Monthly Archives: May 2015

Aboriginal Maths

Misconceptions about Aboriginal cultures and their access to an understanding – and use – of mathematical concepts have had a powerful and enduring impact on beliefs about their level of sophistication. One widely held belief is that Aboriginal cultures had very limited language references to numbers, being associated with a belief that ‘numbers’ are essential for measuring and assessing things (mathematics tasks) this combination has created a perception that these cultures are, therefore primitive and ignorant of facts known to ‘more sophisticated’ cultures.

Were this to be a fact rather than merely a belief, much that is known about the achievements of Aboriginal cultural principles and practices – in regard to living with, and managing, the diversity of environments across the Australian continent – could not have been possible.
In other words perceptions of the ways that Aboriginal cultures built shelters, harvested food stuffs and travelled extensively (to name a few achievements) are seriously hobbled by mistaken beliefs, cultural misperceptions and misunderstandings about what was being observed and recorded by early Europeans.
Two recent books on the history of the development of mathematical concepts provide good examples of how the issue of ‘Aboriginal maths’ is treated in general texts about the present understanding of mathematical knowledge. Both books focus almost entirely on the development of Western/European concepts, giving less attention to knowledge from other cultures and even less to the practical uses and applications of maths. While this is an entirely reasonable approach, given their stated intentions as authors. However each addresses, in quite different ways, the state of current awareness of maths in cultural and social contexts beyond those addressed in their books.

Flaws and Inaccuracies

In his book on ‘From O to Infinity in 26 Centuries – the extraordinary story of Maths‘, Chris Waring  (Michael O’Mara Books UK, 2012) displays a seriously flawed and limited understanding of the nature of Aboriginal occupation of this continent. He indicates no awareness of the complexity and diversity of cultures, differences among national identities as indicated by (for example) language differences, and dismisses their practical capabilities as evidenced a toss the landscape, when he writes that
Australian Aboriginal tribes were living in a hunter-gatherer society when they were first encountered during the eighteenth century. The tribes that possessed a concept of numbers generally had words for one, two and sometimes three. Any numbers larger than three they made by adding together a combination of the first three numbers. So a tribe with the numbers one, two, three would have been able to count to nine by saying one, two, three, three-one, three-two, three-three. The fact that these people had no word for numbers larger that three suggests that they very rarely, if ever, needed to use them.

So much is open to challenge in this bald assertion (no referencing is supplied) that two items will suffice to demonstrate its errors, and illustrate the damage to perceptions about Aboriginal culture, made by such an ill chosen set of words. First, there is no suggestion that the ‘tribes’ might differ greatly across the continent, implying that ‘these people’ were therefore all so similar that a single assertion about a ‘lack of need for numbers’ applied to all without differentiation. If this perspective were to be applied in reverse we can imagine that Dutch, Portuguese and English visitors to ‘Terra Australis’ from the 1600’s onwards were all regarded as members of ‘one tribe’ and whatever characteristics were ascribed to one set of visitors could accurately be ascribed to them all.  We can readily see what a nonsense statement this is.  Yet this is what Waring implies in his dismissive clumping of all ‘these people’ as members of a single undifferentiated entity.
The second challenge raises issues of even more concern. If, as Waring suggests, Aboriginal cultures ‘very rarely, if ever, needed to use’ numbers it indicates his ignorant acceptance of misleading information about those cultures and their achievements. For example an understanding of water flow, fish spawning cycles, weather patterns and food supply and distribution are all explicitly illustrated in the extensive fish trap arrays at Brewarrina, NSW. Similarly, knowledge about load-bearing limits of building materials, tensile strengths of materials and market locations and demands are on display at the Wilgie Mai ochre mine in Western Australia, where it is estimated around 40,000 tons of ochre were produced during approximately 8.000 years of mining. Finally (for now) an in-depth knowledge of numbers is displayed at the astrological site of Wurdi Youang in Victoria, where astrophysicists have demonstrated that the only viable explanation for a highly ordered patterning of stones demonstrates understanding  of the concept of the seasons as marked by the arrival of the solstice –

Waring’s  dismissal of Aboriginal maths exemplifies a ‘Western/Eurocentric’ perspective that seems  unable to see things that do not fit within its view of ‘how things are’, and, moreover, writes as though things could not any other way. We can only wonder how Waring imagined that Aboriginal people lived and thrived for all that time without numbers. Or whether such a thought occurred to him at all.

Appreciating the unknowns

On the other hand Ian Stewart in his book ‘Taming the Infinite – the story of mathematics from the first numbers to chaos theory‘ (Quercus, UK 2008) has a more speculative view on the relationships between culture and maths. While his work focuses on only the last four Millenia and is confined to the northern hemisphere, he does suggest that there is room to explore those relationships and that, perhaps, this need not be done through either a Western worldview or a conventional Mathematical one, when we writes that –
Whether you like maths or not, it is hard to deny the profound effects that numbers have had on the development of human civilisation. The evolution of culture, and that of mathematics , has gone hand in hand for the last four Millenia. It would be difficult to disentangle cause and effect – I would hesitate to argue that mathematical innovation drives cultural change, or that cultural needs determine the direction of mathematical progress. But both of those statements contain a grain of truth, because mathematics and culture co-evolve.

As this project is addressing issues of Aboriginal engineering, Sttewart’s perspective on the co-evolution of maths and culture opens up possibilities for exploring Aboriginal engineering without the need for a prior acceptance of maths as a prerequisite for engineering knowledge.

In the context of widespread evidence of Aboriginal engineering knowledge throughout the Australian landscape, it is important that anyone referring to Aboriginal knowledge and use of maths does not fall into the trap of perpetuating old myths. This is an important aspect of the wider work of this project.

Intersecting Worldviews with which to explore Aboriginal Engineering

Intersecting Worldviews with which to explore Aboriginal Engineering

Wherever there are competing worldviews, there are also competing motivations and agendas. Awareness of this shaped our exploration of how engage with Aboriginal students, and their communities, in regard to developing greater interest in engineering as a career.

In seeking to focus our work we identified three particular worldviews with which to explore aspects of the interactions among engineering activity and community needs and goals. These worldviews were chosen from among the many that are available, and we use them as tools for exploration, without suggesting they are the only ways of seeing the world.

They are, respectively ‘Engineering’, ‘Aboriginal’ and ‘European/Western’. Each shares some features with the other two, and some features with only one other. We use a Venn diagram to represent these worldviews and specifically to focus attention on the Intersection where all three connect and overlap. Exploration of this Intersection is helping conceptualise how to manage relationships among different ways of thinking and identify what needs to be understood in order to achieve mutually acceptable outcomes. The Venn diagram is way of representing all this – it is not a way of quantifying anything.

Engineering worldview

  • Engineers learn to deal with the world, and address human needs, through a uniquely ‘Engineering way of knowing’ that places primary focus on ‘problems’ to be solved. This is coupled with attention to the practicalities of ‘how to’ approach the problem, and develop and implement actual solutions for the problem as it is eventually defined. This mindset is not common to all Western thought nor all Aboriginal thought. It is developed in response to a complex mix of preferences, training, capabilities and interests. An engineer in Western traditions will be doing much the same as an engineer in Aboriginal traditions. They share an interest in solving problems. The principles informing how they do so, differentiates their work.
  • Aboriginal Worldview

Indigenous ways of knowing inform language usage, relationships and connections among the more than 200 Aboriginal (pre contact) Australian nations. However, while Aboriginal culture exhibits all the familiar aspects of human endeavor, its underpinning philosophy and beliefs have an entirely different base to either Western/European or Engineering. The peoples who had successfully inhabited Australian land for between 60,000 and 40,000 years all share core beliefs and traditions, which have, over time, been customized to fit local needs and conditions. The base does not change, but particular features are implemented, and communicated to the young and those from beyond its boundaries, in different ways that are shaped to match the living context of each group. For example relationship with ‘country’ has a very specific meaning and set of core principles for Aboriginal people, as described vividly by Mary Graham

The land is a sacred entity, not property or real estate; it is the great mother of all humanity. The Dreaming is a combination of meaning (about life and all reality), and an action guide to living. The two most important kinds of relationship in life are, firstly, those between land and people and, secondly, those amongst people themselves, the second being always contingent upon the first.

Western/European Worldview

  • Western thinking is frequently characterised as being built on deductive reasoning, the rule of law and monotheism. Logic, objectivity and reason are its touchstones. Also in the mix is what has been called the ‘work ethic’ and a belief that the land and its products are to be possessed. While ‘Western’ is an understood convention to describe the worldview of people whose origins are traceable to the western hemisphere of the world, the ways in which it is enacted are not uniform. Wile sub-groups in this extended geographic area have cultural roots in a Western tradition, details of language usage, social relationships and connection with the physical world, all differ according to political and national norms. Consider, for example, the similarities and differences among English, German and Romanian culture and traditions.

The Intersection

‘Intersection’ is the term commonly used to describe the space in a Venn diagram where related ‘sets’ overlap. In this work we are not implying that there is, or is ever likely to be, easy agreement about how to operate within that space. When a Venn diagram is used to indicate relationships among components in science or maths the intersection includes only those items that are in all subsets. In our use of a three circle Venn diagram the intersection is considered to refer to places, objects and stories about which all three Worldviews have an opinion or claim a stake in its management. We are not suggesting that all three worldviews will – or should – be expressed in the same way, only that they have an interest (of differing strength) in the place, story or object.

‘5 Rights’ – applied to Sandon Point

Values and beliefs influence every aspect of how we suggest managing relationships among the factors in the intersection. In this regard we developed a set of principles we call the ‘5 Rights’ to guide interactions among the three worldviews.

These ‘5 Rights’ are not about entitlements. They are about appropriateness and suitability of behaviours, and are intended to guide thinking and actions in those complex situations where the Worldviews are interacting. The ‘5 Rights’ are

right People

right Place

right Language

right Time

right Way

The following story illustrates their successful application to a specific teaching context.

Sandon Point

Sandon Point is a water front site on the south coast of NSW. In 2000, severe storms revealed it was also the burial site of an Aboriginal man interred around 7,000 years ago. As it was tagged for residential development there ensued a tense tug-of-war between the local Aboriginal community and developers, culminating in the establishment of Sandon Point Aboriginal Tent Embassy (SPATE) – which has now occupied the site for 15 years. From an Aboriginal Worldview the site is sacred. From a Western Worldview it is ‘prime real estate’ and from an Engineering Worldview it is a location where various technical problems exist. The Tent Embassy is a collection of structures sitting on flood prone land that lacks many of the facilities usually associated with residential occupation.

The need to develop Engineering solutions for some of these problems, became the focus of work as part of this project and that has been fertile ground for other aspects of our work. It was not hard to see that looking at this one space from three such different Worldviews leads to very different perspectives about what is significant within, and about, the space. In 2013 Sandon Point was chosen as the context for an assessment task within a first year Engineering subject. The process was aligned with that used for Engineering Without Borders projects – with a major variation. The students were introduced to the site, given detailed information about an Aboriginal perspective on life, society and the importance of the site, and then asked to develop engineering solutions appropriate to the site and culturally acceptable to the residents. Their solutions were shared with the local government authority, which also benefited from the care with which the students attended to the cultural sensitivities of the site while developing 21st century solutions for such problems as water supply, power generation and waste disposal.

With regard to the ‘5 Rights’ here is how they were applied to this context.

Right People

In this project the people involved were SPATE members, local government staff, academic staff and university students. The most vital ‘right people’ were the SPATE members involved, a fact which was highlighted 12 months later, when the absence of those same people meant the project could not be developed further. (see the note on Right Time)

Right Place

Sandon Point is near the university campus and readily accessible. There is quite a lot of readily accessible information about SPATE and the history of its activities. There was a strong need to address the various engineering related topics for the students to exercise their creativity. The students met SPATE representatives on site, enabling them to get a deeply personal sense of what is involved in establishing and maintaining such a place.

Right Language

The situation at SPATE was discussed with the people on site, using their own words to identify their priorities and needs. Similarly discussions with the local government staff were conducted in terms of their perceptions and priorities. While the academic staff involved were the one most directly involved, the students were kept well advised.

Right Time

2013 was a moment in time when everything was aligned for such a project, as noted in ‘Right People’. And this fact emphasises the interconnectedness of all five Rights. By 2014 the series of changes that had occurred meant that Sandon Point could not be revisited in the same way.

Right Way

This is perhaps the most complex factor and is both first and last in terms of sequencing. As with so much else in life there is a ‘right way’ and a ‘wrong way’ to get things done. Approaching a project like this while using an entirely Western worldview would have failed, because that kind of framework seldom allows scope for attending to  philosophical and social beliefs  prior to taking action. Taking time to visit and sit with the Embassy people, providing detailed information about appropriate ways to treat the land. Setting technical criteria to replicate local traditions ensured that students experienced the ‘right way’ of approaching such a context, and their feedback reflected enhanced awareness of what it means to be Indigenous.