Paper short abstract:

Ganma is an allegory 'gifted' by elders of two Yolngu clans to mathematics educators at Yirrkala in the 1980s. A diagram of two rivers which have actual existence meeting in a lagoon forming vortices as waters mix, the allegory piloted the episode of maths curriculum development that followed.

Paper long abstract:

The paper elaborates how a contemporary Indigenous Australian community went about negotiating a place for indigenous thought in their schools' mathematics curriculum. It shows how the Ganma allegory piloted collective moral judgement and governance in the episode.

Determined that the elements of Yolngu Aboriginal conceptual consciousness which lies at the core of their knowledge traditions, should find a place in the modern elementary school mathematics taught in the community school, they engaged in a form of conceptual negotiation with state curriculum officials. The outcome of the negotiations conducted over a period of eight years (1988-1996) was a radically alternative yet still official mathematics curriculum for a group of Yolngu Aboriginal schools in Australia's Northern Territory.

The curriculum, known in some places as "Living Maths," took as analogous two mathetic formalisms that at first glance seem incommensurable. A mathetic formalism is a prescribed base of disciplined of learning, and in modern life the exemplar is the enumerated entity; it performs a stabilising function in social, economic, and political arenas. The primary school curriculum inducts children into the practices by which enumerated entities as formalisms come to life and work. In Yolngu Aboriginal life the analogous mathetic formalism is a genealogical entity. Thinking through the Ganma allegory, a partial but strict analogy between the workings of the enumerated entities of modern life and the workings of the genealogical entities in Yolngu life was effected to become the conceptual core of the four strands of the Living Maths curriculum.