Aboriginal Australian Mathematics: Disparate Mathematics of Land Ownership

A Peircean typology of cultural prime symbols: Culture as category

“…That the universe should be conceptualized as inchoate and dreamlike gives semiotic unity to a culture so often viewed by Westerners as both primitive and irrational. For example, the Aborigines never developed mathematics or even the numerals at all, to the consternation of anthropologists and linguists, who sometimes try to claim that the development of numbers and at least rudimentary mathematics is a cognitive universal; the nearest thing in Aboriginal culture to mathematics-like reckoning is their complex system of kinship (Verran 2000). Counting, after all, involves a very robust and deliberate deixis (Secondness), which would seem to be precluded by a worldview approaching unalloyed Firstness.…”

Morrku Mangawu—Knowledge on the Land: Mobilising Yolŋu Mathematics from Bawaka, North East Arnhem Land, to Reveal the Situatedness of All Knowledges

“…Indeed, Helen Verran, a key contributor to the emergence of the YolNu mathematics curriculum at Yirrkala, makes a case that mathematics and land ownership are intimately related. Verran argues that mathematics of Aboriginal land ownership has historically been ignored, marginalised and denigrated in Australian (and international) politics, law, academia and practice [22]. She goes on to reveal YolNu mathematics as both analogous to western mathematics, yet significantly different, and she re-imagines the implications of this for the politics, negotiation and co-existence of land ownership/s in Australia.…”

“…Not only have legal and political systems been unable to grapple with the challenge of YolNu mathematics but mainstream education systems have also been unable to recognise alternative mathematics and their importance for Indigenous rights and education [22]. YolNu mathematics thus presents a challenge, and critiques the development and pedagogical domination of Western mathematical traditions [23].…”

“…The development of the Gänma mathematics programme is epistemologically dependent upon a number of YolNu metaphors, in particular gänma, that highlight the potential for a two-way system of equal knowledge exchange. As explained above, this exchange is not limited to educational reform but is also implicit in land-rights [22] and is embedded in the wider socio-political desire for autonomy [16]. We explore YolNu mathematics in the school context later in the paper.…”

“…Echoing Verran's work analysing pre-native title attitudes towards Indigenous mathematics in Australia [22], continuing debates in Australia reinforce the ontological arrogance of thinking there is only one form of mathematics-either through the dismissal of Indigenous knowledges or expressions of surprise as other knowledges are "suddenly dis-covered": I don't understand why we are including these [Indigenous] perspectives in these subjects. Science and maths are universal.…”