverse and inclusive discussions of the underlying questions of ‘What is mathematics?’ and ‘Who can do mathematics?’. Although our research originated in a particular national context, the foundational importance of mathematics within and between all societies entails a global response to address these and similar pervasive misconceptions.

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Exploring the Evolutionary Pathways from Number Sense to Numeracy

Frank

2021

Oxford Handbook of Human Symbolic Evolution

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In this chapter, four stages are proposed for the evolutionary development of number systems in humans with special emphasis being given to neurocognitive and linguistic aspects of the evolutionary process. The four stages are: 1) number sense—innate quantitative competence without counting and language; 2) transition to syntactic language and counting skills; 3) transition from finger-counting to numeracy; and 4) establishment of a complex numerical lexicon and its notational instantiation. Evidence drawn from the archaeological record as well as contemporary ethnographic research is used to investigate the symbolic reference gap that exists between the two biologically given systems which allow for quantification judgments and those systems that are truly numerical in nature and hence culturally instantiated. The possible key role played by finger-counting, specifically as a bridging mechanism, in this evolutionary process is also highlighted.

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Body-Part Tally Systems

Cited by 3 publications

References 7 publications

Counting and the ontogenetic origins of exact equality

Counting and the ontogenetic origins of exact equality

Indigenous Mathematics: From Mainstream Misconceptions to Educational Enrichment

Exploring the Evolutionary Pathways from Number Sense to Numeracy

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