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Closing the Gap in Education?

Scholastic Heritage and Success in School Mathematics

Implications for Remote Aboriginal Learners

Robyn Jorgensen

Griffith University

Peter Sullivan

Monash University

In this chapter we draw on our collective experience across two diverse Aboriginal contexts. The first is our research in the Kimberley region, where we have been working on a four-year Australian Research Council-funded project with six communities in the Fitzroy River valley. The second is our research in the Central Desert region of Australia that crosses into three states in Central Australia. These experiences highlight the similarities and differences between Aboriginal communities. For our purposes here, we draw on these experiences to argue the ways in which the practices of school mathematics exemplify the structuring of unequal access to education for many Aboriginal learners. To frame the chapter, we draw on the work of Pierre Bourdieu, to understand how practices function to exclude Aboriginal learners. We use Bourdieu’s ideas to identify particular theoretical constructs through which we are able to frame particular practices that contribute to ‘scholastic mortality’ among Aboriginal learners. However, we then argue that by gaining a better understanding of how such practices work in the reification of educational disadvantage, we are better able to understand structural inequality and propose ways to address it.

Social heritage and success

For Aboriginal1 learners, school represents a new social world where the rules of engagement are different from those of the community and home. For example, Anangu children from Central Australia are very strong in their cultural histories and are encouraged from an early age to be independent and make their own choices – which includes whether or not they come to school. Anangu learners speak their home language of Pitjantjatjara in their homes and communities, so the school represents a foreign-language environment – yet all instruction and concepts are based in a language and culture that are unfamiliar to them. Indeed, the Northern Territory Government recently announced the cessation of bilingual programs in that territory for Aboriginal learners. This is despite the considerable research into bilingual education that supports a transitory period from the home language to Standard Australian English (SAE). In contrast, schools in the Kimberley recently took the opposite approach and introduced home language in the early years of schooling to enable successful transition into school. Much of the pedagogic relay used in schools is so foreign to Anangu learners that learning anything through the instructional mode of classrooms is an alien process. When such factors are considered, the limits to success for Anangu learners become obvious. We have observed similar differences for Kimberley students, who may not be as strong in their original Aboriginal language or culture and now speak a Kriol. However, this Kriol shapes their language and their world view, posing particular challenges to engaging with the discourse of school mathematics and SAE.

To better understand the processes by which the home language of Aboriginal students clashes with and constrains their access to school mathematics, we use the work of Bourdieu to theorise the symbolic violations that occur when the discord between school and Aboriginal learners is foregrounded. While his focus was on social class, Bourdieu explains that educators need to understand the processes around the conversion of social and cultural backgrounds into school success. He argues that:

To fully understand how students from different social backgrounds relate to the world of culture, and more precisely, to the institution of schooling, we need to recapture the logic through which the conversion of social heritage into scholastic heritage operates in different class situations. (Bourdieu et al. 1994, 53)

The notion of social heritage thus becomes a central variable in understanding differential success in school mathematics. Using a Bourdieuian framework, the lack of success for some social groups becomes a non-random event, where it is a product of institutionalised practices of which participants may be totally ignorant. In this case, participants are more likely to be those entrenched in the school system rather than the Anangu learners. In the remote contexts of Central Desert communities of Australia, the clash between the culture of school and the culture of Anangu learners contributes significantly to the success, or lack thereof, for Aboriginal learners. We have also observed these clashes in the Kimberley region.

School mathematics represents a particular and powerful example of how social heritage converts to academic success. Language is an integral part of the social heritage that is brought into school mathematics to become reified as an innate ability that facilitates, or not, success in coming to learn the discipline knowledge within the field of school mathematics. We do not subscribe to this view of innate ability, but ‘ability’ is an entrenched and naïve belief within the field (Zevenbergen 2005). The language, in very broad terms, not only conveys particular concepts but also provides a medium through which those concepts are conveyed. It is therefore important to consider not only the concepts, but also the medium of instruction.

When assuming a Bourdieuian perspective, success in school mathematics is less to do with innate ability and more to do with the relationships between the culture of school mathematics and the culture that the learner brings to the school context. The greater the synergy between the habitus of the student and school mathematics, the greater the probability of success. In Bourdieu’s terms, the habitus thus becomes a form of capital that can be exchanged, within the field of school mathematics, for forms of recognition and validation that convert to symbolic forms of power. Such manifestations of this conversion can be seen in grades, awards, scholarships and other forms of accolade. For Aboriginal students, coming to learn school mathematics requires much more than coming to learn mathematics. Coming to learn mathematics requires a significant cultural and linguistic shift. In the following sections we provide some examples of how this may occur. Variables around language and patterns of interactions must be foregrounded.

Taking the communities of Central Desert lands, a common language among learners is Pitjantjatjara. In Pitjantjatjara there are only six prepositions, whereas English has 64, so one can only imagine how learners make sense of the differences between terms such as near, next to, beside, adjacent, left or right when talking about the relationship between two objects placed alongside each other. Similarly, Pitjantjatjara does not have language for comparisons, so terms such as larger, smaller, taller and tallest are not present in the home language. Whorfian theory (Chandler 1995) would suggest that the language and context shape the need for particular terms. As such, Pitjantjatjara learners not only have to learn the language of prepositions and comparisons, but also the deeply embedded concepts associated with such terminology. This is often difficult for those who have grown up with a language and have accepted the terms and concepts as a normal part of that language and culture. In this context, coming to learn the new concepts requires a reconstruction of fundamental learnings. For Bourdieu, this would require a reconstruction of the habitus. In his theory, the habitus is the internalisation of culture and provides a medium through which people interpret their worlds. The complexity of these relationships can be better understood when considering how difficult it would be for those living in temperate zones to imagine 32 different linguistic terms for the concept of snow. Yet, such challenges are what are imposed on Aboriginal learners as they enter mathematics (and other disciplines) in classroom settings.

The ways of interacting and communicating also need to be considered. One of the major aspects of classroom interactions is questioning. In western schooling the role of questioning is significant, but it violates the everyday use of questioning. Teachers use questions to elicit responses from students, even though they may know the answer. In everyday life the function of questions is to elicit responses for an unsolved problem. From a Bourdieuian perspective, the notion of ‘game’ becomes useful to theorise the role of questioning in classrooms. Bourdieu has employed the metaphor of a game to theorise how social practices enable some participants to be winners and others to be losers. The game metaphor is an apt one, as it offers a theorisation of how the practices within the teaching of mathematics enable some students greater access to mathematical knowledge while excluding others. Bourdieu (1990, 67) explains it in the following way:

The earlier a player enters the game and the less he is aware of the associated learning, the greater his ignorance of all that is tacitly granted through his investment in the field and his interest in its very existence and perpetuation and in everything that is played for it, and his unawareness of the unthought presuppositions the game produces and endlessly reproduces, thereby reproducing the conditions of its own existence.

The game, which in this case is questioning, often revolves around the students having to guess what the teacher wants or what is in the teacher’s head. The purpose of the question is not to find out an unknown piece of information, so when the teacher poses a question such as, ‘What is the sum of 16 and 35?’, the game being played is not one where the answer is unknown, but rather one in which the teacher elicits responses to identify which students have grasped the concept, which students may be experiencing difficulties with this type of addition, or which students have been able to transpose learning from one addition process to another. However, what happens in many Aboriginal classrooms is that the students appear to engage in a different game. Their game is one where they are seeking to please the teacher by offering responses, or offering responses to help the teacher work out the response, since clearly the initial (correct) response was incorrect, as she kept seeking other responses. We have observed this game in the Cape and Strait schools of far north Queensland in our Kimberley project and in the project located in the Central Desert area of Northern Territory. We suggest that in these contexts the mode for eliciting responses has been misinterpreted by the students. We contend that the students have engaged in a parallel game – not the game in which the teachers intended them to engage. The students’ responses are counter to the teacher’s goal and as such can be misinterpreted.

From these examples it begins to emerge that the social background of the students shapes their ways of seeing and interacting in the social world of the classroom. In other words, the habitus of the students provides a lens for seeing, interpreting and interacting in the classroom. However, for many Aboriginal learners that habitus is not aligned with the field of school or school mathematics. In conceptualising this observation within Bourdieu’s framework, what can be seen is that the social heritage of the students is in combat with the implicit rules of the classroom, thus making success in mathematics challenging. The (in)ability to morph from the habitus of the Aboriginal student to that of a learner of school mathematics demands significant reconceptualisation of the social background of the learner. Not only learning the language of English, with all of its nuances, and of mathematical concepts and processes, the Aboriginal learner must also come to understand, participate in and be successful with the dialogic interactions of the classroom banter. These are not insignificant challenges.

The fundamental assumption that underpins this chapter is that the social heritage of learners is a critical factor in their success. Where that social heritage becomes a strong feature of the habitus, which remains impermeable to change, there is a greater risk of failure within the school setting for students whose habitus is not aligned to the field. Using this as a principle, a significant challenge to views about innate ability and its relationship to success in school mathematics, or schooling in general, emerges. We contend that Aboriginal learners are highly intelligent and that their lack of success in schooling is not due to innate inability, but rather a clash between the practices of schooling and the social heritage of the students.

Scholastic mortality

So far we have highlighted the processes through which the field of school mathematics constructs and constrains access for particular learners. These processes are very subtle and often remain hidden to both learners and teachers, who have come to see school mathematics as an apolitical practice. However, this is the exact process through which hegemony is realised. For Aboriginal learners (along with other marginalised learners), the field of school mathematics remains relatively impermeable. This is not due to the innate abilities of learners, but manifests as a form of social marginalisation whereby the social heritage of the learner is at loggerheads with the objective and subjective structuring practices of the field. Consider the Aboriginal learners who come to school without the comparative signifiers and signifieds in their home language. The instructional discourse of the early years, where comparisons are an integral part of that discourse, are nonsensical: ‘Which number is bigger than…?’ ‘How many more is four than five?’ and so on. These types of questions fail to make sense to those whose home language does not have such comparative terms.

Some Aboriginal scholars and activists, such as Sarra (2007) and Pearson (2009), have strong views about the ways in which education needs to be provided for Aboriginal (and Torres Strait Islander) students. These align with the views in this volume expressed by Chris Sarra and Mick Dodson. We concur with the importance they attribute to having high expectations of students (and teachers) and placing the best teachers with Aboriginal students. However, we suggest that even with high expectations and great teachers, what is missing is the understanding of the symbolic violence that Aboriginal learners can experience when educators are not cognisant of the cultural norms and language nuances impacting on learning. What we have attempted to argue here is how coercive this process can be. Educators need to be astutely aware of how culture is implicated in learning and how this can be addressed to reduce the possibility of scholastic mortality among Aboriginal and Torres Strait learners. In the following sections we show how, in a practical sense, the practices of schooling manifest scholastic mortality for Aboriginal learners.

Scholastic mortality and NAPLAN testing

Within the Australian context, a national testing regime has been implemented. Since the mid-1990s, tests have been administered across most Australian schools. The test items have been challenged (Zevenbergen 2005) and shown to have a language and cultural bias. This bias significantly disadvantages Aboriginal learners, but particularly those who live in remote areas. Not only does the language and sociology of the testing process violate the students’ cultural and linguistic norms, but the items also fail to account for the contexts of these students. Imagine the ludicrousness of asking questions about inline skates to students who live in Central Desert regions, or conversions between English and Brunei currencies – yet such examples appeared in the 2008 tests. These may be challenging for urban students due to their context, but would be even more profoundly so for English-as-Foreign-Language learners such as the students in the Kimberley or Central Desert regions.

Funding models and reporting schemes, such as those included on the Australian Curriculum, Assessment and Reporting Authority (ACARA 2010) site, show schools’ results for the NAPLAN tests. The normalising processes associated with this ‘objective’ and standardised testing scheme are highly problematic. It is well documented that students from economically disadvantaged families, students living in rural or remote regions, students whose first language is not SAE and first Australians are the most at risk for poor performance on these tests. When Aboriginal students from Central Australian or Kimberley regions are considered, their levels of educational disadvantage are multiplied. Testing students does not make them smarter, but appropriate intervention can help to address the gross inequalities in education in this nation.

The structuring practices of school mathematics

In this section we draw on some practical examples from our work across Aboriginal contexts to highlight the problematic nature of school mathematics for Aboriginal learners, particularly those in remote areas of Australia. These are the students who are at most risk of scholastic mortality and who are the scapegoats for much current educational policy, especially the national testing regimes of Australia. Bourdieu differentiates between objective and subjective structuring practices. Zevenbergen (2005) has drawn on this framing for understanding the processes of streaming in mainstream schools. This same streaming is currently endemic in Aboriginal schools, where the ‘cream’ of the remote schools is being sent away to elite boarding schools in major urban areas. Despite decades of research into streaming, the highest achieving Aboriginal (and Torres Strait Islander) students are being sent to out-of-country sites to learn western ways of being. Aside from pragmatic issues around support for students out of country who are immersed in upper-class value systems, there remains the challenge of the circumstances for those who remain behind, as well as what happens to those students who leave country and acquire a taste of western life. This ‘brain drain’ from Aboriginal communities represents a challenge to those who remain in-country2 in so many ways.

Such objective structuring practices also need to be considered alongside subjective practices. Practices such as streaming produce effects on learners, who come to see themselves as successful (or not). In doing this, they internalise the outcomes in an insidious way, so that they are unquestioned and the internalisation of success or failure becomes the lens through which the learners see themselves. This subjective structuring practice now shapes how learners interact with mathematics – for example, as engaged or disengaged learners – which comes to influence how they interact with mathematics and education.

The status quo: Doing maths as it has always been done

In terms of curriculum, available text and other resources, assessment and system monitoring tools, and even learning programs, there is an implicit assumption by governments that mathematics will be taught the same way in Indigenous schools as in other schools. Indeed, there have been pushes for school curriculum to remain as it has always been and that anything less is an impoverished curriculum. However, there have been excellent examples of ‘two-way strong’ curriculum that include rigorous western knowledge systems but also embed traditional modes of learning and knowledge so that students get the best of both worlds (Harris 1990). A curriculum focused only on western values fails to recognise the obvious disconnect between ‘the culture of school mathematics and that which the learner brings to the school context’ (Jorgensen [Zevenbergen] in press), and that the chances of learning the conventional curriculum are limited by ‘linguistic, social and cultural habitus’ (5). It also fails to recognise and celebrate the strengths of the Indigenous culture of the groups. In this way the death of Aboriginal culture is almost certain. It should not be an either-or curriculum but one with high expectations of learning in and about both cultures.

In exploring the habitus of teachers and how they have framed mathematics learning, we asked teachers at Nyangatjatjara College to reflect on the challenges they are experiencing in teaching mathematics to Anangu learners, particularly in attempting to teach the students mathematical concepts and processes. They said that students:

  • tend to see mathematics learning as memorisation, and doing mathematics as remembering rather than reasoning
  • give up quickly when confronted with ideas with which they are not familiar
  • are unfamiliar with many fundamental concepts, even those that have practical significance such as comparative measurements and names and properties of plane shapes
  • experienced a curriculum that was not age appropriate and spent much time being taught material that they have previously encountered but not necessarily mastered
  • had difficulty in transferring skills learned in one context to another context
  • found it difficult to work with large numbers and more abstract ideas such as fractions and decimals.

While such difficulties are by no means unique to Indigenous learners, program designers seeking to engage Indigenous learners with school mathematics need to find ways to connect the mathematics to be learnt to the students’ social, cultural and linguistic backgrounds. The comments made by the teachers were framed in deficit models of thinking and failed to account for the differences between the two cultural systems. What remains clear to us is the need to work with teachers to move away from deficit models towards two-way models.

As a further exploration of the disjunction between students’ habitus and the curriculum with which they are expected to engage, we examined the assessment items on the Year 7 calculator-free 2008 Australian numeracy assessment, based on the context of money. It is noted that the government uses the results of this assessment to report on educational progress, and various compliance mechanisms are in place to ensure schools prioritise the content assessed by these tests.

There were four items on money. The first asked: ‘What is $10 as a percentage of $40?’ offering students four choices. Even though adults would more frequently find a given percentage of a money amount, this is a reasonable question. The second question presented drawings of a pair of inline roller skates, a cricket bat and a tennis racquet, labelled respectively at $42, $26 and $98. The question asked: ‘What is the best way to estimate the total cost of these three objects?’ and presented four choices, the correct one being ‘$40 + $30 + $100’. Even ignoring the unrealistic prices for these objects, the items seem a somewhat unusual collection for a national assessment that is presumably intended to be inclusive. Further, the form of the question is dependent on students having had experience with the notion of rounding as a way of progressively estimating money totals. The third item presented a two-way table of data, three rows by three columns, related to mobile phone costs, with a question that required reading and synthesising data from two columns. To answer the question, students needed to interpret text involving over 50 words and symbols, but the mathematical demand was that they merely add 12 and 28. The question assumes familiarity with mobile phone bills, tabulated data and sorting relevant from superfluous information. The fourth question required students to interpret two straight-line graphs and convert British pounds to Brunei dollars. There was a similar complexity to the text of the question and, for those students not familiar with the notion of three-way currency conversions, they would have to infer what the task was asking them to do.

The latter three of these items can hardly be considered culturally inclusive, and the reliance of the items on school content rather than realistic situations is an obvious example of how the social heritage of Aboriginal students is not considered in the design of the questions, thus creating greater opportunities for scholastic mortality. Imagine a question that was embedded in desert knowledge – the backlash from city and non-Aboriginal educators, parents and communities would have been forthcoming – but when the situation is reversed, there is silence as if there is no real educational challenge at all. It is also worth noting that the assessments not only communicate to students that school knowledge is not connected to what they know, but also reinforces to them that they are failing. Thus the objective and subjective structuring practices become obvious.

Finding ways to connect mathematics learning and student experience

In this concluding section, we suggest possible ways forward for teachers working in remote communities. To consider what the characteristics of a relevant curriculum might comprise, what follows draws on a series of teaching explorations at an Indigenous Community School in a remote region of Western Australia, which was part of the Maths in the Kimberley (2010) research project, conducted at the invitation of the Association of Independent Schools of Western Australia.

There are two main dimensions to connecting prospective learning with retrospective experience: the first is to identify ideas with which students are familiar and build on those; the second is to create connections between ideas that are fundamental to a modern mathematics curriculum and students’ prior experience. In exploring the former, it is possible to examine Indigenous languages to check mathematical ideas that are present in the culture. For example, in a publication that is both a language guide and dictionary for the Nyikina language (Jarlmadangah Burru Aboriginal Community 2003), one of the languages in the Kimberley region, there is a developed lexicon for place and direction words. For example, there are 18 different words for describing location, as well as four different expressions for each of the four compass directions, making a total of 34 distinct terms that can be used. It would be possible to use this language as a starting point for an exploration of modern mathematical concepts associated with location, direction, map reading, networks, and possibly even co-ordinate geometry.

In considering the latter dimension, it seems that both traditionally, as reflected in the language, and currently, in terms of the limited use of quantities in their everyday lives, number activities all tend to be remote from students’ experience. To overcome this, we are exploring ways of building connections between money, with which the students have some familiarity, and more abstract number ideas. This has its own challenges.

One of the products of this project is a set of recommendations to teachers that addresses both planning and pedagogy, and that encourages them to accommodate cultural, social and linguistic backgrounds of the students. We are conscious that inexperienced teachers sometimes err by underestimating the potential of the students and set expectations that are too low. Indeed, some structured programs also seem to adopt a deficit approach. Our perspective is that students benefit when teachers set high expectations and expect them to engage in the full range of mathematical actions such as understanding, problem solving and reasoning, not just fluency. On this point we concur with many Aboriginal educators, that having expectations of students (and teachers) is paramount to success in Aboriginal (and Torres Strait) education. In summary, our recommendations to teachers are:

 

  • Identify big ideas that underpin the concepts you are seeking to teach, and communicate to students that these are the goals of the teaching.
  • Build on what the students know, both mathematically and experientially, including creating and connecting students with stories that both contextualise and establish a rationale for the learning.
  • Engage students by utilising a variety of rich and challenging tasks, which allow students opportunities to make decisions and which use a variety of forms of representation.
  • Interact with students while they engage in the experiences; encourage them to interact with each other, including asking and answering questions; and specifically plan to support students who need help and challenge those who are ready.
  • Adopt pedagogies that foster communication and mutual responsibilities, and encourage students to work in small groups, where they can speak in home languages when communicating with each other, and use students’ reporting to the class as a learning opportunity.

 

Each of these recommendations is further elaborated for teachers. To see how they might apply, consider the following activity, adapted from the well-known and well-publicised work of the Shell Centre in the UK.

The task involves a set of cards containing a number of rows like the following (which address subtraction), with each row comprising four ways of representing a particular operation.

 

Image

The task involves connecting representations and being able to see that the mathematics needed to solve the problem in the first box is represented on the other cards. The activity addresses an important mathematical idea, it uses the notion of story, it is a variation on the conventional pen-and-paper form of representation, it is challenging, and it provides content that can form the basis of later reporting back by students.

There is a variety of ways in which the cards can be used. The teacher, for example, can invite students to discuss similarities and differences in the cards, sort them into groups, arrange them into order of difficulty, and so on. Certainly it is intended that students be given opportunities to make their own decisions. There are, though, still substantial challenges in using such a task.

Even though the task is designed to connect to a shopping context, with which it is hoped the students would be familiar, it can be anticipated that specific actions would be needed by the teacher to ensure that the task can be connected to the students’ social, cultural and linguistic backgrounds. For example, it might be necessary for the teachers to do what the National Accelerated Literacy program (Department of Education and Training Northern Territory 2009) terms as ‘putting the language through their system’, or what Munro (2003) calls ‘getting knowledge ready’. This might involve role plays of shopping, including giving change, or particular strategies such as chunking the key phrases in the text and deciding which phrases make a difference to the task and which are irrelevant to the mathematics, and searching for the words that identify the mathematical operation. This means that, after the activity, the reviews not only focus on revising such ideas, but also on the similarities and differences in the mathematical cards, the connections between the cards, and the ways of performing the operations on the cards.

Our experience with the Maths in the Kimberley project indicates that students at all levels can engage effectively with tasks such as these, as long as the teachers anticipate pedagogical pitfalls, and that with appropriate choice of task and pedagogical support, such tasks help form the bridge between the habitus of the students and the demands of school mathematics. By acknowledging the social heritage of the students, realising that this shapes their knowledge and ways of thinking and learning that they bring to the formal school context, and that all students can learn mathematics if they are provided with the right learning environments, then scholastic mortality will be reduced and, we would hope, eradicated. But much of this will depend on reshaping the habitus of teachers working in these regions.

Endnotes

1   As we are drawing on experiences from the Central Desert and the Kimberley regions, we are concerned with Aboriginal learners. We do not address issues around Torres Strait Islander people, but recognise their rights and ties to Australia and indigeneity in Australia.

2   Country is very strong to Aboriginal learners. Taking students out of country often creates new issues for learners, as they want to return to their country.

References

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Bourdieu, P. 1990. The Logic of Practice. Trans. Nice, R. London: Polity Press.

Bourdieu, P. 1991. Language and Symbolic Power. Trans. Raymond, G A M. Cambridge: Polity Press.

Bourdieu, P; Passeron, J C; de Saint Martin, M. 1994. Academic Discourse: Linguistic Misunderstanding and Professorial Power. Trans. Teese, R. Palo Alto: Stanford University Press.

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Closing the Gap in Education?

   by Ilana Snyder and John Nieuwenhuysen