This blogpost is an exact reproduction of an essay I wrote and submitted in October 2018 as a requirement of the course ‘Aboriginal Futures’, an elective I took as part of the Master of Teaching at the University of South Australia. The course aims to ‘explore Aboriginal Futures in contemporary Australian society’ and to provide an ‘opportunity to engage with relevant theory and Aboriginal perspectives and apply these to the questions that Aboriginal Futures raises, including questions about self-determination and the protection of Indigenous Knowledges’ (from the Course Outline).
The overall brief for the essay was to either: (a) choose a theoretical framework to discuss an Indigenous artist’s work and the standpoint represented in their work, or (b) develop a research paper on a topic of great interest in relation to professional or personal practice.
I chose to use the essay as an opportunity to read more deeply into issues of mathematics education in Australia in relation to the experience of Indigenous peoples. The essay had specific requirements in terms of length, inclusion of course readings, and skills to be demonstrated. The style is necessarily impersonal. I humbly offer this for broader consumption as I think that sharing my evolving understandings will provide an opportunity for others to contribute to my education on this topic.
Introduction
The participation and achievement of Indigenous students in science, engineering and mathematics is significantly lower than their non-Indigenous peers, leading many to believe that Indigenous students do not have an aptitude for scientific disciplines. This belief is a myth.
This paper dispels the misconception by presenting several examples of the ingenuity of pre-colonial Indigenous science (a term which includes cognate fields such as engineering and mathematics). However, setting history straight is only part of the equation. By examining the origins of the myth, this paper hopes to understand how to rectify inequalities in mathematics education in ways that draw on and elevate Indigenous knowledge systems.
Pre-colonial Indigenous engagement with science
Indigenous people have inhabited Australia for more than 65,000 years (Clarkson et al, 2017). Aboriginal Australians are well established as the first astronomers. Many sources, including oral traditions, art and artefacts, indicate that their detailed understanding of the sky enabled navigation and an ability to predict tides, eclipses and the motion of celestial bodies. (See Norris and Harney (2014) for a lengthy reference list.) For another example from science, Bruce Pascoe’s acclaimed book ‘Dark Emu’ (2018) disrupts conventional thinking by showing that pre-colonial Aboriginal Australians possessed sophisticated knowledge of agriculture. Pascoe (2018) gives powerful evidence of Aboriginal people pursuing the five activities that Europeans deemed as signifying the development of agriculture: selecting seed, preparing the soil, harvesting, storing surpluses, and erecting permanent housing for large populations.
Engineering knowledge is apparent in the range and complexity of Aboriginal-designed houses built from a variety of materials, including stone (Memmott 2007). The fish traps at Brewarrina are one of humankind’s oldest still-standing man-made structures, and are ‘unequivocal evidence of a deep understanding of engineering principles, applied physics, ecology and hydrology’ (Ball 2015, p. 17). While mathematical knowledge is evident in astronomy, agriculture and engineering, it also extended beyond physical applications. For example, intricate kinship systems, developed over thousands of years, are complex arrangements that rely on ‘cyclical, recursive patterns’ which can be found within numbers and other areas of mathematics (Matthews 2005, p. 5).
This handful of examples demonstrates a breadth and longevity of Indigenous knowledge in science, engineering and mathematics. And yet, the response to Pascoe’s book has been widespread astonishment amongst non-Indigenous readers, with the evidence of agricultural societies and of stone engineering techniques sharply inverting their beliefs about pre-colonial Australia. How did this paucity of knowledge regarding Indigenous scientific achievements and the myth that Indigenous people ‘don’t do science’ come about?
A deficit view of Indigenous science
Eurocentric perspectives have dominated scientific discourse in Australia since colonisation, determining whose knowledge is legitimate. The innate superiority with which Europeans and the British came to see themselves emerged during the Enlightenment (Smith 1999, p. 58), the period of European history known as the ‘Age of Reason’ for its emphasis on the scientific method. The development of modern science is often used to indicate how progressive, rational and civilised the West is in contrast with the primitive ‘rest’ (Harding 1993, p. 7).
Imperialism was also borne out of economic, industrial and military dominance, and came to be interpreted as the difference between the ‘savage’ and ‘civilised man’ (Hollinsworth 2006, p. 30; Pascoe 2018, p. 3). This was the prism through which the British approached first contact. Ironically, prejudicially framing Indigenous Australians as ‘savages’ and ‘primitives’ overwhelmed the capacity of Anglo-Europeans to apply proper scientific methods; for instance, Nakata (1998) provides detailed examples of questionable scientific practices and inference in the 1898 Cambridge Anthropological Expedition to the Torres Strait.
A view prevalent until the early 1900s was that biological differences placed different groups of people (‘races’) on a single path of evolutionary development, from primitive to advanced (Hollinsworth 2006, p. 37). A similar construct held (and arguably still broadly holds) for scientific and technological achievement, that is, a single line of progress exists from the most primitive societies to the most advanced. It was thought that every culture would eventually reach the same milestones. Conversely, if a culture does not achieve a milestone, the implication is that it is inferior. That there were no wheels in Australia until Europeans arrived was used to conclude that Indigenous cultures were technologically simplistic (Pearcey 1998).
A more unscrupulous demonstration of this way of thinking comes from mathematics. The general perception by Western researchers until the mid-twentieth century was that Aboriginal counting systems were simple and, therefore, that Aboriginal cultures were mathematically naïve. However, Harris (1987) provides proof from several Aboriginal languages to dispute the misperception, declaring that scholars deliberately ignored the evidence so as to promote a view of cultural and intellectual Aboriginal inferiority.
Not all evidence of technological and scientific knowledge was wilfully ignored or mischaracterised by the colonisers, but it was also not made more widely known. Many of the journal extracts from explorers, surveyors and pastoralists included in Pascoe’s book describe, sometimes admiringly, the innovation of Indigenous people across the country. It is not difficult to understand why they kept their discoveries private—it is easier to justify colonising and conquering a primitive civilisation. More pointedly, their observations demonstrated land tenure, which ran counter to the portrayal of Aboriginal people as nomads. The notion that Australia was inhabited by nomadic people, rather than occupied by them, underpins the ‘doctrine of terra nullius’ and the right to take possession of the land.
The effects on Indigenous and non-Indigenous science
Framing Indigenous people as incapable of scientific thought and refusing to acknowledge evidence of Indigenous science preserved a view that science can only be done and interpreted by dominant groups in the West. The ramifications of denying Indigenous people participation in the intellectual community, except as objects to be studied, are far-reaching and will be elaborated later. Many Indigenous people hold the view that they are the most researched groups in the world (Smith 1999, p. 3; Mack and Gower 2001), and yet have rarely seen any benefit from research. Even in the modern world, research projects involving Indigenous peoples are still sometimes seen as a tool for colonisation; Smith (1999, p. 99) gives ten recent and diverse examples, from genetic to spiritual exploitation.
As has already been mentioned, science is affected by political, economic and social interests. These factors influence the way in which scientists interpret data, judge which knowledge is valid, and decide which problems to pursue. Harding (1993, p. 2) characterises a ‘racial economy’ of Western science, in which institutions, assumptions and practices distribute the benefits of Western sciences along racial lines, widening the gap between the haves and the have nots. To give one example, Freemantle and McAullay (cited in Laycock et al. 2011, p. 21), note that ‘prior to 1976, no Australian jurisdiction separately identified Indigenous persons in vital statistics or hospital-based collections’. The shortage of accurate, consistent and complete Indigenous health data, which occurred in part due to a lack of Government interest in collecting it, has directly contributed to health inequity in Australia.
Although the scientific method that underpins most Western research is meant to enshrine objectivity through systematic observation and testing of hypotheses, research is always filtered through the worldview of the scientist. These biases can give rise to an unexpected form of scientific illiteracy suffered by those who are highly educated—scientists and other dominant groups in the West (Harding 1993, p. 1). One consequence is a partial or distorted view of knowledge. For example, Harris observes that the deliberate mischaracterisation of Indigenous concepts of number, which entered the literature in the 1860s, ‘profoundly influenced the thinking of several generations of anthropologists and linguists’ (1997, p. 30). A failure to be willing to learn from Indigenous science impedes progress in many ways. Pascoe (2018) explains how serious consideration of Indigenous farming practices could revolutionise Australian agriculture and benefit future prosperity (p. 63–67, p. 209–217).
Examining Indigenous knowledge systems from a Western standpoint has inherent limitations. In his study of Yolngu mathematics, Cooke (1990) is conscious that the operational definition of mathematics arises ‘from its characteristics and prominence as a basis for the schema of European culture’ (p. 4), noting that the Westerner looking into the Yolngu world may easily overlook evidence of Yolngu mathematical imagery if they are searching for European-style markers of symbols and diagrams (p. 37). Cooke also considers what might be lost in translation, observing that (p. 2):
… by removing words, concepts, and structures from their Aboriginal context and putting them into a European box called ‘mathematics’, I have inevitably lost much of the full significance of their meanings and have certainly not done justice to the intricacy and complexity of the Yolngu world.
Over time, scholars in different fields began to seek an insider’s point of view—that of the ‘native’. Known broadly as ‘Indigenous knowledge’, the ethno- prefix has been applied to describe the study of traditional knowledge in terms of internal elements of the culture, rather than by reference to any existing external scheme. This approach has given rise to new fields of study, such as ethnobiology, ethnochemistry, ethnoengineering, and ethnomedicine.
Ethnomathematics
The term ‘ethnomathematics’ was coined by d’Ambrosio (1985, p. 45) to describe ‘the mathematics which is practiced among identifiable cultural groups’. There is no consistent view of ethnomathematics in the literature, and its meaning has progressively shifted. In his PhD thesis, Barton (1996, p. 3–8) charts the evolution of the term ethnomathematics from describing particular mathematical practices, to explaining the knowledge behind those practices and, eventually, to a research program investigating the ways different cultures mathematise (that is, translate informal concepts into a mathematical framework).
Ethnomathematics has attracted criticism on two main fronts: epistemological and pedagogical (Pais 2011). The first criticism connects to the struggle many people have in accepting that mathematics and culture can be fundamentally linked. In their minds, the universality of mathematics is meant to transcend specific cultures. Barton (1996a, p. 215) concludes that ethnomathematics is not mathematics, but a ‘tool in which we may make better sense of our world, both as we see, and as others see it’ (p. 229). The pedagogical criticism of ethnomathematics relates to the ways in which ethnomathematical ideas are included in formal education. We now consider this point in more detail.
Indigenous participation in mathematics education
Australia’s Indigenous students are being left behind in mathematics education. Indigenous 15-year-olds are approximately two-and-a-half years behind their non-Indigenous peers in schooling. Indigenous students are overrepresented at the lower end of mathematical literacy, with half of all Indigenous students deemed ‘low performers’ compared to 18 percent of non-Indigenous students (Dreise and Thomson 2014, p. 1).
Chris Matthews, an Indigenous mathematician and prominent voice in this space, argues that Indigenous education must be understood in the context of the historical positioning of Indigenous cultures as a primitive, simplistic society (2005, p. 2), and with recognition of the lasting effects of marginalisation and exploitation. Education can be perceived to have a role in the colonising process by institutionalising the oppositionality of European and Indigenous ways of being (Pearce 2001, p. 5), for example, by requiring students to speak in a language other than their own and to participate in pedagogical practices that are culturally different.
Being ‘smart’ may also be considered by some Indigenous students as a Western attribute (Sarra 2011, p. 109; Pearce 2001, p. 3). This poses an impossible dilemma: either ‘play dumb’ and have the teacher regard them (and, by extension, all Indigenous people) as academically incapable, or speak up and betray cultural identity.
Matthews et al. (2005, p. 1) identify two fundamental problems. The first is that educators have little faith in Indigenous students’ mathematical abilities, blaming poor academic performance on social and cultural complexities (Sarra 2011, p. 108), without proper consideration of the dilemma just mentioned. This can lead to a ‘dumbing down’ or a lighter version of the curriculum (Matthews et al. 2005, p. 2; Pais 2011, p. 213). Research also suggests teachers respond more favourably to students who are culturally similar to them (Pearce 2001, p. 6) and, with few Indigenous teachers, this may be a difficult problem to quickly overcome.
The second fundamental problem is that Indigenous students find little relevance within mathematics, often struggling with Western concepts, content and pedagogies. A common approach is to use students’ ethnomathematical knowledge to construct a ‘bridge’ for the learning of more formal mathematics. While this method is seen as one way to valorise students’ cultures, it can reinforce the hegemony of Western mathematics, especially when traditional knowledge is used as a ‘curiosity, an illustration, a “starter” to the real mathematics’ (Pais 2011, p. 222). Used in this way, ethnomathematics can jeopardise cultural identity and magnify ‘otherness’.
Here I make a third criticism of ethnomathematics: that use of the prefix ‘ethno-‘ will always position Indigenous knowledge systems as separate and inferior to ‘mainstream’ knowledge. Both this and the epistemological criticisms of ethnomathematics can be resolved by redefining what is meant by mathematics. Cooke (1990, p. 5) proposes that we view mathematics as ‘society’s system for encoding, interpreting and organising the patterns and relationships emerging from the human experience of physical and social phenomena’ and goes on to say that ‘whilst this process is common to all cultures the resulting schemata can be fundamentally different’. With this new definition, Western mathematics is only one type of mathematics. This is a revolutionary view, and a point of contention in the literature.
Rather than use a one-way bridge, ‘two-way/both-way teaching’ is a method in which teaching and learning occurs in a neutral, negotiated space—the ‘third space’—in which neither culture presumes superiority (Purdie et al. 2011, p. xx). One of the most cited examples of this culturally responsive pedagogy is Garma Maths, taught at Yirrkala Community School in Arnhem Land. In the local language, the ‘Garma’ is an open meeting place where everyone comes together. Western and Yolngu mathematics are presented alongside each other, tying the formal logical concepts of Yongu life and thought with Western mathematics (Nicol and Robinson 2010, pp. 502‒503).
Culturally responsive pedagogies also draw on Aboriginal ways of learning. Storytelling is included in the eight ways of Aboriginal learning introduced by Yunkaporta (2010), and has been successfully used to explore algebraic concepts in the Maths as Storytelling (MAST) approach (Matthews 2008, pp. 48‒50). Yunkaporta (2010) elaborates on using the eight ways in the teaching of Aboriginal languages in schools. Conceptualising how to bring all eight ways to the teaching of mathematics would be an exciting enterprise!
Conclusions
The scientist Carl Sagan said: ‘You have to know the past to understand the present.’ This paper briefly surveyed evidence showing that Indigenous Australians were the first scientists, engineers and mathematicians. Yet despite this strong history, Indigenous students are being left behind in mathematics education. This paper has examined how racial prejudices led British colonisers to ignore, downplay, and misrepresent Indigenous science, with effects that reverberate into the present for both Indigenous and non-Indigenous Australians.
One consequence of disregarding Indigenous science is a Eurocentric education system that marginalises Indigenous peoples, devalues Indigenous knowledges, and discredits the abilities of Indigenous students. With a focus on mathematics education, this paper described how contextualising learning with Indigenous knowledge and perspectives can help redress educational inequities. However care must be taken so that traditional knowledge is not reduced to a quaint cultural artefact. In the most effective approaches, Indigenous and Western mathematics are situated alongside each other, with neither claiming cultural or intellectual superiority. Although this ‘third space’ may challenge entrenched views of what it means to know and do mathematics, it also provides an important opportunity for both cultures to learn from each other.
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Wonder in Mathematics 