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Mathematics education in North East Arnhem Land Mathematics education in North East Arnhem Land

Short articles
Authors: Chris Matthews
Mathematics education in North East Arnhem Land

In his first Teacher article on mathematics from an Indigenous perspective, Professor Chris Matthews introduced the concept of two-ways learning. The second instalment discussed the interconnected relationships of Gurruṯu, and shared an activity for teachers and students to explore the connections and patterns in family trees. In this final article, he explores mathematics education at Yirrkala School.

I would like to acknowledge ŋarraku Mukul mala (my Aunties) Yalmay Yunupiŋu, Merrkiyawuy Ganambarr-Stubbs and Banbapuy Ganambarr for being my teachers and accepting me as part of their family. Without them this article would not have been possible. 

In my previous article, we explored the very basic level of Gurruṯu, which Yolŋu children living in the community of Yirrkala in North East Arnhem Land, are immersed in from birth. The article focused on a simplified version of the Mälk system (only allowing ‘first choice’ or preference marriage), which is a system of two interconnected cycles. I also shared an activity to give you an appreciation of the Mälk system’s complexity.

Gurruṯu, in its entirety, is far more complex with 16 relationship names placed in multiple interconnected cycles, at different scales, that defines a person’s connection to Country and all the elements of the world. In this article, I’ll share how mathematics is taught to students at Yirrkala School and how it balances both western and Indigenous knowledge.

Gurruṯu and mathematics

As I’ve been developing my understanding of Mälk and Gurruṯu, I’ve seen many connections with mathematics. One of the foundation concepts in Gurruṯu is moiety: Yirritja and Dhuwa, which is a binary relationship that maintains balance in the system. In mathematics, there are many binary relationships that also maintain balance, such as inverse operations, positive and negative numbers and so on.

Gurruṯu is about understanding cycles and their connection to environmental cycles, which can be used to teach circles, rotation and recursion, to name a few. Gurruṯu is also about systems of relationships, which is connected with concepts such as functions, graphs and networks.

In essence, both Gurruṯu and mathematics aim to understand the multiple connections of the world and, consequently, share many similar structures that can be used to bridge the two knowledge systems.

In the Yolŋu education system, children are raised to be system thinkers. They are raised with an understanding of how systems work, the philosophies and knowledge that underpin the system, the laws that maintain the system, the different parts of the system and how these parts are interconnected. These skills should give Yolŋu children an advantage in studying mathematics from a systems perspective and engaging in higher level mathematics.

Given the reality of a Yolŋu education and its connection to mathematics education, why then are Yolŋu students still underperforming in the Australian education system in mathematics?

A systems failure

Our education system continues to fail all Aboriginal and Torres Strait Islander students because it is still firmly rooted in its foundational concept of Terra Nullius. In other words, the system does not inherently value nor have any understanding of Aboriginal and Torres Strait Islander culture. Consequently, Aboriginal and Torres Strait Islander people are still confronted and dealing with colonisation in education in a multitude of ways.

For first language speaking communities, one of these ways is not having the right to learn and be assessed in your own language. For example, the system requires students to take NAPLAN in English and answer questions that contain culturally biased content. The results are then used to judge the students’ literacy and numeracy levels.

In addition, the majority of teachers in these communities are non-Indigenous teachers who have been trained to teach in English to meet the curriculum standards and have received a minimal education in any Aboriginal and/or Torres Strait Islander cultures. It is only when the teachers enter these communities that the formal and informal cross-cultural training begins. This puts pressure on both the teacher and Aboriginal and Torres Strait Islander educators who are working with them.

When combined with the high turnover of teachers in these schools, Aboriginal and Torres Strait Islander educators are left feeling like they are always starting from square one. This dynamic has persisted for decades and makes it difficult to establish an education for students that is firmly grounded in the students’ culture and world view, as well as bridging the cultural divide to the Australian Curriculum.

Mathematics education at Yirrkala School

From the vision of Dr Mandawuy Yinupiŋu, Yirrkala School has developed a mathematics curriculum that is called Garma Living Maths. Garma is an open ceremony where ideas are shared openly to explore them from different standpoints. In the Garma Living Maths Curriculum, Western and Yolŋu knowledge must be balanced (i.e. one is not more important than the other) and connections are made that inform the teaching and learning at the school.

For example, the curriculum has two main strands: Gurruṯu and Djalkiri. At the moment, the Gurruṯu strand is connected with the teaching of the number system drawing on the recursive pattern in both systems. In the Djalkiri strand, Yolŋu students learn how they are connected to Country and how they are situated in the landscape, which connects with mathematical ideas of space, direction, coordinate system, mapping and so on.

Garma Living Maths has only been made possible because non-Indigenous educators, Yolŋu Elders and Yolŋu educators have worked together in partnership to bring the two knowledge systems together to create meaningful learning experiences for Yolŋu students. I feel very honoured to be part of the Garma process, to further develop Garma Living Maths with my Aunties and other Yolŋu and non-Indigenous educators and being part of creating a mathematics education that fully realises the significance of Gurruṯu, Yolŋu mathematics, and its connection to Western mathematics.

Teacher and student activity

Using your family tree diagram (from the activity described in my previous article), extend your diagram to include great grandparents and great grandchildren showing the mälk and moiety of each group. Demonstrate that mälk and moiety also are in a cycle of four over the generations. What could be the implications of this? Who could you marry in the system?

Late last year, Professor Chris Matthews shared details with Teacher magazine of the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA) 2020 Conference. Due to COVID-19, ATSIMA 2020 conference in Yirrkala Community is postponed until 2021. To keep up-to-date with conference announcements and other activities, you can join ATSIMA as a member at atsima.com. 

In his first Teacher article on mathematics from an Indigenous perspective, Professor Chris Matthews introduced the concept of two-ways learning. The second instalment discussed the interconnected relationships of Gurruṯu, and shared an activity for teachers and students to explore the connections and patterns in family trees. In this final article, he explores mathematics education at Yirrkala School.

I would like to acknowledge ŋarraku Mukul mala (my Aunties) Yalmay Yunupiŋu, Merrkiyawuy Ganambarr-Stubbs and Banbapuy Ganambarr for being my teachers and accepting me as part of their family. Without them this article would not have been possible. 

In my previous article, we explored the very basic level of Gurruṯu, which Yolŋu children living in the community of Yirrkala in North East Arnhem Land, are immersed in from birth. The article focused on a simplified version of the Mälk system (only allowing ‘first choice’ or preference marriage), which is a system of two interconnected cycles. I also shared an activity to give you an appreciation of the Mälk system’s complexity.

Gurruṯu, in its entirety, is far more complex with 16 relationship names placed in multiple interconnected cycles, at different scales, that defines a person’s connection to Country and all the elements of the world. In this article, I’ll share how mathematics is taught to students at Yirrkala School and how it balances both western and Indigenous knowledge.

Gurruṯu and mathematics

As I’ve been developing my understanding of Mälk and Gurruṯu, I’ve seen many connections with mathematics. One of the foundation concepts in Gurruṯu is moiety: Yirritja and Dhuwa, which is a binary relationship that maintains balance in the system. In mathematics, there are many binary relationships that also maintain balance, such as inverse operations, positive and negative numbers and so on.

Gurruṯu is about understanding cycles and their connection to environmental cycles, which can be used to teach circles, rotation and recursion, to name a few. Gurruṯu is also about systems of relationships, which is connected with concepts such as functions, graphs and networks.

In essence, both Gurruṯu and mathematics aim to understand the multiple connections of the world and, consequently, share many similar structures that can be used to bridge the two knowledge systems.

In the Yolŋu education system, children are raised to be system thinkers. They are raised with an understanding of how systems work, the philosophies and knowledge that underpin the system, the laws that maintain the system, the different parts of the system and how these parts are interconnected. These skills should give Yolŋu children an advantage in studying mathematics from a systems perspective and engaging in higher level mathematics.

Given the reality of a Yolŋu education and its connection to mathematics education, why then are Yolŋu students still underperforming in the Australian education system in mathematics?

A systems failure

Our education system continues to fail all Aboriginal and Torres Strait Islander students because it is still firmly rooted in its foundational concept of Terra Nullius. In other words, the system does not inherently value nor have any understanding of Aboriginal and Torres Strait Islander culture. Consequently, Aboriginal and Torres Strait Islander people are still confronted and dealing with colonisation in education in a multitude of ways.

For first language speaking communities, one of these ways is not having the right to learn and be assessed in your own language. For example, the system requires students to take NAPLAN in English and answer questions that contain culturally biased content. The results are then used to judge the students’ literacy and numeracy levels.

In addition, the majority of teachers in these communities are non-Indigenous teachers who have been trained to teach in English to meet the curriculum standards and have received a minimal education in any Aboriginal and/or Torres Strait Islander cultures. It is only when the teachers enter these communities that the formal and informal cross-cultural training begins. This puts pressure on both the teacher and Aboriginal and Torres Strait Islander educators who are working with them.

When combined with the high turnover of teachers in these schools, Aboriginal and Torres Strait Islander educators are left feeling like they are always starting from square one. This dynamic has persisted for decades and makes it difficult to establish an education for students that is firmly grounded in the students’ culture and world view, as well as bridging the cultural divide to the Australian Curriculum.

Mathematics education at Yirrkala School

From the vision of Dr Mandawuy Yinupiŋu, Yirrkala School has developed a mathematics curriculum that is called Garma Living Maths. Garma is an open ceremony where ideas are shared openly to explore them from different standpoints. In the Garma Living Maths Curriculum, Western and Yolŋu knowledge must be balanced (i.e. one is not more important than the other) and connections are made that inform the teaching and learning at the school.

For example, the curriculum has two main strands: Gurruṯu and Djalkiri. At the moment, the Gurruṯu strand is connected with the teaching of the number system drawing on the recursive pattern in both systems. In the Djalkiri strand, Yolŋu students learn how they are connected to Country and how they are situated in the landscape, which connects with mathematical ideas of space, direction, coordinate system, mapping and so on.

Garma Living Maths has only been made possible because non-Indigenous educators, Yolŋu Elders and Yolŋu educators have worked together in partnership to bring the two knowledge systems together to create meaningful learning experiences for Yolŋu students. I feel very honoured to be part of the Garma process, to further develop Garma Living Maths with my Aunties and other Yolŋu and non-Indigenous educators and being part of creating a mathematics education that fully realises the significance of Gurruṯu, Yolŋu mathematics, and its connection to Western mathematics.

Teacher and student activity

Using your family tree diagram (from the activity described in my previous article), extend your diagram to include great grandparents and great grandchildren showing the mälk and moiety of each group. Demonstrate that mälk and moiety also are in a cycle of four over the generations. What could be the implications of this? Who could you marry in the system?

Late last year, Professor Chris Matthews shared details with Teacher magazine of the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA) 2020 Conference. Due to COVID-19, ATSIMA 2020 conference in Yirrkala Community is postponed until 2021. To keep up-to-date with conference announcements and other activities, you can join ATSIMA as a member at atsima.com. 

Professor Chris Matthew says, ‘In essence, both Gurruṯu and mathematics aim to understand the multiple connections of the world and, consequently, share many similar structures that can be used to bridge the two knowledge systems.’

How could you integrate the knowledge of Indigenous Australians into your teaching to help bridge the gap between western and Indigenous knowledge systems? What impact could this have on your students?

Professor Chris Matthew says, ‘In essence, both Gurruṯu and mathematics aim to understand the multiple connections of the world and, consequently, share many similar structures that can be used to bridge the two knowledge systems.’

How could you integrate the knowledge of Indigenous Australians into your teaching to help bridge the gap between western and Indigenous knowledge systems? What impact could this have on your students?


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