We have chosen to call this section Number Patterns in recognition that we are not just talking about the mathematics taught in mainstream schools in Australia. There are both very complex systems of number patterns to consider (e.g. rules and patterns around who can marry in order to maintain good genetic vigour in the population) and concepts that are unfamiliar to mainstream mathematics (e.g. why count people when you can name them?). This section includes resources from a range of knowledge keepers and educators, presenting diverse perspectives on how mathematics manifests in Indigenous knowledge systems.
Associate Dean of Science (Indigenous Leadership) at the University of Technology Sydney and Quandamooka man, Chris Matthews, describes mathematics as an expression of culture that provides another way to view the world. It is not owned by only one culture, nor does it have a correct or incorrect way of expressing it. While many of these resources talk about teaching Indigenous students mathematics, within these discussions lies quite a lot of information about Indigenous mathematics which can be used in consultation with appropriate local or institutional Indigenous groups, to determine interesting mathematic examples to teach mainstream/non-Indigenous students too. You might learn a new perspective on mathematics while you are reading and writing. This mathematics page will not lead you to a list of Indigenous Mathematics lessons that you might utilise for mainstream maths and science students at a tertiary level. In fact, I’m not sure any exist. It’s for those making it to this site to make and share the first resources in a respectful and inclusive manner.
One fabulous and deep resource is the website 8ways. The 8 ways pedagogy originated by Tyson Yukaporta in his PhD thesis work, is popular and well established. This website brings together a lot of work on the topic. It is important to note that the 8-ways pedagogy was initially designed around an effort to bring Indigenous pedagogies to the cultural interface between Indigenous learners and a non-Indigenous system. Like most, if not all pedagogies, there is something that can be learnt from the 8-ways approach for any student.
Please be sure if you are going to use these 8-ways resources you adhere to the protocols determined for the operation of the site and the sharing of related information.
The traditional owners of Western New South Wales should be acknowledged if this is used for any other purpose, and permissions sought via DET’s Bangamalanha Centre at Arthur St in Dubbo, Western NSW. (ph 02 6841 3852)
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ATSIMA and Professor Chris Matthews
In the field of Mathematics, Australia is very fortunate to have the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA) whom are an Indigenous led, non-profit group representing various organisations, communities, and individuals to promote mathematic outcomes of Indigenous students. While much of the material on this website is focused purely at teaching Indigenous students, the resources can be used to familiarise yourself with how Indigenous thinking towards mathematics ins often different and why. For example, this recent talk by Assoc. Prof. Chris Matthews is for an early years teacher audience but I found it to be excellent general background.
A/Prof Chris Matthews proposes the following framework for considering mathematics. Chris sees very strong connections between culture and mathematics, partially expressed below in figure 1. Teacher Magazine holds three publications that while they are partly about teaching Indigenous students, they are also about the culture of teaching mathematics.
‘Forty-thousand years of Indigenous maths can get kids into numbers today’ in the Guardian highlights the importance of valuing Indigenous mathematics. This article includes a description of the idea of moieties in Indigenous mathematics and how mathematics is a cultural expression that provides another way of viewing the world.
Additional Mathematics approaches
Yumi Deadly Maths is a movement which like 8-ways started off with a focus on Indigenous students but has now diversified to other areas, for example, teaching those who consistently struggle to pass maths and low SES groups. This is an excellent program to highlight if you have Science Education students in your cohort.
‘Ethnomathematics’ (Dr Kay Owens of Charles Sturt University) summarises examples of ethnomathematics from across the globe, including that of Indigenous Australians. This can be great background if you are looking to investigate issues of mathematics and culture more broadly or wish to find additional background reading for either yourself or your student.
‘Explainer: how does the Aboriginal numeric system work?’ is an opinion piece by D’harawal knowledge keeper, Shannon Foster (the University of Sydney) which details a number of Aboriginal counting conventions, and presents the holistic nature of Indigenous mathematics. If you want academic detail ‘Mathematics of Yolgnu Aboriginal Australians’ (Helen Verran of Charles Darwin University) details the mathematics of the Yolgnu people in North Australia. This is one of the examples that Chris Matthews also discusses in his video, however, this piece contains significantly more detail including a discussion about how we might compare Indigenous and Western mathematics systems. Please note this piece uses “indigenous” to refer to Aboriginal people several times. This is not good practice as the use of a lowercase “i” indicates plants and animals and is therefore obviously not appropriate for people. However, we have shared the piece here as pieces that are this detailed are rare. This piece explores various mathematical objects and concepts by detailing the real-life application of these perspectives including how mapping and codifying are important tools for determining Yolngu marriage arrangements.
Finally, Narragunnawali provides ‘Mathematics: Resource Guide’ which is a collection of Mathematics related resources in relation to Indigenous peoples in Australia. It ranges from details of successful and well know Indigneous Mathematicians, prizes, teaching resources and important dates. Importantly it explains that;
“while this guide has been distinguished according to the distinct Subject/Learning Area of Mathematics, traditional Aboriginal and Torres Strait Islander mathematics also has a very intricate and important interrelationship with other subject/learning areas such as Languages, Science, Technologies, and Humanities and Social Sciences—Geography.It is for this reason that, in many ways, through “removing words, concepts and structures from their Aboriginal context and putting them into a European box called mathematics… [one can inevitably lose] much of the full significance of their meaning and… [not do] justice to the intricacy and complexity” of the Aboriginal and Torres Strait Islander contexts and cultures to which they are tied”Cook, M. (1990) Seeing Yolgnu, Seeing Mathematics, Bachelor, NT