Teaching and learning Maths: using Maths apps

Benefits of apps to the Maths teaching and learning process

With the widespread introduction of mobile learning technology to Australian classrooms (i.e. iPads), an unprecedented development of educational software (apps) takes aim to complement traditional teaching. The potential benefits of apps need to be critically appraised for their pedagogical content, learning-area specific knowledge and technological requirements and ease of implementation (Handal, Campbell, Cavanagh, & Petocz, 2016). The emerging research suggests that the use of iPads in primary school Mathematics classrooms has great potential to develop and maintain positive student attitudes (Hilton, 2016) and support self-paced learning. However, research also points out that individual apps can have both supportive and inhibitive consequences on students’ learning performance and efficiency, depending on the student, prior instruction and the phase in the learning and teaching cycle (Moyer-Packenham, 2016).

Examples of three Maths apps

  1. Mathletics by 3P Learning Australia, Sydney. Mathletics is the most widely used app in Australian primary schools with comprehensive modules that complement for the K-12 Maths curriculum. (see more detail below)

Screenshot of Live Mathletics challenge

  1. Khan Academy, Mountain View, California.
    Khan Academy started out as a content provider of free educational movies and since evolved into student-centred learning app with a strong focus on Maths, with recent initiatives towards more international curriculum alignments (Khan Academy, 2017).

 Khan Academy Maths opening page

  1. LÜK-App by Westermann Gruppe, Braunschweig, Germany.
    German curriculum-aligned quality app with a unique gamified approach towards learning, including all areas of Maths covered in primary schools (no German knowledge required)
LÜK app Maths task example

LÜK app Maths task example

Detailed description of Mathletics

Mathletics software is developed in Sydney since 2004 and is marketing itself by stating that Australian schools that use Mathletics are performing significantly better in NAPLAN tests, irrespective of their socio-economic and regional status (Stokes, 2015). While running as an app, Mathletics is more of a comprehensive cloud-based educational platform offering school and class management tools, individual student learning pathways, global online competitions, and professional teacher training courses. The author has been using this app with his daughter throughout F-Year 3 and is particularly impressed with the pedagogical quality that went into the sequential buildup of mathematical concepts, the comprehensive content and close alignment with the Australian Curriculum (Australian Curriculum, Assessment and Reporting Authority, 2017), the quality of technological implementation and support. It is one of the few Maths apps that combines declarative, procedural and conceptual knowledges (Larkin, 2015).


  • Australian Curriculum, Assessment and Reporting Authority. (2017). Home/ F-10 Curriculum/ Mathematics.
  • Handal, B., Campbell, C., Cavanagh, M., & Petocz, P. (2016). Characterising the perceived value of mathematics educational apps in preservice teachers. Mathematics Education Research Journal, 28(1), 199-221.
  • Hilton, A. (2016). Engaging Primary School Students in Mathematics: Can iPads Make a Difference?. International Journal of Science and Mathematics Education, 1-21. DOI 10.1007/s10763-016-9771-5
  • Khan Academy. (2017). An uncommon approach to the Common Core.
  • Larkin, K. (2015). “An App! An App! My Kingdom for An App”: An 18-Month Quest to Determine Whether Apps Support Mathematical Knowledge Building. In Digital Games and Mathematics Learning (pp. 251-276). Springer Netherlands.
  • Moyer-Packenham, P. S., Bullock, E. K., Shumway, J. F., Tucker, S. I., Watts, C. M., Westenskow, A., … & Jordan, K. (2016). The role of affordances in children’s learning performance and efficiency when using virtual manipulative mathematics touch-screen apps. Mathematics Education Research Journal, 28(1), 79-105.
  • Stokes, T. (2015). National Numeracy Study Mathletics and NAPLAN. 3P Learning Australia Pty Ltd.

Teaching and learning Maths: multiple representations of concepts

Multiple representations

The representation of mathematical concepts and objects plays an important discipline-specific role. Doing Maths relies on using representations for otherwise inaccessible mathematical objects. The concept of multiple representations (MR) has been introduced to teaching and learning of mathematics in the 1980’s (i.e. Janvier, 1987). Some primary school curricula (e.g. Germany) highlight MR as a key mathematical idea (Leitidee) (Walther, Heuvel-Panhuizen, Granzer, & Köller, 2012), while the Australian Curriculum (v8.2) includes specific references to some year-level proficiency standards (ACARA, 2016). This could reflect that different mathematical content domains apply particular kinds of representations (Dreher & Kuntze, 2015).

Benefits and difficulties

Research emphasises both the importance of MR to developing mathematical understanding and the difficulties that can be faced by learners (Ainsworth, 1999). Multiple representations can make all facets of mathematical objects visible. The ability to move between different representations is key to develop multi-faceted conceptual mathematical thinking and problem solving skills (Dreher & Kuntze, 2015). The difficulty with MR is that no single representation of a mathematical object is self-explanatory. Each representation requires understanding of how this representation is to be interpreted mathematically, and how it is connected to corresponding other representations of the object. These connections must be made explicit and require learning that engages higher cognitive levels. Interpreting individual representations, making connections between MR of corresponding mathematical objects, and changing between MR can present significant obstacle to learners (Ainsworth, 1999).

Sequencing the introduction of multiple representations

Booker, Bond, Sparrow & Swan (2015) highlight the importance of gradually sequencing the introduction of MR from the concrete to the abstract over time and identify the functions that MR can serve in developing mathematical understanding.

One such sequence is illustrated for content domain ‘geometry’ (compare ACMMG137) by applying the five ways of working (Battista, 2007).

Step 1: Visualisation of spatial arrangements – Students are provided with the following A4 template and are asked to cut out Tangram pieces along the blue lines and arrange them in one row by size.

A4 tangram template for students to cut out

Step 2: Development of verbal and written communication skills – Students are asked to discuss and describe their size order using explicitly taught concepts of ‘area’ and the small triangle as ‘1 unit’.

Tangram pieces sorted by size

Step 3: Symbolic representation through drawing and model making – Students are asked to colour their tangram pieces and puzzle the objects of projected image below (rotation, transformation)

Example colours for student tangrams

Step 4: Concrete and abstract logical thinking – Students are asked to create a column chart of the number of units (triangles) within each shape (colour). Students are allowed to cut one set of shapes into triangles (working in pairs).

Column chart depicting number of triangle units for each (coloured) tangram piece

Step 5: Application of geometrical concepts and knowledge – Students are asked to investigate how many different parallelograms they can form and the number of units required. Next, they measure and calculate the base unit and apply multiplication to calculate the areas.


Smallest possible parallelogram consisting of 2 small triangle units

2 units, 2 x 8 cm2 = 16 cm2

Largest possible parallelogram consisting of 16 small triangle units

16 units, 16 x 8 cm2 = 128 cm2


  • Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33(2), 131-152.
  • Australian Curriculum, Assessment and Reporting Authority. (2016). Home/ F-10 Curriculum/ Mathematics.
  • Booker, G., Bond, D., Sparrow, L., & Swan, P. (2015). Teaching primary mathematics. Fifth edition. Pearson Higher Education AU.
  • Battista, M. T. (2007). The development of geometric and spatial thinking. In Lester, F.K.Jr. (Eds) Second handbook of research on mathematics teaching and learning, Volume 2. National Council of Teachers of Mathematics, 843-908.
  • Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89-114.
  • Janvier, C. E. (1987). Problems of representation in the teaching and learning of mathematics. Centre Interdisciplinaire de Recherche sur l’Apprentissage et le Développement en Education, Université du Quebec, Montréal. Lawrence Erlbaum Associates.
  • Walther, G., Heuvel-Panhuizen, M. V. D., Granzer, D., & Köller, O. (2012). Bildungsstandards für die Grundschule: Mathematik konkret. Humboldt-Universität zu Berlin, Institut zur Qualitätsentwicklung im Bildungswesen.

Teaching and learning Maths: constructing a rubric

Purpose of a rubric

A rubric is a tabular set of criteria for assessing student knowledge, performance or products, informing the teaching and learning practice. Each line details criteria that are being assessed, each column the expected or achieved quality of learning (depth of understanding, extent of knowledge and sophistication of skill) by the student.

Rubrics are an assessment and reporting tool used to make expectations explicit to students, identify areas that require practice, and for self-assessment purposes (State of Victoria, Department of Education and Training, 2013). Rubrics are used to report learning outcomes to students, parents and carers, and can guide them towards flipped-classroom activities to improve individual results.

Key points in constructing a rubric

Formal grade achievements follow the five letter ratings, where ‘C’ indicates that a student is performing at the standard expected of students in that year group (ACARA, 2012).

Descriptors can be adapted and simplified for formative assessment purposes. The teacher selects aspects that are being assessed (criteria) and describes how achievements will be measured. ‘SMART’ criteria (O’Neill, 2000) (‘S’ – specific, ‘M’ – measurable, ‘A’ – attainable and agreed, ‘R’ – relevant to curriculum, ‘T’ – time-bound which means year-level appropriate) and Bloom’s taxonomy (Anderson, Krathwohl, & Bloom, 2001) can guide this process. Rubrics need to be designed and written in a language accessible to students, parents and carers.

Setting SMART goals for your students


This is an example for a 3-criteria, 3-descriptor rubric Year 6 lesson based on content descriptor ACMMG137 “solve problems involving the comparison of lengths and areas using appropriate units“. It is designed for formative teacher assessment, and to provide students with feedback on how they currently meet expectations and what differentiated homework tasks will help them to improve results.

excellent satisfactory practice more!
‘Area’ conceptual understanding

Excellent understanding, demonstrated in designing tangram shapes of equal area

Homework: Solve expert puzzles

You can define and explain ‘area’ but need more practice in applying your knowledge

Homework: Watch tangram movie and play more tangram

Your understanding of area needs more practice

Homework: Review area movie and tangram movie

‘Area’ problems with simple units

You are fluent in generalising any tangram puzzle in terms of parts and multiples of units

Homework: Design a tangram puzzle for the class to solve next lesson

You competently calculate basic areas as parts or multiples of tangram triangles. Practice applying this understanding to more creative tangram figures

Homework: Create figures 1, 3 and 4 and write down the number of small triangles required for each animal head

You can describe the shapes but need more practice to calculate how they relate to each other in terms of ‘area’

Homework: Complete worksheet by writing down the number of small triangles required for each shape

‘Area’ problems with metric units

You are fluent in reframing geometric shapes in ways that allow you to calculate their area

Homework: Work on area calculations for more complex shapes in this worksheet

You can calculate areas of simple geometric forms by describing them as parts or multiples of rectangles. Work towards extending your understanding to complex shapes

Homework: Complete area calculation worksheet

You can measure the sides of geometric shapes but need more practice calculating their related ‘areas’

Homework: Review area movie and calculate these areas of shapes

Structuring slides of associated lesson


Teaching and learning Maths: unit and lesson planning process

Purpose of mathematics planning

Unit and lesson planning are critical steps in the teaching and learning cycle among assessment, programming, implementation, evaluation and reflection. The objective of the planning process is to provide all students with appropriate learning experiences that meet the demands of the curriculum in terms of expected learning outcomes.

Major steps in the planning process

  1. Relate teaching and learning goals to the Australian Curriculum (ACARA, 2016) relevant year-level descriptions, content and proficiency strands
  2. Check year-level achievement standards and illustrations of graded work sample portfolios to inform assessment criteria guiding planning process
  3. Develop challenging but achievable goals, considering the individual learning needs of all students based on diagnostic and formative assessments
  4. Design sequence of activities, instructional scaffolding and learning extensions that build on existing student knowledge following the ‘gradual release of responsibility’ model (Fisher & Frey, 2007)
  5. Evaluate achieved learning outcomes to inform subsequent lesson planning and to ensure that all students are on a trajectory to achieve best possible outcomes

Personal reflection on the process

The described back-mapping approach makes teaching and learning goals explicit and central to the planning process. By making learning intentions and expected outcomes explicit to the students at the beginning of each lesson and reviewing both at the end, students can develop a clear understanding of expectations and a reflective practice.

Planning is essential to deliver effective lessons that engage all students with appropriate learning activities. These can be informed by Bloom’s taxonomy of learning (Anderson, Krathwohl, & Bloom, 2001), as well as Gardner’s multiple intelligences (Gardner, 2006) to cater for the full spectrum of abilities with group work, targeted teacher aide support, differentiated homework and modifications to assessments.

Blooms taxonomy applied to Maths

Blooms taxonomy applied to teaching and learning Maths (Resource can be downloaded for free on Tes Global Ltd)


  • Australian Curriculum, Assessment and Reporting Authority. (2017). Home/ F-10 Curriculum/ Mathematics.
  • Anderson, L. W., Krathwohl, D. R., & Bloom, B. S. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Allyn & Bacon.
  • Fisher, D., & Frey, N. (2007). Scaffolded Writing Instruction: Teaching with a Gradual-Release
    Framework. Education Review//Reseñas Educativas.
  • Gardner, H. (2006). Multiple intelligences: New horizons. Basic books.
  • Queensland Curriculum and Assessment Authority. (2016). P–10 Mathematics Australian Curriculum and resources.

My Girragundji – quality Aboriginal literature for the Australian classroom


Cover of My Girragundji, written by Meme McDonald and Boori Monty Pryor in 1998

My Girragundji is an 84-page novel written by Meme McDonald and Boori Monty Pryor (McDonald & Pryor, 1998). It tells the story of how a young Aboriginal boy overcomes his fears of visits from the hairyman at night, of approaching his first girl friend Sharyn, of migaloos (white people), and of dealing with the bullies at school. In the course of the story, the boy develops a special relationship with a little tree frog called Girragundji that helps him connect to his Aboriginal ancestors and to build a positive sense of self

Boori Monty Pryor was the Australian Children’s Laureate during 2012-13, along with Alison Lester. Meme McDonald is a founding member and stage director of the WEST Theatre Company, children’s book author and recipient of the 2012 Ros Bower Award  for an outstanding, life-long contribution to community arts and cultural development.

The book trailer above includes paragraphs that describe the first encounter between the first-person narrator and the frog in what is the central transition between paralysis and courage.

Selection criteria and Australian Curriculum connections

In the Australian Curriculum (AC), Literature is one of three inter-related developmental sequences or ‘strands’, together with Language and Literacy. The explicit aim of the Literature strand is to provide students with “access [to] a broad range of literary texts and develop an informed appreciation of literature” (National Curriculum Board, 2009, p.5). In the latest iteration of the AC v8.2, the Australian Curriculum, Assessment and Reporting Authority (ACARA) describes quality literature as satisfying some of the following criteria and enduring values (ACARA, 2016a):

  1. Artistic value
  2. Personal value
  3. Social value
  4. Cultural value
  5. Aesthetic value
  6. Attract contemporary attention
  7. Potential for enriching students’ lives and expanding scope of experience
  8. Represent effective and interesting features of form and style

These criteria are developed in further detail in the literature companion for teachers published by the Primary English Teaching Association Australia (PEETA) (McDonald & Walsh, 2013).

Enduring artistic value can be defined as the quality that writers develop in their work and how this resonates with readers over time (e.g. Walmsley, 2012). My Girragundji is a popular book with young Australian readers and has recently been turned into a stage play and film script (McDonald, 2013).

Personal values relate to personal resonance, emotional connections, empathy and inspiration developed in the reader by reading a book (e.g. Carnwath & Brown, 2014). Students are likely to be drawn into the first-hand narrative of the boy and main character in My Girrragundji and empathise with his challenges. Students might also become inspired by the idea of developing strength from a relationship with a pet or totem.

Social values relate to social benefits such as civic engagement. The Melbourne Declaration on Educational Goals for Young Australians states the imperative for all young Australians to become active and informed citizens and to develop reconciliation between Indigenous and non-Indigenous Australians (Barr et al., 2008). The cross-curriculum priority (CCP) Aboriginal and Torres Strait Islander histories and cultures (ACARA, 2016b) applies this contemporary goal by placing attention on advocating and teaching Indigenous perspectives and understanding for all students to engage in reconciliation. In My Girragundji, some passages directly address reconciliation, such as “That’s our special place where the river meets the sea. It’s their place really, my Aunty Joyce and Uncle Arthur’s place. But they reckon it’s our place, and Dad doesn’t argue with that ‘cause he reckons that’s right. They’re white and we’re black and I don’t know whose place the Bohle is, it just is, and they’ll always be our aunty and uncle.” (McDonald & Pryor, 1998, p.43-44). In 2012, Pryor was made the inaugural Australian Children’s Laureate for his stories that “[…] create positive visions of the future for both Indigenous and all Australians” (Australian Children’s Literature Alliance, 2016).

Cultural values relate to the process of producing and negotiating value between different cultural organisations and expressions (Carnwath & Brown, 2014; Agha, 2003). Inclusive teachers must make an effort to embrace diversity and include literature that portrays the full range of ethnicities, cultures, languages/dialects, religions, family structures and socioeconomic statuses within the classroom (Boyd et al. 2015; Harrison, 2016). My Girragundji provides an authentic contemporary window into a socioeconomically disadvantaged Indigenous community, describing the challenges and demands on an age peer in an engaging and at times humorous way that will expand the scope of experience for many mainstream class students. In the face of adversity, the first-person narrator develops resilience and a proud sense of self, based on connection to country and culture. The book provides insight into local Aboriginal culture and helps to build empathy, recognition and support for Indigenous students from similar background in the class. For Indigenous students, My Girragundji can express and reinforce cultural identity and a pride in Aboriginal English, thereby enriching all students’ lives.

Aesthetic value has been described as the “benign capacity” of quality literature to be experienced and appreciated as something cohesive, harmonious in form, content and symbology, and as a capacity to emotionally move the reader (Beardsley, 1981, p.240). My Girragundji is emotionally engaging, the language original and fresh, with photos and illustrations of high standard. The creative use of fonts and Aboriginal English, including terms such as jalbu (young woman or girl), migaloo (white-skinned person), wirrell (shell fish for eating), creates a text with many effective and interesting features of form and style.

The English curriculum advice for every year level is to work with a range of literary texts, including “Australian literature, […] oral narrative traditions of Aboriginal and Torres Strait Islander Peoples, as well as the contemporary literature of these two cultural groups, […]” (ACARA, 2016c). The State of Queensland, Queensland Curriculum and Assessment Authority (QCCA) provides additional guidelines for embedding Aboriginal and Torres Strait Islander perspectives in schools, recommending five criteria for evaluating the quality of a teaching and learning resource (QCCA, 2010):

  1. Authenticity
  2. Balanced nature of the presentation
  3. Aboriginal and/or Torres Strait Islander participation
  4. Accuracy and support
  5. Exclusion of content of a secret or sacred nature

My Girragundji is an authentic text, co-authored by Indigenous writer Boori Monty Pryor. Pryor was awarded the Promotion of Indigenous Culture award from the National Aboriginal Islander Observance Committee in 1993. The story is written in the first-narrator perspective of an unnamed ten or eleven year old Aboriginal boy, closely modelled on Pryor’s childhood memories. It can therefore be considered accurate and  balanced in nature of the presentation, illustrating contemporary non-‘exotic’ aspects of Indigenous culture and perspectives other than representations of male adults. By concluding in a chapter ‘How My Girragundji was written’, the authors acknowledge the participation of the Yarrabah community. The acknowledgements make it explicit that the local community was actively involved in taking photographs and reviewing the story, guaranteeing that no content of a secret or sacred nature was included. My Girragundji specifically addresses the CCP organising ideas OI.2, OI.5 and OI.6 (ACARA, 2016b) and focuses on Indigenous perspectives such as ways of valuing, being, doing and knowing, as opposed to potentially problematic indigenised content (Lowe & Yunkaporta, 2013).

The topic and language of the book, as well as the similar age of the main character make My Girragundji most suitable to Years 5 and 6 students. A strong link to the year-level English curriculum description is evident, as readers are to explore a range of non-stereotypical characters and texts including junior and early adolescent novels that explore “themes of interpersonal relationships and ethical dilemmas within real-world and fantasy settings” (ACARA. 2016c).

In Year 5, the most applicable CD from the Literature strand in ‘responding to literature’ is ACELT1609 “present a point of view about particular literary texts using appropriate metalanguage, and reflecting on the viewpoints of others”. The students could reflect on Indigenous viewpoints, experiences and opinions expressed in the book, possibly in a format where they are required to create their own text on a hairyman exploring what keeps them awake at night. Alternatively, students could develop a script for a stage play on episodes of the book presenting one or more perspectives of themes in the book such as growing up, family conflict, friendship, bullying and spirituality (see also link to Literacy CD in ‘creating text’ ACELY1714) (ACARA, 2016).

In Year 6, the most applicable CD from the Literature strand in ‘literature and context’ is ACELT1613 “make connections between students’ own experiences and those of characters and events represented in texts drawn from different historical, social and cultural contexts”. This CD can be applied to build the field knowledge on contemporary Indigenous communities at the beginning of the unit. The ‘responding to literature’ CD ACELT1615 “identify and explain how choices in language, for example modality, emphasis, repetition and metaphor, influence personal response to different texts” is well suited to engage students with the unique style of writing and Aboriginal English, followed up by a closer examination and analysis using ‘examining literature’ CD ACELT1617 “identify the relationship between words, sounds, imagery and language patterns in narratives and poetry such as ballads, limericks and free verse”. Students could extract sad and funny passages from the book and discuss how the authors play with language features to achieve particular purposes and effects (see also link to Language CD in ‘text structure and organisation’ ACELA1518) (ACARA, 2016).

Current debates about the use of quality literature in Australian classrooms

The Australian Curriculum only defines types of texts that need to be studied from Foundation to Year 10 and provides the set of criteria discussed above on what quality literature looks like. The English curriculum recommendations further highlight the importance of incorporating Australian literature, including oral narrative traditions and contemporary literature of Aboriginal and Torres Strait Islander peoples, as well as classic and contemporary world literature, in particular texts from and about Asia. As for what makes and who selects the best literature for schools, three debates are particular pertinent to the current situation in Australia:

  1. The extent to which the English curriculum is balanced or distorted by emphasising Indigenous Australian and world literature, and the value of a classical Western literature canon for Australian students
  2. The competition between teachers, schools, states, and commercial publishing houses for the authority to choose classroom literature
  3. The value of print-based literature versus digital media and its impact on reading

In the 2014 review of the Australian Curriculum by the Australian Government, Department of Education and Training (DET), a number of reviewers such as the Institute of Public Affairs objected to the emphasis on Aboriginal and Torres Strait Islander peoples’ literature and its literary heritage, calling for a greater focus on Western literature in the English classroom, (DET, 2014a; Riddle & Honana, 2014, Forrest & Schodde, 2014). This view was supported by specialist consultant Spurr, appointed to make recommendations to the federal government’s review of the national English curriculum. Spurr remarked that “[…] in the three points on which all curriculum subjects must be focused – Aboriginal and Torres Strait Island peoples; the Asian region, and sustainability – mandating priorities that could be a distraction from the core work of the curriculum, bearing no direct relation to the educational and disciplinary purposes that the curriculum for the study of literature in English is designed to facilitate and fulfil. ” (DET, 2014b, p.4). Spurr has since resigned from his professoral post following the exposure of a series of personal inflammatory emails that included derogatory references to Aboriginals, Asians and women casting doubt on the integrity of the review (Alcorn, 2014). On the other side of the debate, the Australian Association for the Teaching of English (AATE) supports the CCPs as important issues that need to be addressed in a national school curriculum at this point in the Australian history (AATE, 2014). This view coincides with a progressive understanding of the role of education in a pluralistic society, which affirms students’ understanding of their home and community cultures while helping them to participate in today’s multi-cultural and globalised world (Banks, 2013).

Closely related to the debate on English literature versus world literature is the question about the nature and value of teaching a classic literary canon, and the role that new literature and media should play in the classroom. Kevin Donnelly, the conservative education critic appointed to co-head the 2014 Australian curriculum review, strongly advocates Harald Bloom’s concept of a Western literature canon. He is of the opinion that English as a subject should focus on “enduring literary works that are part of the Western tradition” including “seminal authors such as Shakespeare, Swift, Dickens, Austen, Orwell, Lawson or Malouf”, as opposed to the AC “exploding the definition of literature to include “multi-modal texts”, and suggesting that students should spend time studying “tween mags, avatars, social networking and manga”” (Donnelly, 2010). Harald Bloom’s concept of a Western canon (Bloom, 1994) had sparked “canon wars” in the late ‘80s in which traditionalists advocated a curriculum focusing on classic works of predominantly British literature, while progressive academics promoted teaching an expanding body of works and a focus on modes of inquiry and interpretation (Donadio, 2007). In reference to the current “literacy war” in Australia, Ilana Snyder describes the position of teachers that argue for a dynamic repertoire of literature, reflecting the rapid changes in our society and world of ideas (Snyder, 2008).  This position is supported by the AATE, who advocate that until Year 10 individual schools are in the best position to implement the curriculum with texts that their English teachers assess as most suitable for particular classes and communities. AATE explicitly rejects the idea of a literature canon stating “[…] we consider it would be inappropriate for any specific texts to be mandated for use” (AATE, 2014).

The idea that teachers choose the most appropriate texts can however be undermined by a more prescriptive implementation of the AC at state land school levels, and by schools buying into commercial reading programs. In Queensland, the DET provides state schools with comprehensive electronic curriculum planning and resource materials, referred to as Curriculum into the Classroom or C2C. The English C2C units include digital and print-based texts as teacher resources and classroom sets (DET, 2015). While DET explicitly states that it supports schools in applying flexibility to “adopt or adapt the materials to suit the learning needs of their students and local contexts” (2015), its sample teaching episodes are often implemented with minimal modifications. The C2C writers therefore are in a powerful position to promote particular works of literature. Many schools purchase a core reading program, conveniently packaged as sets of identical books for students, including a teacher’s edition of the book with worksheets and assessment tasks. Some literacy teachers are favourable of basal reader programs, suggesting that these schemes provide a convenient backbone for their lesson planning and free time up to provide better differentiation, including the provision of supplemental reading for more advanced readers (Reisboard & Jay, 2013). On the other side, many academics and educators point out that commercial reading programs have a number of limitations compared to teacher-selected quality literature. These include that the textbooks are often repetitive, less engaging, fail to build on prior student knowledge and do not develop metacognitive thinking (Dewitz & Jones, 2013).

Reading programs are increasingly integrating children’s books with digital multi-media content for computers and iPads, such as the Reading Eggs products (ABC Reading Eggs, 2016). Recent research suggests that in particular struggling readers are more likely to engage in reading on digital platforms that can support their reading experience with rich features, such as multi-modal content, interactive navigation, animated images and adaptable font sizes (Hughes, 2013). Teachers that like to curate their own quality literature for digital devices can face a number of technical challenges and limitations, such as a more limited range of digital children books and small screens (e.g. Mardis & Everhart, 2013).

While literacy teachers are navigating shifting policy directions and experimenting with the promises and limitations of engaging students in digital texts and reading apps (Hutchison et al., 2012), it is perhaps instructive to highlight one aspect of quality literature which is not explicitly stated in the AC criteria and often missing in the public debate: reading enjoyment.  By selecting literature that is interesting, relevant and moderately challenging, students are most likely to engage in reading and develop an intrinsic reading motivation (Gambrell, 2015). If reading enjoyment is one of the strongest predictor for educational success (Kucirkova, Littleton, Cremin, 2015;  Clark & De Zoysa, 2011), debates on classroom literature canons and formats, should perhaps be placed into the hands of the students, coached by their teachers and the school librarian (Strauss, 2014).


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Chris Garner’s ideas on transforming the teacher in Indigenous education

The 16 minute YouTube video below Chris Garner – Transforming the Teacher in Indigenous Education was recorded at the 2014 inaugural TEDxDarwin event. Chris Garner discusses his experiences and views on Indigenous education in Australia. Garner is a senior secondary school teacher for Indigenous Education at the Marrara Christian College in Darwin, a Preschool to Year-12 college offering a boarding program for Indigenous students. Garner also owns the online training provider Cross Cultural Training Australia and has developed courses including Aboriginal culture for early years educators (Cross Cultural Training Australia, 2016).

Garner’s presentation addresses Australia’s failure to improve educational outcomes for many Indigenous Australians. Improving Indigenous education has been highlighted in the Melbourne Declaration on Educational Goals for Young Australians as a key priority to be addressed in this decade (Barr et al., 2008). The Australian Government is committed towards closing the gap between Indigenous and mainstream students’ education, with policy strategies aimed at increasing Indigenous school attendance rates and transitioning young Indigenous adults into workplaces (The Education Council, 2015). However, since the declaration only few improvements in school educational outcomes have been achieved for Aboriginal and Torres Strait Islander people. While the gap in literacy and numeracy skills between Australian Indigenous and non-Indigenous students is narrowing in primary school years, more than three quarters of Indigenous students still achieved at or below the National Minimum Standard in 2013. Year-12 attainment increased from 45 to 59 percent from 2008 to 2013, but remains well below the the non-Indigenous rates of 86 and 88 percent (Australian Government Productivity Commission, 2014).

Presentation summary

Garner is presenting a pedagogical approach towards closing the educational gap. In his initial analysis, he equates success in the western educational system with helping students to discover their potential and encourage their effort. Garner next suggests that what is lacking in Indigenous education in Australia is relevance; the link between the curriculum and student’s lives and expected roles in their home communities, as well as realistic job prospects. Garner suggests that real-life relevance of the curriculum is what can motivate Indigenous students to study and graduate. His hypothesis is supported by data on Indigenous retention and graduation rates from Marrara College collected over six years. Accordingly, Indigenous Year-12 graduation rates increased at Marrara College from 2.2% in 2008 to to 96% in 2014. (compared to Northern Territories rates of  32% for Indigenous students versus 71% for Non-Indigenous students). In addition, the rate of Indigenous students in employment following graduation was raised to 98% (compared to the national average of 33% for Indigenous, and 71% non-Indigenous Australians).

The Indigenous program at Marrara School is following a student-centric pedagogy and combining it with comprehensive case management and culturally-adapted teaching strategies. The teacher spends the first three weeks with new boarding school students to learn more about their background, the framework of traditional obligations, expectations and social norms in which they operate, regional job opportunities, personal interests and anything else that will inform the student’s outlook on their education. This information is used to contextualise numeracy and literacy content knowledge and to align learning objectives with the desired outcomes and visions of their students (e.g. becoming a healthcare worker, mechanic, finance officer). The teacher is developing connections between school learning and the roles students want to play back in their community, thereby demonstrating how curriculum content will help them to achieve these. This requires modified learning and assessment activities. For example, traditional activities of everyday life are performed with the students first, to consequently relate these to literacy and numeracy aspects back in the classroom. Educational success is reframed as success towards the individual’s desired outcomes, as opposed to performance in standardised tests often geared towards tertiary education. The school also develops partnerships with potential employers in their communities to offer final-year students opportunities for work placements and apprenticeships, at a time when traditional expectations and community pressure on students increase, often resulting in school dropout. Students are further explicitly educated in how to navigate the Australian system, including how to sign up for vocational courses and apply for scholarships.


Bourdieu’s theory of social practice can serve as a framework to better understanding the underlying challenges of Indigenous education resulting in the observed low school attendance, retention and graduation rates (Bourdieu, 1983, 1986). A key concept of the theory is ‘social capital’, a resource of social networks, norms and values such as trust, and actual and potential assets shared within a network of relationships defined by mutual acquaintance and recognition (Mignone, 2009). These networks are expressed as privileged or marginalised groups within society that collectively support their members. Social capital is unequally distributed and reflect the wider social standing of individuals and groups in terms of other capitals, including economic, cultural, and symbolic standing. Social capital is the product of history. For Indigenous Australians, historical experience is one of dispossession, cultural, political and economic marginalisation, and restricted access to influence, resources and information (Browne-Yung et al., 2013). This cultural experience can be passed on by social reproduction, a process where aspects of society such as privilege and marginalisation are transferred from generation to generation. In Australia, the curriculum is largely developed by privileged urban academics and professionals, which is then taught by middle class teachers with a dominantly ‘western’ cultural background including English as first – and often only – language. According to Bourdieu (1983; 1986, p. 248-9), the economic, cultural, social, and symbolic capital by the dominant actors are related to positions of social space – the professional and personal network of actors – who will use all forms of capitals to reproduce and entrench their positions and perpetuate structured inequality (Tzanakis, 2013). Indigenous students from remote, low socio-economic and culturally different backgrounds are disadvantaged and underrepresented in terms of the economic, socio-cultural, and political participation and control over influencing educational standards and the curriculum. It is against this backdrop, that the Indigenous program at Marrara College has developed a supportive learning environment for Indigenous students, to enhance their confidence, self-esteem and cultural identity, and improve learning outcomes through the provision of culturally-relevant curriculum choices (Wadham, Pudsey, & Boyd, 2007).

While Indigenous students may be poorly equipped with the cultural capital required to perform well in mainstream Australian educational systems, there is also the related concept of different ‘funds of knowledge’ (Klenowski, 2009). The funds of knowledge can be understood as a “virtual schoolbag full of things they have already learned at home, with their friends, and in and from the world in which they live” (Thomson, 2002, p.1). For Indigenous students, the virtual schoolbag may include local knowledge about nature, oral languages, dreamtime stories, how to collect and hunt for food, cook and care for siblings and elders. All of these are unrelated and may even be in conflict to school rules and behaviour expectations, book knowledge and arithmetic skills that are valued by the school institution and curriculum. In contrast to other Australian schools, Marrara College is actively engaging with the virtual schoolbag of their Indigenous students, by incorporating their funds of knowledge as starting points to make mainstream curriculum knowledge more relevant and applied. In many respects, this approach is following the framework of productive pedagogies (Hayes, Lingard, & Mills, 2000). Productive pedagogies emerged out of the Queensland School Reform Longitudinal Study conducted in the years 1998 to 2001, and was distilled into four common elements (Mills et al., 2009):

  1. intellectual quality
  2. relevance – subsequently redefined as connectedness
  3. supportive classroom environment
  4. recognition of difference – subsequently redefined as ‘valuing and working with difference’

The pedagogy described by Garner fosters the development of deep and applied understanding and knowledge through inquiry-based learning from experiences relevant to his students’ lives, encourages a supportive learning environment with good teacher-student and school-community relationships, and applies a high degree of differentiation by identifying, recognising and incorporating the cultural funds of knowledge of Indigenous students.

In addition to the expected curricular learning outcomes and pedagogy, schools operate in ways that can disadvantage certain students which can be summarised as the hidden curriculum. A hidden curriculum is the often implicit ways in which different school systems and teachers allocate responsibilities and resources, thereby privileging one group of students over another (Gale & Densmore, 2000; Thomson, 2002). The concept of hidden curriculum was first developed by Snyder to describes the socialisation process in the classroom as one of two curricula, with the hidden curriculum comprising the unstated academic and social norms that places limits on independent development in students (Snyder, 1970). A supportive school system is based on supportive and unbiased teacher-student relationships (Frymier & Houser, 2000), a dimension particularly important in the boarding school environments that Indigenous students from remote communities are sent to for their education. From this perspective, the policy of Marrara College to award Indigenous students responsibilities and roles as student leaders or teacher aides, is a constructive approach to use the hidden curriculum to positive effect.

Aboriginal lawyer and policy maker Noel Pearson has been mentioned in Garner’s presentation to take a different view. Pearson has been influential in designing Indigenous education policies in North Queensland (Ford, 2012). In a public policy paper, Pearson states: “Too many of the programs and strategies that have failed have done so because they have not maintained high standards or high expectations. Instead, in attempting to ‘understand’ the problems, they end up accommodating or acquiescing to the problems. Indeed, they end up perpetuating the problems” (Pearson, 2004). Pearson’s criticism reflects a sociological concept exemplified in Bourdieu’s approach to habitus, in which social structure, including marginalisation of certain groups, is reproduced by the affected individuals themselves, responding to the expectations of society by internalising and embodying their perceived ‘acceptable’ and ‘legitimate’ place, roles and aspirations (Bourdieu, 1986; Tzanakis, 2013). However, while it is more difficult for marginalised students to overcome their habitus (Thomson, 2002), the theoretical concept is epistemologically not deterministic (Hilgers, 2009) and therefore allows for social mobility.

In contrast to the constructivist pedagogy deployed at Garner’s school, the education program devised by Pearson applies a proprietary Direct Instruction syllabus developed in Oregon, United States. Direct instruction (DI) is a pedagogy that teaches by explicit, guided teacher instructions and strict lesson plans. Initially developed in the mid 1980s to address the problems of inner-city Baltimore schools, it has been commercialised by SRA/McGraw-Hill (McGraw-Hill Education, 2016).Direct instruction pedagogy has been a critical component of Project Follow Through, the largest historical education experiment to improve education of disadvantaged students in the Unites States (1986-1995), as a continuation and extension of the Head Start program, which delivered education and other services to disadvantaged preschool children (Watkins, 1997). The effectiveness of DI has been demonstrated to accelerate academic outcomes in at-risk students (Engelmann, 1999). In contrast to the productive pedagogies, DI does not encourage the engagement with student’s cultural resources, background knowledge and community context. It applies strict tracking of student progress and places students and teachers into a rigid relationship that makes it difficult to develop mutual trust (Luke, 2014). Haberman (1991) has delivered a scathing critique of DI pedagogies as delivered by ‘Head Start’. In his opinion the program forces students into compliance and results in resentment and resistance rather than learning of life skills and academic knowledge, referring to DI as “pedagogy of poverty”. A pedagogy of poverty is emphasising the compliance with rules and following scripted directions at the expense of student-directed learning and critical thinking. This is often encouraged by students’ dysfunctional behaviour and low SES parents’ expectations of classroom practice. (Groundwater-Smith, 2009).

Direct instruction pedagogies have become more widespread in public schools in The United States in recent years (Haberman, 2010), and are internationally tested in at-risk schools including in North Queensland (Dow, 2011). Introduced in 2010 in Aurukun in combination with punitive welfare reforms coercing parents into ‘income management’, DI pedagogy has recently been discussed as one potential factor leading to the ongoing schooling crises in Aurukun resulting in the temporarily closure of its primary school and evacuation of its staff (Robertson, 2016). In light of these news and prior experience with DI, a culturally-based, community-focused, and individually scaffolded pedagogy like the one Garner promotes in his TED talk, receives the support from Indigenous educationalist Chris Sarra, founder and chairman of the Stronger Smarter Institute for improving educational outcomes for Indigenous Australian schoolchildren (Sarra, 2011). Sarra, an outspoken opponent to the commercial DI curriculum for years, suggests remedial approaches that have been successfully implemented at Marrara College in his response to the unfolding crisis “If the government was serious about providing quality education they could […] have a specialist curriculum writer go to Aurukun, live in Aurukun, sit down with people and design a local school curriculum” (Robertson, 2016). Other researchers on Indigenous education in Australia concur that successful pedagogies require building supportive links between schools and Indigenous communities that inform curriculum development and teaching practice (Luke, 2008, 2009).


Quality education is important on an individual level, by improving socio-economic prospects, social standing, and the ability to make informed choices in life (Helliwell & Putnam, 1999).Quality education is also important on a national level, by improving public health and safety, social mobility, and overall performance in a global knowledge and innovation-based economy (Barr et al., 2008; Organisation for Economic Co-operation and Development, 2012). While it is easy to agree on equal entitlement to education, applying equality into practice in terms of equitable teaching and needs-based school programs are more contested across political lines (Connors & McMorrow, 2015). It is against this backdrop that different school policies and pedagogies as those discussed at Marrara College and Aurukun State School are developed, funded and implemented.

Garner’s presentation highlights that equitable teaching needs to accommodate individual needs. The Indigenous education program at Marrara College is an inspiring example of curriculum modifications, productive pedagogy and teaching strategies that can motivate and empower disadvantaged young people to obtain an education that can positively transform their lives and that of their communities. In light of the political dimension of the debate on making Australia’s education more equitable, Garner’s conclusion that it does not require a “revolution of the [educational] system but evolution of the teacher” can provide both hope and direction. Garner has demonstrated all the skills that according to Groundwater-Smith (2009) make effective teachers; mainly the ability to motivate and engage students, choosing meaningful instructional methods, and demonstrate good interpersonal skills. Groundwater-Smith also highlights the importance of having high expectations of students irrespective of their ethnicity or socio-cultural background, an aspect of major concern to Noel Pearson (2004). Consequently, it takes knowledgeable teachers and a culturally-responsive pedagogy to unpack the curriculum and develop assessment practices that make education equally accessible to Indigenous students and acknowledge different ways of knowing, learning and being. Marginalised identities can be overcome and recast in the process of reshaping education. Recently documented Indigenous academic success in Australian tertiary education (Klenowski, 2009) is aligned with Coleman’s definition of social capital as a bonding mechanism towards achieving a common goal, and as a “resource for action” (1988). By empowering Indigenous students to persevere and become their own agents of change, they can create a new form of cultural capital (Pechenkina, 2014; Browne-Yung et al., 2013). At Marrara College, this is achieved by providing Indigenous students with an education that improves social and economic standing in their remote communities on the basis of shared values and trust.


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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.

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.


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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Six interrelated communication processes or language modes

The fundamentals of language learning can be divided into six interrelated communication processes or language macro skills. Listening, reading and viewing are the receptive language macro skills, and speaking, writing and presenting are the productive skills (Barrot, 2016). All six are explicitly addressed in this teaching and learning episode:

listening to texts

Listening is easily overlooked as a passive skill in literacy pedagogies (Bozorgian, 2012), but essential for students to understand and follow explanations and instructions, and to socially participate in the class. The provision of visual support, paralinguistic cues and talking with clear pronunciation and emphasis are important means to support aural language comprehension in literacy learners (Vandergrift, 2015).

reading texts

Reading is the skill where the reader creates meaning from written text. In the the early primary school years, students are “reading to learn” while in upper primary years are increasingly expected to “read to learn” (Duke et al., 2003). This requires critical literacy skills that go beyond developing decoding competence in what Peter Freebody and Allan Luke refer to as the four roles of the reader (Freebody & Luke, 1990; Luke & Freebody, 1999; Luke, 2000): code breaker, text participant, text user and text analyst.

 viewing texts

Viewing is a recent addition to the traditional four language macroskills on account of the increasing importance of visual media (Barrot, 2016). Viewing is making meaning from non-print multimedia and visual images and can be used as tool to develop cultural knowledge. As the receptive mode addressing multi-media and digital literacies, it has been included in a reconceptualised version of the ‘four resources model’ (Serafini, 2012; Hinrichsen & Coombs, 2014).

speaking texts

Speaking is the productive skill in which students convey their ideas and understanding to others. Academic oral communication shares many features with written communication (Barrot, 2016). Oral competency is based on the knowledge and practice of vocabulary, pronunciation and functional grammar (Nation & Newton, 2008). Literacy students need opportunities to develop and practice English phonetic and phonological skills. These include the pronunciation of new words based on speech sounds, sound patterns, word and sentence stress and intonation patterns (Brown, 2014). Further, students need to develop fluency in speaking in applied social contexts by participating and engaging in task-oriented classroom conversations (Williams, 2001; Gibbons, 2008; Gibbons, 2015). In particular mixed-ability group work provides all learners with the opportunity to practise speaking in socially-meaningful task-oriented context (Gibbons, 2015; Im & Martin, 2015).

writing texts

Writing allows students to capture and document their ideas and understanding. It provides knowledge to both writer and reader (Barrot, 2016), which is why it is often the preferred active mode for summative assessments. For over thirty years, Australian schools have been following the genre-based approach towards teaching writing which informs the Australian Curriculum (Hammond, 1987; Derewianka, 2012).


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QAR – Exploring Question-Answer Relationships

Question-Answer Relationships (QAR) is an explicit reading comprehension instruction model for teaching students about reciprocal question-answer relationships. Most recently popularised by Sheena Cameron in her book Teaching Reading Comprehension Strategies (Cameron, 2009), the QAR model is based on a reading strategy developed by Taffy E. Raphael at the University of Illinois in the early 1980s (Raphael, 1982). The idea of QARs is to engage students in thinking about and discussing what they read, progressing from literal text evidence to text synthesis and inference.

In the original concept, students were taught three types of questions that can be asked about texts and ways to find answers. The students need to locate the response information, which shifts with the type of question from a particular sentence, to multiple passages across a text, to drawing on prior experiences and background knowledge about similar or related texts and genres.

Original QAR model by Taffy E. Raphael (1982, p. 188)

Original QAR model by Taffy E. Raphael (1982, p. 188)

Taffy Raphael called the three type of QAR questions:

Right There: Right There questions are answered by pointing to a literal reference. Students are required to “… find the words used to create the question and look at the other words in that sentence to find the answer” (1982, p.187). The students learn how to find information by looking for key words. I call these questions On the Line questions, because the answers generally require pointing to one line in the text.

Think & Search: Think & Search questions are answered by synthesising different passages of a text. Students are required to integrate literal information “… , so students must skim across text segments to find the question and response information” (1982, p.187). The students learn how to find and integrate information based on their prior knowledge about text structures and by applying reading strategies such as skim reading. I call these questions Across the Lines questions, because answers generally require pointing at multiple paragraphs (or lines) in the text.

On My Own: On My Own questions demand thinking beyond the text and “… require the student to determine what background knowledge can be applied to the question” (1982, p.187). The students learn to think beyond the provided textual information, to question texts and to develop critical literacy skills. I call these questions Beyond the Lines questions, because they can be answered without referring to the text at all.

Taffy Raphael subsequently expanded her original model to include Author & You questions (Raphael, 1986): Author & You questions require inference from the students, who learn that some answers “... must come from the readers’ own knowledge base, but only in connection with information presented by the author” (1986, 519). Students learn how two very different resources of information, those that must e acquired from the text and those that are based on their prior knowledge and understanding, must be considered to answer some questions. These questions support reading strategies such as inference. I call these questions Between the Lines questions, because answers require to “read between the lines” by integrating the author’s text and the readers’ existing knowledge.

The revised QAR taxonomy is divided into two major categories: In the Book with the answer resources Right There and Think & Search, and In My Head with the answer resources Author & Me and On My Own (Raphael, 1986).

Updated conceptual QAR model now including four types of question-answer relationships (Raphael, 1986, p.517)

Updated conceptual QAR model now including four types of question-answer relationships (Raphael, 1986, p.517)

The QAR model provides a practical literacy resource to develop three comprehension strategies: (1) locating information; (2) determining how text structures convey information and can be synthesised; and (3) determining when inferences are required or invited. Students learn that depending on the type of question, answers may involve both literal and referential comprehension, references to the text as well as their interpretations that rely on their personal knowledge bases.

It is instructive to align the QAR model with the Four Roles of a Reader model, originally developed by Peter Freebody and Allan Luke (1990). This model emphasises the four interrelated essential roles of a reader: (1) decoding text as a ‘code-breaker’; (2) developing semantic meaning as a ‘text-participant’; (3) developing functional meaning as a ‘text-user’; and (4) critically analysing text as a ‘text analyst’.

The Four Resources of Reading by Freebody & Luke (1990) as compiled by the Barefoot Literacy Project

Right There questions operate at the level of key words and Code Breaking. Think & Search questions require text comprehension strategies that build on knowledge about language and genre conventions required to Make Meaning. The Author & You questions asks readers to respond and connect to the texts, to bring in their prior knowledge and “communicate” with the text as Text Users. Finally, On My Own questions demand critical engagement from readers in the form of Text Analysis. Readers are asked to draw on other texts or use the text as a stepping stone into inquiries that go well beyond the read text.

Early QAR Resource packages, such as that developed by the Irish National Behaviour Support Service (NBSS) are using four quadrants that are very similar to the Four Roles of a Reader model.

QAR teaching resource by NBSS (p.4)

QAR teaching resource by NBSS (p.4).

Since, a plethora of teaching resources based on the QAR model have been developed, including such some useful tools that include example questions such as QAR bookmarks by Sheena Cameron (2009). Deb Lawrence from Queensland wrote a useful four-step instructional guide detailing ideas on how to introduce QAR in the classroom (Lawrence, 2015), including:

  1. Introducing the question types
  2. Teaching about clues for identifying the question types
  3. Modelling how to think aloud
  4. Teaching about text organisations

The last step is about unpacking literature genre convention and nicely links with a number of functional grammar-related content descriptors (see below).

QAR bookmark

Photo copy of QAR bookmark as part of the comprehensive digital resources developed by Sheenan Cameron (2009).


  • Cameron, S. (2009). Teaching reading comprehension strategies. North Shore: Pearson.
  • Freebody, P., & Luke, A. (1990). Literacies programs: Debates and demands in cultural context. Prospect: Australian Journal of TESOL, 5(7), 7-16.
  • Lawrence, D. (2015). Why use Question-Answer Relationships (QAR) as a comprehension strategy?. Literacy Learning: The Middle Years, 23(1), i-vii.
  • Raphael, T. E. (1982). Question-answering strategies for children. The Reading Teacher, 36(2), 186-190.
  • Raphael, T. E. (1986). Teaching question answer relationships, revisited. The Reading Teacher, 39(6), 516-522.

Relevance to Australian Curriculum content descriptors:

  • Foundation: Use comprehension strategies to understand and discuss texts listened to, viewed or read independently (ACELY1650)
  • Year 1: Understand that the purposes texts serve shape their structure in predictable ways (ACELA1447)
  • Year 1: Use comprehension strategies to build literal and inferred meaning about key events, ideas and information in texts that they listen to, view and read by drawing on growing knowledge of context, text structures and language features (ACELY1660)
  • Year 2: Use comprehension strategies to build literal and inferred meaning and begin to analyse texts by drawing on growing knowledge of context, language and visual features and print and multimodal text structures (ACELY1670)
  • Year 3: Identify the point of view in a text and suggest alternative points of view (ACELY1675)
  • Year 3: Understand that paragraphs are a key organisational feature of written texts (ACELA1479)
  • Year 3: Use comprehension strategies to build literal and inferred meaning and begin to evaluate texts by drawing on a growing knowledge of context, text structures and language features (ACELY1680)
  • Year 4: Use comprehension strategies to build literal and inferred meaning to expand content knowledge, integrating and linking ideas and analysing and evaluating texts (ACELY1692)
  • Year 5: Understand how to move beyond making bare assertions and take account of differing perspectives and points of view (ACELA1502)
  • Year 5: Investigate how the organisation of texts into chapters, headings, subheadings, home pages and sub pages for online texts and according to chronology or topic can be used to predict content and assist navigation (ACELA1797)
  • Year 5: Understand how texts vary in purpose, structure and topic as well as the degree of formality (ACELA1504)
  • Year 5: Recognise that ideas in literary texts can be conveyed from different viewpoints, which can lead to different kinds of interpretations and responses (ACELT1610)