I was lucky enough to complete part of my practicum at Marparu school in North East Arnhem land. I also researched strategies for teaching numeracy in Aboriginal communities. As a teacher in Arnhem Land, one needs to teach within the context of Yolngu culture. There needs to be an effort made to bridge the gap by teaching in a culturally appropriate and effective way.
Teachers need to be prepared to teach numeracy from an ESL perspective and inside a two-way learning framework - Yolngu nation and broader Australian nation. In this way, one can make
“explicit the difference between Western mathematics and Aboriginal mathematics and value both equally.” Frigo T. (1999)
As a teacher, I try to contextualize the learning concepts into Yolngu life - to strip back the lessons from the prerequisite background knowledge of Western culture and start by building from what the students already know. This means trying to associate lessons to what is culturally relevant making the learning meaningful to my students.
“Wherever possible, mathematics should be represented in a culturally relevant manner, using situations that the students find interesting and familiar.” EZIEFE, (p.181 )
Language and cultural barriers coupled with the pressures of national curriculum requirements and routine testing makes this a challenging task. It is for this reason that
“Effective mathematics teaching for indigenous language speaking students needs to be based on fair expectations of both students and teachers. Concepts of ‘ age appropriate learning’ and ‘school readiness’ needs to be based on fair expectations of both students and teachers.“ Edmonds-Wathen C. (2015)
I will expand out the rationale around these discoveries in my research which is attached.
Marparu school had an excellent approach to practical numeracy for daily life by having the local shop run by the students of the school under the guidance of teachers. This gave them a sense of ownership, purpose and practicality to their learning experience.
During my studies at CDU I investigated the idea of broadening the concept of numeracy so that it can be applied cross-culturally, by expanding out the concept to a symbolic way of representing things in order to describe the world.
This expansion and simplification of concept allows for application to my teaching context in a way that can both incorporate the exploration of numeracy, drawing from Yolngu culture and make it possible to apply to the practical mathematical literacy skills needed in interactions with systems requiring these skills in the broader Australian community.
My research into this topic has led to a number of additional discoveries from my original assignment, that can be applied in order to enrich and extend numeracy literacy skills for Yolngu students living on remote community.
I will expand out the rationale around these discoveries in the following paragraphs.
My teaching context is to the students of Marparu - A remote Yolngu homelands school in North East Arnhem land. It is of utmost importance to contextualise my teaching methods to Yolngu culture, and in doing so acknowledge the relevance/ importance of the Yolngu culture within which they live. This is likely to yield a more connected understanding of the numeracy concepts at hand.
Teaching numeracy from a Yolngu perspective has the advantage of connecting newly learned knowledge to cultural knowledge that is already known, as well as allowing recognition of Yolngu traditional culture as a meaningful part of students education.
This is in the hope that coming to school (and learning numeracy skills) doesn’t always require learning within the balanda (non indigenous) framework, but a learning environment where by students can identify with the cultural context in which the learning is taking place. As a recent article on this the topic of maths decolonisation highlighted
“Students mathematical identities – how they see themselves as learners of mathematics and the extent to which mathematics is meaningful to them – are important when thinking about teaching and learning in mathematics.” Brodie K. (October 14, 2016)
In keeping with this perspective, in my previous assignment I concluded with a wish to explore what opportunities may come from looking at numeracy from a new cultural perspective?
As Selin puts it -
“With this comes the possibility that we might make our futures different from our past. Specifically, we might find ways to go beyond colonialism in dealing with difference in doing mathematics and logics” Selin.H. (2011)
In order to re-contextualise and improve teaching numeracy to Yolngu students, there is
“a necessity for educators to discover ways of bringing to Indigenous students an understanding of Western mathematics” Rudder J.
Rethinking the key concepts of numeracy through the lens of ethnomathematics is a positive Segway for
“a cooperative approach between Indigenous and non-Indigenous educators ( that ) has developed” Rudder J.
By definition, ethnomathematics is
“a field that recognises the numeracy concepts already inherent in all cultures.( It is ) to do with perceptions associated with evaluations, qualities, quantities, and the relationships between aspects of known realities, including both spiritual and physical aspects. It is part of, and an expression of, any people’s or group’s worldview or cosmology.” Rudder J.
In this way non indigenous teachers like myself coming into a Yolngu learning environment, might recognise that the very foundations of many of the concepts that the curriculum requires us to teach, involve a prerequisite of western cultural knowledge that may not be present for many of the Yolngu students. This is because
“mathematics is a cultural construct that evolves within and with language in response to people’s needs” Barton (2009) - Bishop (2009) as cited in Edmonds-Wathen C. (2015)
In the previous assignment I discussed how ‘Gurrutu’ - the kinship system)
“provides an opportunity for Yolngu to gain with the assistance of a familiar context, an insight into the nature of Western mathematical thinking ….. (It) provides the framework around which the Yolngu world at all levels is organised, and as such is Yolngu mathematics.” Cooke M. (1990 - p.20)
However, how to use this important cultural concept to effectively teach concepts of numeracy is a complex question.
Further research into the topic of using the example of ‘Gurrutu’ to teach mathematical concepts has solidified that it would be culturally appropriate to call on the assistance of Yolngu co- teachers to help teach this part of the unit.
In addition to this, I have chosen to borrow from a series of group activities developed and trialled in Yolngu communities by educator and academic Keppert. He writes
“ These insights may lead to a more appropriate maths program and particularly one that begins with an understanding of the students world” Keppert B. (1991 - p.5)
The series of lessons begins with the teacher. In order to educate others, we as teachers must have a thorough understanding of the topic ourselves. In addition to this
“integrating the learners culture and environment into mathematics instruction (has had)a positive effect and overwhelming influence on a group of undergraduate, pre-service Aboriginal teachers” _EZIEFE (p.176)
The lesson is a peer teacher activity that seeks to illustrate that
“Just as we have an abstract system of number, Aboriginal community also functions with a complex and abstract system of relationships.” Keppert B. (1991 - p.33)
Inside the activity, each of the teachers has the task of identifying their relationship to each other, using the the aid of different coloured strings to represent the various relationships. ThIs activity allowed for an abstract system to become concrete.
Making concrete abstract ideas is key to some of the numeracy barriers that many Aboriginal children face. Referring to Yolngu children in Millingimbi (a nearby community to Marparu) Keppert commented
“The Millingimbi child faced with the abstract concept and school mathematics, may learn to count and do calculations by rote, yet fail to see the world from the same mathematical perspective as the teacher” Keppert. B. (1991 - p.33)
The use of real objects (the string) combined with subject matter (Gurrutu) that is both known and relevant to the students is likely to yield a far more positive learning experience and result.
The second activity I hope to try with students and staff learned from Keppert’s work allows for teacher / peer review, using the concept of malk (skin name) - a part of the complex ‘Gurrutu’ system with Yolngu and non Yolngu staff. The activity is described by Keppert here.
“In groups according to their malk the teachers were asked to stand forming one large circle. By drawing a chalk circle, then segments on the carpet to make a pie graph it is possible to represent some Aboriginal knowledge in an abstract mathematical way of expressing part of what the Aboriginal teachers already know about ‘malk’ (skin names). One can also use this same activity to investigate fractions by counting those standing in each segment against the total in the survey. The Aboriginal staff already know who is there and what subsections they are from, but what I am hoping they will gain from this activity is the ability to rename their perceptions of sub sections into maths concepts.“ Keppert B. (1991 - p.34)
Although Gurrutu can certainly be used to help students and Yolngu teachers to make connections between Western and Yolngu concepts of numeracy, it is important not to simplify this ancient system in order to fit the box of Western numeracy that we are trying to fit it into. Academic Cooke acknowledges this potential misrepresentation writing
“It should be noted that 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 meaning and have certainly not done justice to the intricacy and complexity of the Yolngu world.“ Cooke (1990)
Language comprehension is a significant barrier to successful outcomes in the teaching of numeracy that cannot be overlooked.There is a strong recommendation amongst researchers in the field, that teachers in predominantly Indigenous language communities gain training in ESL and approach the teaching of numeracy within this context. Indeed the board of education points out that
“mathematics is essentially a linguistic exercise and a very complex one for Aboriginal students given their diverse backgrounds and language needs.“ Frigo T. (1999)
Not only is it likely for students to lack the English vocabulary required for learning abstract concepts further, quite simply, for the teaching of many western mathematical concepts, it is not possible to make a direct translation, because it does not actually exist in the local vernacular. For this reason the research emphasises
“ the importance of ensuring clarity around the specific conceptual knowledge being addressed, along with a need to minimise problematic culture - based assumptions (e.g that sharing implies equal division“ (p338, Wilkinson and Bradbury, 2013)
Another teaching resource I would like to call upon that attempts to improve the language barrier to learning is ‘Talking Namba’. This NT Education department’s initiative provides active strategies, to help Indigenous students to build the skills of mathematics wherever possible
“in a culturally relevant manner, using situations that the students find interesting and familiar” (p181, EZIEFE, 2002)
“involve(S) working with paraprofessional Indigenous teachers to develop effective instructional approaches, with a strong focus on the use of first language.“ Wilkinson M. & Bradbury J. (2013 - p.337)
In conclusion, my research into this topic has identified a number of pre-existing barriers to effective teaching of numeracy literacy skills to Yolngu students on community.
My reflection on this topic has involved first hand observations during my time teaching and interacting with students at Marparu, interviews with experienced teachers, professionals and academics in the field as well as reading a broad variety of resources, based on both policy and practical teaching ideas, so that I might get a thorough understanding of the challenges involved.
One only needs to glance at the alarming statistics for literacy in numeracy within Indigenous communities throughout Australia, to see that improving our approach to teaching these students is urgent.
Wilkinson and Bradbury summarise the necessary actions writing
“focus on language, clear intent, engaging activities, a variety of concrete representations, explicit concept building from concrete to abstract representations , building automaticity where appropriate (and) building on what students know” Wilkinson M. & Bradbury J. (2013 - p.337)
Another most important factor in the learning outcomes of our students that should always be enacted is a positive attitude to their learning capabilities.
“Research in schools has shown that one of the key factors in students’ mathematics achievement, is a teacher who believes that they ( The students) can do mathematics.“ Brodie K. (October 14, 2016 - Yes, mathematics can be decolonized. Here’s how to begin)
ACARA, Curriculum Mathematics retrieved from here
Brodie. K, (October 14, 2016) “Yes, mathematics can be decolonized. Here’s how to begin” Retrieived from here
Bucknall. G, (1995) AIATSIS Library, S 37/4, “Building bridges between Aboriginal and western mathematics”, Retrieved from here
Cooke. M ( 1990) “ Seeing Yolngu mathematics” Retrieved from here
Edmonds-Wathen, C. (2015). Indigenous language speaking students learning mathematics in English: Expectations of and for teachers. Australian Journal of Indigenous Education, 44(1), 48-58. doi:10.1017/jie.2015.9
Eziefe A. (2002) Mathematics and culture Nexus: The Interactions of Culture and Mathematics in and Aboriginal Classroom. International Education Journal. Vol 3 (3) 176-187. link
Frigo T. (1999) Resources and Teaching Strategies To Support Aboriginal Children’s Numeracy Learning. Retrieved from here
Selin (2011) Mathematics Across Cultures, Netherlands, Springer
Keppert B. (1991) Mathematics for Aboriginal students who have a different world view
Mason and Wilder (2006) Designing and Mathematical Tasks, St Albans, Tarquin
Northern Territory Department of Education and Training (2011) Strong Literacy and Numeracy in Communities project. Retrieved from here
Rudder J. Ethno mathematics in Australia, Retrieved from here
Trevor Stockley (The effectiveness of the National Assessment Program - Literacy and Numeracy Submission 12)
Wilkinson M. & Bradbury J. (2013). Number and two languages in the early years: Report on a project with paraprofessional Indigenous teachers in two NT northeast Arnhem Yolŋu schools. Australian Review of Applied Linguistics, 36(3), 335-354.