The cultural interface in education

Martin Nakata’s seminal research on the cultural interface, initially applied to Torres Strait Islanders’ perspectives and experiences (1997) and consequently discussed more broadly in the context of Aboriginal and Torres Strait Islander studies and education (Nakata, 2007), can inform Indigenous education in Australia. The theoretical concepts of the cultural interface have been applied to the Australian school context, working on the interface of local Indigenous ways of knowing, being and learning and the demands of mainstream curricula (Yunkaporta & McGinty, 2009; Lowe & Yunkaporta, 2013). Further, the cultural interface informed research and development of Indigenous pedagogies (Yunkaporta, 2009; Yunkaporta & Kirby, 2011).

Professor Martin Nakata is the Director of Nura Gili at the University of New South Wales (UNSW) and holds the title of Chair of Australian Indigenous Education.

In this post, the cultural interface and related concepts are used to inform a culturally-responsive teaching practice in relationship to both non-Indigenous and Indigenous Australian school students. Such practice includes the development of culturally safe classrooms, the selection and presentation of culturally-appropriate curriculum content and the application of inclusive pedagogies. The post starts with introducing the theoretical foundations and concepts of the cultural interface, in particular the ‘corpus’ of Indigenous studies, ‘contested knowledge spaces’ and the ‘Indigenous standpoint theory’. Next, the cultural interface is applied to the classroom context, discussing implications for teaching Indigenous students, making curriculum choices and developing a culturally-safe teaching and learning space.

Next, the cultural interface is reviewed in terms of how it can inform the teaching of Aboriginal and Torres Strait Islander Studies, highlighting potential issues around representation of Indigenous content and knowledge. This is followed by investigating the 8 ways of Aboriginal learning (Yunkaporta & McGinty, 2009), a culturally-responsive pedagogical framework, as well as related Indigenous pedagogical concepts that draw upon the cultural interface to embed Indigenous perspectives (e.g. Grant, 1998; Graham, 1999; Carter, Cooper, & Anderson, 2016). The post concludes with a reflection on how the cultural interface can influence the teaching practice.

Summary of key concepts

Martin Nakata (2007) describes the dichotomy of non-Indigenous and Indigenous knowledge systems as a cultural interface of contested knowledge spaces. The disparate nature of western and Indigenous knowledge systems include different cosmologies (what can be known and the role of belief in evidence), ontologies (what makes knowledge), and epistemologies (who can be the knower, how truth is established and tested and the nature of inferencing). The cultural interface is also the intersection between non-Indigenous and Indigenous ways of:

  • knowing – including teaching and learning, making sense of the world,
  • being –  including self perception and perception of realities, as well as the process of making meaning, and
  • doing – what and how knowledge gets operationalised, including cultural and social practices.

Many aspects between western and Indigenous systems are different and on the surface can often appear contradictory and incompatible, such as a scientific geological description of landscape evolution versus its corresponding local dreamtime story. However, inherent in the cultural interface is the potential for a non-oppositional space of dialogue and reconciliation. Nakata and others (e.g. Green & Oppliger, 2007; Bala & Joseph, 2007; Yunkaporta, 2009) highlight opportunities for working at the cultural interface in a spirit of synergistic dialogue, mutual respect, reconciliation, and developing higher-order knowledge and innovation. In order to realise these opportunities, the recognition of institutionalised unequal power relationships between non-Indigenous and Indigenous participants in mainstream schooling, curricula content and pedagogies is essential. This recognition must come from a place of acknowledgment of the long and ongoing history of distorted representations of Indigenous knowledge and perspectives in Australia.

Nakata (2007) introduces the Indigenous standpoint theory as a tool for Indigenous participants to navigate the cultural interface . The standpoint theory is a theoretical approach that originated out of the feminist movement and articulates the experience of marginalised social groups who have been assigned a place and voice in society by others (Hartsock, 1983; O’Brien Hallstein, 2000). Accordingly, the social position of the knower defines his/her starting point, scope and experience of and engagement with potential knowledge. The Indigenous standpoint is produced by Indigenous experience and is an intellectual device to construct and reconcile an experiential subjective truth with dominant non-Indigenous theoretical knowledge. It allows Indigenous peoples to speak from their own cultural standpoint, maintain their forms of knowledge and present their own epistemological truth (Foley, 2006). The standpoint theory elevates the fact that knowledge, truth and experiences are intersubjective between participants. It also provides a rationale that not all conflicting truths need to be resolved (Nakata, 2007). Therefore, the Indigenous standpoint theory provides a conceptual entry point to a more level discourse otherwise framed by dominant western ontologies, epistemologies and objectified knowledge about Indigenous cultures.

Corpus is a term used in linguistics to describe a collection of samples of ‘real world’ data or texts. Nakata (2007) adapted the term in his Indigenous standpoint theory to describe and criticise the corpus of objectified knowledge, a body of cumulative knowledge produced about Indigenous peoples by non-Indigenous researchers studying Indigenous people, cultures and beliefs. This corpus is generated across academic disciplines, legislative and administrative bodies, and is distorted by the perceptual limitations and social agendas of the non-Indigenous knowledge makers. The corpus has historical foundations in anthropology. A good part of the corpus of objectified knowledge about Indigenous people is construed to justify and rationalise views of social Darwinism and white supremacy (Francis, 1996). It continues to define non-Indigenous and Indigenous relationships such as justifying the imposition of bureaucratic, managerial and disciplinary actions, and promoting deficit-framed stereotypes (Yunkaporta & McGinty, 2009; Fforde et al., 2013). Today, the corpus is increasingly inclusive of authentic Indigenous voices, but remains firmly seated within western knowledge-making traditions and paradigms (Nakata, 2007).

Implications of the cultural interface for working with Indigenous Australian students

Indigenous students are located at the cultural coalface of contested positions between traditional cultural knowledge, contemporary and often socially marginalised realities, projections of objectified “Indigenous” knowledge, and western curriculum demands. Life at school and at home can be a constant negotiation between contrary viewpoints, a tug-of-war between demands for alignment with either side, conflicting allegiances, a choice between opposition and assimilation. This can lead to ambiguity, internal conflict and physical and mental exhaustion (Nakata, 2007). The situation is compounded by the fact that Indigenous students often lack initiated traditional knowledge and the academic English meta-language to explain and argue their views and challenge the objectified corpus and any stereotypes.

In this situation, the first step towards working with Indigenous students in the classroom is to create a culturally-safe space. This can be achieved by a number of initiatives. At the classroom level, an inclusive environment must be established. Representations of Indigenous stereotypes and any deficit-framed depictions must be avoided, such as an overly focus on exhibiting traditional “primitive” tools and tokenistic artwork without local context and meaning (Yunkaporta, 2009). Instead, these representations can be replaced by a ‘Welcome to Country’ delivered by a local Elder, regular ‘Acknowledgment to Country’ (McKenna, 2014), representations of contemporary Indigenous culture and role models such as Indigenous sport heroes, artists, writers, inventors or Australians of the Year (Korff, 2016). Further, engagement with Indigenous parents and community leaders in the selection of authentic and meaningful material for displays can make a real difference in creating a culturally-responsive teaching and learning space (Harrison & Greenfield, 2011).

At the next level, valuing and utilising Indigenous staff and parents, including Indigenous teachers and teacher aides can make a significant impact in helping Indigenous students to navigate the cultural interface at school (Sarra, 2005; Queensland Government, Department of Education and Training (DET), 2015). The Queensland Government framework ‘Embedding Aboriginal and Torres Strait Islander Perspectives in schools (EATSIPS) (2015) provides additional guidelines for planning and developing culturally-appropriate curriculum materials, including aspects of how to best incorporate authentic Indigenous perspectives in content selection, as well as advice on culturally-appropriate pedagogies that value knowledges and resources Indigenous students bring to the classroom, elaborated in more detail below. Perhaps the most important aspect for working with Indigenous students at the cultural interface in school is to engage synergistically in the overlap between non-Indigenous and Indigenous realities and ways of knowing (Yunkaporta & McGinty, 2009).

Teaching Aboriginal and Torres Strait Islander Studies and representation of Indigenous peoples and cultures

Teaching Aboriginal and Torres Strait Islander content in the classroom requires a number of considerations. The first relate to the selection of teaching and learning material. Martin Nakata is explicit about problems inherent in the corpus of objectified knowledge about Indigenous Australians (2007). Many resources can be distorted and questionable, by promoting inaccurate generalisations, stereotypes and deficit perspectives. In order to address the potential for misrepresentations, the State of Queensland, Queensland Curriculum and Assessment Authority (QCCA) provides additional guidelines for embedding Aboriginal and Torres Strait Islander perspectives in schools by recommending five criteria for evaluating Indigenous teaching and learning resources (QCCA, 2010):

  1. Authenticity – including accuracy of statements made about Indigenous Australians, misrepresentation of Indigenous land use (e.g. terra nullius myth) and Indigenous resistance to European occupation, any generalisations made across multiple different groups of Indigenous peoples
  2. Balanced nature of presentation – critically review material for author bias, trivialisation and over-representations (e.g. importance of men’s roles, exclusive focus on Indigenous art in curriculum), negative stereotypes, overly focus on traditional and exotic cultural aspects
  3. Aboriginal and/or Torres Strait Islander participation – participation and acknowledgment of Indigenous authors in the research, writing and presentation processes
  4. Accuracy and support – looking for local relevance of material and endorsement by the relevant local Aboriginal education consultative and/or Indigenous community groups
  5. Exclusion of content of secret or sacred nature – engage in consultation with local Indigenous community to review material for any presentations of secret and/or sacred items, practices, sites, representations, as well as photographs and the names of deceased

While the above criteria address some of the main concerns about appropriate selection of Indigenous resources for the classroom, a critical application of the cultural interface concept is also concerned with how this material is presented (Nakata, 2007). First of all, there is the integrity of the knower, knowledge and practices. Some knowledge must be learned from the traditional holders of knowledge (i.e. Elders), while other knowledge is limited to local context and might require initiation. The teacher needs to develop a critical awareness on what can be presented, how and why, reviewing the value and application for her or his students, as well as any potential commercial or political interest behind resources. Finally, there is the peril of framing Indigenous knowledges in opposition to culturally-valued paradigms, such as Science. As Nakata remarked, Indigenous knowledge cannot simply be inserted into the curriculum without first developing critical awareness and acknowledgment of differences in knowledge spaces, in particular the discursive practices of the subject, differences in paradigms, philosophical positions, production technologies and practices and, last but not least, languages (2007). However, despite all these difficulties navigating the cultural interface between different systems of knowledges, the incorporation of Indigenous knowledge and perspectives into the classroom is an invaluable opportunity for students to generate dialogical exchange, reconciliation and create new knowledge (Bala & Joseph, 2007).

Pedagogical frameworks working at the cultural interface and embedding Indigenous perspectives

A number of pedagogies have explored ways to embed Indigenous cultural knowledge and lived experiences in ways that engage Indigenous students in the curriculum (Martin, Nakata, Nakata & Day, 2015). Perhaps the single most comprehensive pedagogical framework informed by the overlap of Indigenous and non-Indigenous learning processes at the cultural interface is the 8 ways of Aboriginal learning (8ways) (Yunkaporta & Kirby, 2011).

 8 Aboriginal Ways of Learning

8 Aboriginal Ways of Learning

This framework was developed by the James Cook University School of Indigenous Studies in collaboration with the Western New South Wales Regional Aboriginal Education Team and DET staff in 2007-2009 and emphasises Indigenous processes of knowledge transmission as opposed to the introduction of “indigenised” curriculum content. All eight pedagogical approaches are mutually beneficial for non-Indigenous and Indigenous students and include (Yunkaporta, 2009):

  1. deconstruct/reconstruct – starting all teaching and learning activities or texts with the big concepts and connections before going into details, elsewhere also referred to as holistic learning (Ryan, 1992)
  2. learning maps – developing concept maps and visual models as an anchor and reference point to the learning subject, elsewhere explored as narrative-spatial mapping of songlines as a culturally-specific and traditional mnemonic device (Uttal, 2000)
  3. community links – encouraging student engagement by positioning teaching and learning episodes in relation to community life and values, based on the premise that motivation for learning comes from social inclusion and building relationships (Kearney, McIntosh, Perry, Dockett, & Clayton, 2014)
  4. symbols and images – using concrete images and abstract symbols to support visual-spatial learners and to generate symbolic cues and anchors for teaching and learning units (Yunkaporta & McGinty, 2009)
  5. non-verbal – allowing students to critically test new knowledge non-verbally through experience, introspection and practice (Wheaton, 2000)
  6. land-links – place-based education building on Indigenous connections between place/space and knowledge, supporting experiential learning and emphasising local relevance, ecological applications and outdoor education (Cameron, 2014)
  7. story-sharing – actively involving students in introspection and analysis through personal narratives, a traditional knowledge-transmission format that is central in all Indigenous pedagogies (Wheaton, 2000)
  8. non-linear – by supporting non-sequential, cyclical and lateral thinking, any perceived dichotomies of opposing views at the cultural interface can be avoided by allowing for complementary experiences and knowledges, as well as encouraging creative thinking (e.g. De Bono, 2010)


Elements of the the 8ways pedagogical framework can be found in other pedagogies working at the cultural interface. Uncle Ernie Grant’s My Land My Tracks (1998) connects the concept of land, language and culture in the context of time, place and relationships, thereby focusing on land links and community links. YuMi Deadly Maths (Carter et al., 2016) emphasises aspects of working with symbols and images and the deconstruction and reconstruction of knowledge. Aunty Mary Graham emphasises the importance of non-linear logic in accommodating logically opposing knowledge systems at the cultural interface (Graham, 1999). The 8ways framework is also compatible with the Productive Pedagogies framework that emerged out of the Queensland School Reform Longitudinal Study and informs inclusive teaching practices in Australia with particular emphasis on high intellectual quality, relevance and connectedness to students’ lives, creating supportive classroom environments, and valuing and working with difference (Mills et al., 2009). The promotion of high intellectual expectations combined with the provision of high support and scaffolding is an important addition to the 8ways pedagogical framework and addresses the first goal of the Melbourne Declaration on Educational Goals for Young Australians which explicitly states the importance of promoting high expectations for the learning outcomes of Indigenous students (Barr et al., 2008).

Relevance of the cultural interface for teaching practice

The ‘cultural interface’ between non-Indigenous and Indigenous participants in a teaching and learning community is one of contested knowledge spaces framed by challenges as well as great opportunities (Nakata, 2007). In order to navigate this interface, teachers first and foremost need to be respectful of and interested in Indigenous cultures, perspectives and knowledge-making practices. Teachers will also need to be critically aware of their own cultural capital and be sensitive to its potentially marked incongruence with the cultural and social capitals or “virtual schoolbags” of their students (Thomson, 2002). Indigenous students face many “foreign” curriculum demands, economic, political, ideological, linguistic and pedagogical practices in mainstream schools. This situation can result in the rejection of and opposition to a school system perceived as disempowering and irrelevant (Groundwater-Smith, 2009). Therefore, teachers need to be clear about the historical and cultural nature of the curriculum and discipline knowledges, and not simply assume the dominant heuristic method to be universal and superior to others. It is essential for teachers to refuse the misperception that schools can only offer constrained choices between non-Indigenous and Indigenous knowledge and perspectives. Here, working with the cultural interface can offer a shared or third cultural space (DET, 2010) with promises of cogenerative dialogue, reconciliation, and new knowledge creation (Nakata, 2007; Bala & Joseph, 2007; Yunkaporta, 2009).

Teachers needs to be careful not to teach a simplistic and imagined Indigenous past. Instead they need to support students with the knowledge, skills and practices that will allow them to confidently establish their unique perspectives in our complex, ever-evolving and increasingly global world. Indigenous knowledges are best included in respectful consultation with socially-recognised ‘knowers’ among Indigenous parents and the local Indigenous community (Kearney et al., 2014). Teachers need to be aware that some knowledge requires a spiritual and location-based context that might extend beyond the possibilities of their classroom (DET, 2015).

The constant demands of navigating multiple cultural ways of valuing, being, doing and knowing (Lowe & Yunkaporta, 2013) can create physical, cognitive and emotional tensions in Indigenous students, their parents and carers (Nakata, 2007). Therefore, it is essential that teachers create a culturally safe and inclusive teaching and learning space in their classrooms, and look for opportunities in the curriculum to include authentic and relevant Indigenous perspectives and content. Perhaps most importantly, teachers should work with culturally-responsive pedagogies in “doing knowledge” that engage and empower all his students (Woods, 2013). Finally, teachers must challenge the institutionalised deficit induction around Indigenous students and their capabilities (Yunkaporta & McGinty, 2009) by setting high academic expectations (Sarra, 2005; Mills et al., 2009; Woods, 2013; Chaffey, Bailey, & Vine, 2015).

All of this can seem a daunting task. However, the fact that education is one fundamental pathway towards offering Indigenous Australians a more prosperous future, strong and positive identities and opportunities to better support their families and communities, can serve as a strong motivation. Teachers will receive support on the way of their professional journey, through recognition of their efforts by Indigenous students, parents and community members, as well as across the teaching profession which increasingly recognises the need to improve educational outcomes for Aboriginal and Torres Strait Islander students (Barr et al., 2008; Burgess & Berwick, 2009; Australian Institute for Teaching and School Leadership, 2014, i.e. Australian Professional Standards for Teachers 1.4 & 2.4).

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On the importance of being numerate

Numeracy, also called Quantitative literacy and Quantitative reasoning, is a relatively new term describing the applied facets of mathematics in daily life and modern society. The Australian Curriculum defines numeracy as “… the knowledge, skills, behaviours and dispositions … to use mathematics in a wide range of situations. It involves […] recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully” (Australian Curriculum, Assessment and Reporting Authority, 2016a).

Applied mathematics were used in certain professions since pre-historic times. The great ancient civilisations that built perfectly geometric pyramids, temples and planned cities on the river banks of the Nile, Euphrates and Tigris, and Indus-Sarasvati developed an advanced understanding of numbers. However, the conceptional leaps in our theoretical understanding of mathematical concepts, as for example those developed by Thales of Miletus and Pythagoras of Samos in the 6th century BCE, were not widely applied until the Renaissance. Only since the 17th century, did mathematics really start to inform all areas of human endeavour, including the Arts, Humanities, and Science, becoming an increasingly central tool to manage and model our affairs and the environment (Madison & Steen, 2007). Fast forward to the 21st century and mathematics and numeracy are at the core of how individuals and society operate, connecting everything in the ‘Internet of Everything’ (IoE) linking people, things, processes, and ‘Big Data’ (Karvalics, 2014). As a result, numeracy is fast becoming a central pillar of education, with school curricula all over the world being rewritten in its favour.

Initially, the term numeracy was introduced within the school context by two influential school reports in the United Kingdom (UK) in 1959 and 1982, defining numeracy skills relating to what students “can do” with mathematical knowledge, as opposed to what mathematics students “know”. Since the beginning of the new millennium, the OECD Program for International Student Assessment (PISA) started assessing numeracy skills internationally, thereby further promoting its prominence in curricula (Madison & Steen, 2007). This post outlines the importance of being numerate for the individual and society at large, and discusses the role that we can play as effective primary school teachers in developing critical numeracy skills in our students.

The importance of numeracy skills for the individual

According to late Lynn Steen’s widely cited monograph (Vacher, 2016) on numeracy “Mathematics and democracy: The case for quantitative literacy” (Steen, 2001b), numeracy skills are required in all quantitative aspects of life, such as solving practical everyday problems and logical reasoning. This requires individuals to have the ability and inclination to draw on a range of mathematical concepts and tools, and to display a strong number and symbol sense (Goos, Dole, & Geiger, 2012). In contrast to formal mathematics that operate within an abstract world, numeracy is mathematical knowledge and skills applied to ‘real world’ situations. Numeracy skills shape the reality of 21st century citizens in very concrete ways:

  • Mobility: With an urbanisation rate of close to 90%, most Australians are dependent on public transport or the road system to navigate from home to work and to access basic services such hospitals or shopping centres. To effectively use public transport, a number of numeracy skills are required, including the ability to read time tables, calculate the estimated time of arrival, transfer times, change platforms, and to understand the fare system often involving machines, swipe cards, PIN numbers and complex tariffs. Using the public road system involves even more complex numeracy skills, such as the ability to read street symbols (eg. traffic signs), monitor travel speed, estimate safe driving distance, and calculate optimal routes involving maps or tools such as a GPS. For most individuals, the desire for spatial mobility can extend beyond the city they live in, for example when planning an overseas trip, which would involve the comparison of complex fares including taxes, hotel rents, sequential check-in and transfer procedures, limits on luggage number and weight, as well as time-zone and currency related conversions.
https://en.wikipedia.org/wiki/Pythagoras

Numeracy in action: public transport

  • Health: The correlation between poor health literacy and poor health is well documented. Health literacy, can be defined as the degree to which an individual can make informed health-related decisions based on acquiring, processing and understanding basic health information and services (Mantwill, Monestel-Umaña, & Schulz, 2015). Numeracy plays a dominant part in health literacy, and includes aspects such as understanding nutrition information on food labels, interpreting clinical data (eg. blood sugar readings), refilling prescriptions and adjusting medications, and understanding probability in health risks. Numeracy skills are particularly important for patients with chronic illnesses that rely on self-management and self-administration of treatments (Rothman, Montori, Cherrington, & Pignone, 2008). More indirectly, health can be effected by poor self-esteem and depression which is often accompanied with poor literacy and numeracy skills.
nutrition fact label

Numeracy in action: healthy nutrition

  • Wealth: The biggest impact of poor numeracy skills on personal wealth is arguably in the form of foregone or lower earnings reflected in typically higher unemployment or temporal employment rates and lower wages. While difficult to quantify, because of the close association between poor numeracy skills and other potentially controlling factors (eg. poor literacy, gender, race), there is a strong correlation between numeracy skills, employment rates, and wage distribution (Grinyer, 2005; Pro Bono Economics, 2014). Individuals with low numeracy skills are not only statistically more likely to earn less, but also face difficulties in controlling their household spending. Poor numeracy is adversely affecting individuals in managing spending when it comes to shopping, leisure, as well as more complex financial products such as mortgages and other forms of credit and debt, including any associated levels of interest (Graffeo, Polonio, & Bonini, 2015; Pro Bono Economics, 2014).
interest amortisation chart

Numeracy in action: finance

  • Decision making: Informed decision making plays a critical role in our ability to take control of our life, by helping us to realise opportunities and limi risks. Numeracy skills impact all aspects of logical thinking and strategic planning: from the accurate analysis of the present situation, the pursuit and acquisition of relevant missing information and knowledge, to the weighting of advantages and risks (Goos et al., 2012). Most informed decisions are based on a thorough evaluation of quantitative, spatial and probabilistic information, and require a high level of number and symbol sense, as well as the ability to project different scenarios along timelines into the future.
decision making

Numeracy in action: informed decision making

  • Personal stability: As a result of the interplay of these factors within the wider social context that an individual operates in, poor numeracy skills can adversely impact self confidence and personal stability. Adults with poor numeracy skills are often characterised by impulsive and erratic behaviours, emotions, and a lack of self-regulation strategies. The development of numeracy skills directly contribute to growth in personal and social confidence. While the relationship between crime and numeracy is another area that is difficult to define in terms of statistical significance and causes and effect, the majority of adults in UK police custody are found to display substandard numeracy skills (Parsons & Bynner, 2005, figure 8, p.29).

Numeracy in action: self efficacy

The importance of numeracy skills for society

How numeracy skills within a population impact a society at large is a relatively new research field with the first comprehensive study undertaken by the (US) National Council on Education and the Disciplines (NCED) at the beginning of our new millennium (Steen, 2001b). However, as the NCED Executive Director at the time pointed out, the potential impact of literacy and numeracy on society has been understood since WWI, quoting John Dewey (1931) in that “successful democracy is conceivable only when and where individuals are able to ‘think for themselves,’ ‘judge independently,’ and discriminate between good and bad information” (Orrill, 2001). In our data-driven information age, the level of numeracy of its citizens has significant implications for a society:

  • Democracy: A democracy is based on citizens executing their rights to shape political decisions by forming opinions on a wide range of subjects. Historically unprecedented quality of (and access to) numerical information can strengthen the foundations of democratic by informing public discourse and civic decision making. However, if large parts of the society lack the ability to think numerically, to recognise how quantitative information and their presentation can inform and shape (manipulate) opinions on political, social, and environmental issues, they cannot fully participate (Orrill, 2001). As a result, poor numeracy skills across a population can pose a real danger to democratic societies by potentially strengthening populist movements and demagogues who master the art of manipulating data and discourse with misinformation.

Numeracy in action: informed voters

  • Economy: In recognition of the increasing importance of numeracy on the national economy, some governments like in the UK started to commission studies investigating the economical costs associated with poor adult numeracy (Pro Bono Economics, 2014). First estimates go into the tens of billions of dollars and are calculated based on forgone or lower tax revenues, lower productivity of the workforce, and exchequer costs associated with benefit payments to jobseekers and jobless. As economies are becoming more global, competitive, and based on advanced knowledge and skills, the overall level of adult numeracy is increasingly defining the place of a society in the global market space.

Numeracy in action: economic growth

  • Social: The impact of quantitative literacy levels on society extends well beyond the political system and national economy into the social realm. As broached above, there is relationship between poor numeracy on individual physical and mental health, which can negatively impact both health and criminal justice systems. While difficult to measure and quantify, the assumption can be made that misguided decisions based on ignored or misread numerical data will limit the prospects and prosperity of future generations and ultimately strain the social fabric of a society.

Numeracy and our role as teachers

The mismatch of traditional mathematics curricula and the demands of today’s societies for applied quantitative literacy skills became apparent only in recent years. There is also a dawning realisation that numeracy cannot be taught alone within the mathematics classroom, but instead requires a dedicated approach across all learning areas (Steen, 2001a; Wade, 2001). “Numeracy is not just one among many subjects but an integral part of all subjects” (Quantitative Literacy Design Team, 2001, p.6).  In developing the Australian Curriculum, Australia seized the historic chance to highlight numeracy content and opportunities across all key learning areas (Australian Curriculum, Assessment and Reporting Authority, 2016a). It is now our role as teachers to develop and realise numeracy opportunities in the classroom.

The first step towards effectively teaching numeracy is developing a solid theoretical understanding of all numeracy components that can be applied within the classroom context. This can be informed by the “quantitative literacy elements” compiled by NCES (Quantitative Literacy Design Team, 2001, pp.8-9):

  • developing confidence in estimating, calculating, interpreting, and presenting quantitative data
  • developing appreciation of the role of numeracy in the ‘real world’, linking to technological progress, scientific inquiry
  • developing competence in reading and analysing data, including creating an awareness for errors
  • developing logical thinking and decision making based on evidence, evaluation, and risks and benefits assessment
  • developing practical skills in approaching ‘real world’ problems with numerical tools
  • developing number sense in understanding the meaning and relationships of numbers, units, mathematical operations in context
  • developing symbol sense in understanding syntax and grammar of mathematical symbols

The next step is to investigate and highlight numeracy opportunities specific to key learning areas in the Australian Curriculum (Australian Curriculum, Assessment and Reporting Authority, 2016b):

  • English: numeracy skills support reading comprehension and writing, in particular relating to document structure, systematic procedures, and the detection of assumptions in scientific texts
  • Health and Physical Education: numeracy skills are required to understand time and unit measurements, statistics related to competitions and training, monitoring of health or performance related parameters, and developing team strategies
  • Humanities and Social Science: numeracy skills assist in understanding data either from censuses, historical and archaeological records, and to read and communicate information in graphs and infographics. In Economics and Business, number sense and logical thinking can be developed by evaluating opportunities and risks
  • Mathematics: provides the required tools and problem-solving strategies for numeracy skills
  • Science: numeracy skills are developed by interpreting statistics (eg. laboratory experiments), probability and calculus (eg. rates of change, heredity). Chemistry and Physics provide great opportunities to develop and apply symbol and number sense
  • Technologies: offer a range of numeracy applications including those related to geometry, computer algorithms, and database queries
  • The Arts: are increasingly based on digital technology and editing tools. However, even traditional Music and Dance education offer numeracy aspects such as rhythm and balance, providing “embodied” numeracy opportunities

Our role as teachers is to employ effective numeracy teaching strategies. In recent years, a number of studies in Australia and overseas evaluated teacher knowledge and classroom culture to define the most successful numeracy teaching approaches (Stephens & Australian Council for Educational Research, 2009). Mathematical Pedagogical Content Knowledge (MPCK) is the ability of teachers to make mathematical content accessible to students by building on prior knowledge and skills to bridge knowledge gaps. MPCK was found to be the most important variable that defines effective numeracy teachers. A number of “scaffolding practices” can support numeracy learning, including teaching strategies such as excavating, collaborating, probing, orienting (Stephens & Australian Council for Educational Research, 2009, table 5.1, p.31).

In terms of classroom organisation, a UK study by Askew, Brown, Rhodes, Johnson and Wiliam (1997) concludes that the most effective teachers of numeracy are ‘connectionist teachers’; teachers who use children’s prior knowledge and approaches and employ teaching strategies that emphasise making practical connections with mathematical concepts. All this suggests that numeracy is best taught by combining ‘constructivist learning’, where students build new knowledge on top of prior knowledge through exploration, with elements of pedagogically informed ‘direct teaching’, where teachers provide high-level questioning, guidance, and probing. This is supported by recent studies that conclude that the approach of combining ‘direct teaching’ with instructional interactions between teacher and students are most effective in teaching mathematical ideas, terminology and procedures, while cultivating student engagement and content relevancy (Stephens & Australian Council for Educational Research, 2009). Instructional interactions include discussions that encourage students to explain their thinking, share approaches to problem solving, and transfer existing skills to new contexts.

Finally, there are the practical teachings tools and activities to consider. Research suggests that while ‘ability grouping’ students in general can be problematic, task-specific work in small mixed-ability groups are likely to benefit low-ability and average-ability students (Council of Australian Governments & Human Capital Working Group, 2008). As for finding activities that are appropriate to the year level and target specific aspects of numeracy, professional journals such as the “Australian Primary Mathematics Classroom” (eg. Muir, 2012, on number sense; Hurrell, 2013  on measurements), dedicated numeracy content websites such Numeracy Continuum (New South Wales, Department of Education, 2016), and professional content forums such as Australian Curriculum Lessons (Australian Curriculum Lessons, 2016) all provide great points of departure.

Conclusion

The primary school students of today will grow up in and shape a world that is increasingly defined by digital data and processes that will require solid numeracy skills to master. It has become increasingly evident over the last decades that poor quantitative literacy skills have direct and substantial implications for individuals and the society at large. As a result, teaching numeracy skills becomes a priority for schools everywhere. While based on formal mathematics, numeracy is much more than Maths. Numeracy is applied quantitative knowledge and skills and expands into all key learning areas. It is a new “language” or literacy that teachers need to teach within and outside the mathematics classroom. To quote late Lynn Steen: “numeracy will thrive […] because it is the natural tool for comprehending information in the computer age. As variables and equations created the mathematical language of science, so digital data are creating a new language of information technology” (2001b, p.111).

While this might seem a daunting task to some classroom teachers, at least in Australia can build on the new Australian Curriculum that emphasises numeracy across all key learning areas. There is also a growing number of resources providing profession digital content that can inform our teaching strategies and support our lesson planning. Numeracy is now considered so important in Primary Schools that other learning areas are being reduced and combined to achieve a “laser-like focus on literacy and numeracy” (Education Minister Christopher Pyne, 2015, cited in The Australian (Bita, 2015).

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