Inclusive Principles and Practices in Literacy Education Examining the Literacy within Numeracy to Provide Access to the Curriculum for All David Evans, Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) Article information: To cite this document: David Evans, "Examining the Literacy within Numeracy to Provide Access to the Curriculum for All" In Inclusive Principles and Practices in Literacy Education. Published online: 18 Jul 2017; 35-51. Permanent link to this document: https://doi.org/10.1108/S1479-363620170000011003 Downloaded on: 25 October 2017, At: 23:01 (PT) References: this document contains references to 0 other documents. To copy this document: permissions@emeraldinsight.com The fulltext of this document has been downloaded 18 times since 2017* Users who downloaded this article also downloaded: (2017),"Multiliteracies, Multimodality, New Literacies and …. What Do These Mean for Literacy Education?", International Perspectives on Inclusive Education, Vol. 11 pp. 19-33 <a href="https://doi.org/10.1108/S1479-363620170000011002">https:// doi.org/10.1108/S1479-363620170000011002</a> Access to this document was granted through an Emerald subscription provided by emerald-srm:401304 [] For Authors If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.com Emerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services. Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) *Related content and download information correct at time of download. Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) EXAMINING THE LITERACY WITHIN NUMERACY TO PROVIDE ACCESS TO THE CURRICULUM FOR ALL David Evans ABSTRACT Being numerate involves the ability to use mathematical knowledge meaningfully across multiple contexts allowing us to order our day, optimise our health and well-being, and function in technology rich environments. Addressing numeracy from the early years of learning, and across all areas of the education curriculum, is key to lifelong learning and quality of life. Being numerate, however, is more than mathematical knowledge; the language that underpins it heavily impacts how we become numerate. This chapter examines numeracy, or mathematical literacy, investigating how literacy can include, and exclude, students from opportunities to learn at school and beyond. This chapter will also examine how numeracy can be used to provide access to educational curricula and personalised goals for students with diverse learning needs in ways that many have ignored. Keywords: Numeracy; curriculum access; personalised learning; mathematical literacy; mathematical knowledge; inclusive education Inclusive Principles and Practices in Literacy Education International Perspectives on Inclusive Education, Volume 11, 35 51 Copyright r 2017 by Emerald Publishing Limited All rights of reproduction in any form reserved ISSN: 1479-3636/doi:10.1108/S1479-363620170000011003 35 36 DAVID EVANS Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) INTRODUCTION The principles of inclusion underpin the right for all children and youth to access a quality education. This right has been heightened and supported internationally through the Salamanca Statementf (United Nations Educational, Scientific and Cultural Organization [UNESCO], 1994), and the Convention on the Right of Persons with Disabilities (United Nations, 2006). The Salamanca Statement put to the international community that the principles of inclusion were a key to ‘combating discriminatory attitudes, creating welcoming communities, building an inclusive society and achieving education for all’ (UNESCO, 1994, p. ix). The United Nations Convention on the Right of Persons with Disabilities in Article 24 (United Nations, 2006) reinforces the right of children and youth to access and participate in a quality education. A key message in Article 24 is that students not be excluded from a primary or secondary education. Further, that persons with disability be provided reasonable accommodations and individualised supports that maximises their opportunities for full academic and social participation on the same basis as students without disability. The discussion and debate that surrounds the principles of inclusion and inclusive practice is steeped in social justice and equity (Kozleski & Waitoller, 2010; Slee, 2013), focused on policy and legislative constructs, and the context of education (Ryndak, Moore, Orlando, & Delano, 2008 2009). This passionate debate has helped inform the construction of conventions, policy and legislation. The ongoing debate around the principles of inclusion has supported the development of inclusive practices that support education for all students, in particular, the education of students with disability. In a review of the literature Hoppey and McLeskey (2014) posed that quality inclusive education comprises two key themes: cultural and organisation qualities, and the quality of classroom instruction. The first theme highlights central tenets within the debate over the past two decades of the principles of inclusion. The role of the principal and school leadership are central to this theme (MacFarlane & Woolfosn, 2013). The principal is seen as being important in accessing and distributing resources, and buffering staff from external pressures (Hoppey & McLeskey, 2013). The second theme alludes to key variables that underpin research around teacher attitudes (e.g. professional knowledge, quality instruction). Teachers report positive attitudes towards inclusion when they have access to professional learning that supports the enrichment of this professional knowledge (MacFarlane & Woolfosn, 2013; Tsakiridou & Polyzopoulou, 2014). While these studies highlight the importance of quality instruction and teacher attitudes, debate is emerging that discusses and engages with the role of curriculum and instruction. International research and professional dialogue around curriculum for students with disability over the past decade has focused on access to the general Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) Examining the Literacy within Numeracy 37 curriculum (Browder & Spooner, 2011; Spooner, McKissick, Hudson, & Browder, 2014). Access to the general curriculum is defined as delivering students with disability educational programs that derive from the same grade equivalent curriculum content as their peers (Ryndak et al., 2008 2009). Achieving this access continues to be surrounded by tension and debate. In their paper titled ‘I can identify Saturn but I can’t brush my teeth’ (p. 11), Ayres, Lowrey, Douglas, and Sievers (2011) typified concern about students with complex education needs accessing the general education material. In defending the right for students with complex education needs to access the general curriculum, Ayres et al. highlight short-term and long-term benefits for students when they are provided access to the general curriculum on the same basis as their peers without disabilities. While this discussion is based primarily on work out of North America, a similar debate is being undertaken in the Australian context. In the 2014 Review of the Australian Curriculum, it was stated: [the] ‘… Reviewers are convinced the Australian Curriculum is manifestly deficient in its inclusiveness and accommodation of the learning needs of students with disability’ (Australian Government, 2014, p. 5). In their disbelief that existing alternate curriculum had not been adopted, the conceptual alignment with access to the general curriculum was passed over by the reviewers in favour of a developmental approach to curriculum development (i.e. where students with disabilities engage with a different curriculum that aligns with their students’ mental age). This focus on developmental trajectories lowers expectations, and leads to reduced outcomes and quality of life in the longer term (Ayres et al., 2011; Ryndak et al., 2008 2009; Wehmeyer, 2014). This move towards developing a different or alternate curriculum excludes students with disabilities from participation on the same basis as students without disabilities. In dismissing the approach developed within the Australian Curriculum where teachers are advised to ‘align’ their planning with the age equivalent level of the student (ACARA, 2017), teachers are missing an opportunity to provide age and functionally relevant curriculum to all students. A key driver within this approach is using the General Capabilities to access age appropriate content while also addressing the personal needs of students. The General Capabilities: ‘… encompass the knowledge, skills, behaviours and dispositions that, together with curriculum content in each learning area and the crosscurriculum priorities, will assist students to live and work successfully in the twenty-first century’ (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2016a). Two general capabilities that attract considerable attention are literacy and numeracy. Literacy is key to participating in an inclusive world, and is defined in the initial chapter of this book. Numeracy is often seen as the ‘poor cousin’ to literacy, and relegated to a secondary role. Yet numeracy plays an equally important part in our lives as does literacy, and requires attention to the same extent. The failure to achieve proficiency in key numeracy skills and knowledge 38 DAVID EVANS Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) can exclude us all from everyday functions making us dependent on others. More concerning is that poor numeracy skills can impact health, well-being and overall standard and quality of life (van Garderen, Poch, Jackson, & Roberts, 2017; Huntsinger, Jose, & Luo, 2016). Hence, an alternate view of numeracy is to consider it as ‘mathematical’ literacy (Commonwealth of Australia, 2008; Jablonka, 2003; National Numeracy, 2016). In considering it as literacy, numeracy needs to be tailored for use in the world that each student functions, and aspires to live within. NUMERACY AND MATHEMATICS As a ‘poor cousin’, numeracy is often forgotten or not considered in educational programs. Numeracy is seen as the domain of the mathematics curriculum and/or mathematics teacher. While mathematics and numeracy are related they are not the same. While the concepts of mathematics and numeracy are often confused or used interchangeably, defining both concepts appears more obtuse. An examination of the Australian Curriculum, for example, found a clear definition of numeracy yet not so for mathematics. In searching for definitions of mathematics, it became apparent that mathematics knowledge or proficiency was a preferred term. The use of mathematical proficiency is found within the Australian Curriculum and defined by the National Research Council (2001) as comprising five interwoven strands: procedural proficiency, conceptual understanding, strategic competence, and adaptive reasoning, productive disposition. The depiction of these five stands interwoven to make a rope highlights the need for all aspects to be given attention in developing mathematical proficiency. Mathematical proficiency captures the need for mathematical knowledge (e.g. conceptual understanding), as well as the motivation and skill to use this knowledge (e.g. adaptive disposition). What is clear from the conceptualisation of mathematical proficiency is that mathematics has a language that can be used across discipline areas as a tool for inquiry, justification and explanation. The importance of mathematics and its use in society is reflected in differing international and national developments. The Organization for Economic Cooperation and Development (OECD) through its Program for International Student Assessment (PISA) examines the use of mathematics, or numeracy, in a range of contexts. The OECD PISA report for 2012 defined numeracy or mathematical literacy as: … an individual’s capacity to formulate, employ and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts, and tools to describe, explain and predict phenomena. It assists individuals in recognising the role that mathematics plays in the world and to make the well-founded judgements and decisions needed by constructive, engaged and reflective citizens. (OECD, 2014, p. 37) Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) Examining the Literacy within Numeracy 39 At the national level, the Australian Curriculum makes a distinction structurally between mathematics and numeracy. Mathematics is part of the content dimension of the Australian Curriculum, while numeracy is part of the General Capabilities. The Australian Curriculum defines numeracy as students ‘… recognising and understanding the role of mathematics in the world and having the dispositions to use mathematical knowledge and skills purposely’ (ACARA, 2016b). Mathematical proficiency requires mathematical knowledge to be seen ‘… as sensible, useful and worthwhile…’ (National Research Council et al. 2001, p. 116). It requires us to see that mathematics can be used in our everyday life events to support ones living, well-being and economic stability. This critical use of mathematics in context is the conceptual basis of numeracy. The National Numeracy Review Report (Commonwealth of Australia, 2008) defined numeracy involving ‘students in recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully’ (ACARA, 2016b). Numeracy is more than about numbers, shapes or measures; its more than recounting times tables. It is about using mathematical knowledge in everyday events and activities (e.g. using number facts to quickly and efficiently use money). In developing mathematical knowledge, however, it requires the learner to discuss, reflect, explain and justify beyond a proof. It requires one to use mathematical literacy and language to support the development of mathematical proficiency. As part of developing this proficiency, it is important that a disposition to use mathematics as a tool to meet daily demands is supported. This everyday use of mathematical knowledge in the real world requires a literacy to navigate the semantic nuances of mathematics. To be numerate is for everyone; it supports general well-being, prosperity and everyday existence (Cheong, Walker, & Rosenblatt, 2016). The following discussion focuses on how mathematical literacy or numeracy can be supported, and reduce it becoming a barrier to richer learning across all curriculum. This discussion will also focus on how numeracy can be used to empower teachers to develop quality educational programs that provide students with diverse learning needs access to the curriculum on the same basis as their peers. VOCABULARY AND MATHEMATICAL KNOWLEDGE Vocabulary is the knowledge of word meanings (Riccomini, Smith, Hughes, & Fries, 2015). In schools, it is the ability of the student to hear or read words and know their meaning; it also involves the student using words in a way that assists convey meaning through writing and speaking. Students who attain greater quality and quantity of vocabulary knowledge during early childhood Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) 40 DAVID EVANS often experience enhanced educational, social and personal outcomes in the long-term (Duncan et al., 2007; Morgan, Farkas, Hillemeier, Hammer, & Maczuga, 2015). Further, explicit and carefully planned instruction in vocabulary can enhance opportunities for students to engage in education programs in early childhood (Morgan et al., 2015), primary and secondary (Kamil et al., 2008) programs. Mathematics and its subsequent use places a heavy demand on the flexible and proficient use of vocabulary knowledge to support learning (van der Walt, Maree, & Ellis, 2008). Yet, the explicit and systematic teaching of mathematical vocabulary is typically missing from educational programs (Riccomini & Witzel, 2010). As a consequence, vocabulary and language becomes a barrier to students accessing mathematics knowledge and using this knowledge within everyday life (Thomas, Garderen, Scheurmann, & Lee, 2015). It is often a contributing factor to students developing an anxiety towards mathematics and/or drop out mathematics later in schooling (Commonwealth of Australia, 2008). The use of words and their meanings within mathematics assists students develop the knowledge of mathematics. It supports students to develop mathematical proficiency through justifying, reasoning and communicating mathematical concepts and strategies. Yet these same words can be confusing to and confused by students. Words, for example, can have multiple and quite disparate meanings (Thompson & Rubinstein, 2000). When asking students which number is closer to five, six or nine, some younger students may look for a ruler (i.e. closer is related to distance) while others will respond in regards to quantity. Other words have close pronunciation, but vary in quantity by powers of 10 (e.g. thousandth and thousand). Vocabulary also plays a significant role in students establishing conceptual understating within mathematics. In developing this understanding, it is important that students be able to explain verbally, in writing, through symbols or use of concrete materials mathematical concepts and reasoning (Gersten et al., 2009). If students are not proficient in the use of mathematical terms and vocabulary they will experience difficulty establishing these key understandings at a deeper level. This barrier of language will impact adversely on the development of mathematical proficiency. Explicit and systematic vocabulary instruction should be part of every mathematics lesson (Riccomini et al., 2015). In the early years, instruction is best conducted through direct and explicit teaching of concepts, and systematically supported through the use of the concept across multiple examples and contexts. As students reach middle school and secondary school, vocabulary instruction could be purposefully embedded within class instruction. Ongoing planned revision, and purposeful use of key mathematical vocabulary (e.g. talking, listening, writing), is key for ensuring all students retain use of language. In building students’ vocabulary within mathematics, and in the use of mathematical knowledge, there is a need to carefully identify language and Examining the Literacy within Numeracy 41 words that may pose a barrier for students. Through identifying mathematical terms and words for explicit instruction, teachers can identify strategies to reduce or moderate the language demands that are placed on students, and prevent them from participating fully (Thomas et al., 2015). Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) LITERACY AND EARLY NUMERACY The language of mathematics, beyond single words and concepts, is important to developing mathematical proficiency. This language of mathematics is no more evident that in the early years of schooling where children are formally introduced to mathematics (Toll & Van Luit, 2014). The informal use of mathematical concepts prior to coming to school is highly predictive of later mathematical and literacy development. Students develop skills in distinguishing magnitude of non-symbolic quantities, for example, considered to be important in comparing and approximating quantities (Barth, La Mont, Lipton, & Spelke, 2005). It is the development of these early language concepts that can impact on later achievements in mathematics, other content areas, and wellbeing (Baroody, Eiland, & Thompson, 2009; National Research Council, 2001; Torbeyns, Gilmore, & Verschaffel, 2015). On reaching school, young students are formally introduced to early mathematical content and language. These early years of schooling are crucial to later mathematics achievement. Duncan et al. (2007) reported, ‘early math concepts [such] as knowledge of numbers and ordinality were the most powerful predictors of later learning (the average effect size of school-entry math skills was .34 and every bit as large as early reading skills in predicting later reading achievement)’ (p. 1443). In a later study, Watts et al. (2015) also reported a strong relationship between achievement in year one and that in later schooling after controlling for knowledge of reading and cognitive skills. A key feature of effective early mathematics programs is they follow a developmental progression of mathematical development (Frye et al., 2013). Elements within a developmental progression recommended by Frye et al. (e.g. meaningful object counting, counting-based comparisons of collections larger than three, and mental comparisons) place high demands on vocabulary and language use. In completing a subitising task, for example, students need to be able to retrieve the word ‘three’ in response to seeing three fingers. Children also need to be aware the word ‘three’ can be used to name three blocks, and three buckets, and represented as a symbol ‘3’. Another early development skill involves mental comparisons or magnitude. During prior to school experiences, children will make gross comparisons amongst quantities. These judgments of magnitude are predictive of early mathematics achievement, as well as later achievement (Moore, vanMarle, & Geary, 2016). While the expressive language needed in these early years is quite Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) 42 DAVID EVANS restricted, this language has considerable power in communicating and demonstrating an understanding of mathematical knowledge in everyday contexts. In the early years of schooling, the demands in regards to demonstrating an understanding of a magnitude of number shifts. Students are required to be more specific about magnitude. Instead of indicating that a group of objects are more, less, bigger or smaller, they are now expected to be more specific (e.g. 7 is two more than 5). They need to be able to use a language of mathematical to be able to justify and defend their responses. The early mathematics literature provides evidence that use of these skills like magnitude and counting in a fluid and flexible manner is key to developing mathematical proficiency and preventing difficulties in mathematics (Gray & Reeve, 2016; Moore et al., 2016). This fluidity and flexibility in early mathematical skills and knowledge is often referred to as number sense. Gersten and Chard (1999) define number sense as: ‘a child’s fluidity and flexibility with number, the sense of what numbers mean, and an ability to perform mental mathematics and to look at the world and make comparisons’ (p. 20). Berch (2005) distilled from the literature a broad set of characteristics that are reported in the research literature to underpin the conceptual nature of number sense. This discussion highlights the view that number sense in its most rudimentary form occurs ‘spontaneously without much explicit instruction’ (Dehaene, 1997, p. 245). Jordan, Kaplan, Olah, and Locuniak (2006) support Berch’s position that number sense develops into a multifaceted concept through explicit instruction provided in the early years of schooling. Central to this discussion is that while number sense has an intuitive component to it, there is a need for young students to manipulate language concepts fluidly and flexibly. Failure to develop this proficiency has been linked to later difficulties in mathematics, use of mathematics generally and access to disciplines of high demand in the 21st century (e.g. Science, Technology, Engineering and Mathematics (STEM); Dyson, Jordan, & Glutting, 2013). Number sense for young children comprises a number of elements (Jordan et al., 2006). Jordan et al. and Berch (2005), for example, identify counting, number knowledge, perception of quantity changes, estimation, magnitude, and ability to move between real world or concrete examples and mathematical representations as some of the key elements of number sense. There is clear evidence that number sense can be taught (Aunio, Hautamaki, & Van Luit, 2005; Griffin, 2004), and especially beneficial to students from disadvantaged background (Dyson et al., 2013). The intuitive and developmental nature of number sense is key to everyday existence (Torbeyns et al., 2015). As adults, we use our sense of number in estimation, space and measurement to navigate our worlds. While number sense and early mathematical knowledge and language continues to emerge as an important construct in early learning and development (Griffin, 2004), its use across everyday domains highlights it as an enabler for access to personalised learning and across all curriculum domains (Bennison, 2015). Examining the Literacy within Numeracy 43 Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) NUMERACY AS AN ENABLER OF INCLUSIVE PRACTICE The use of mathematical knowledge in everyday activities and tasks places numeracy as a key enabler of quality of life, employment and leisure. Despite the importance of numeracy in our lives, mathematics continues to be a subject that many people shy away from. The power of this interplay between mathematical knowledge and the use of this knowledge to enhance everyday actions seems to be lost. This dilemma is no less evident than in everyday schooling where the power of identifying and embedding numeracy is lost in many curriculum areas. Bennison (2015) summarises this conundrum in the following way: ‘If all teachers are able to identify and exploit the numeracy learning opportunities that exist in the subjects they teach, then students’ numeracy capabilities along with learning in each subject is likely to be enhanced’ (p. 561). Further, the harnessing of numeracy (and literacy) can provide access to the curriculum by all students. Numeracy within and across Curricula and Education Students from Australian schools are increasingly completing 13 years of schooling without a subject in mathematics (Commonwealth of Australia, 2008), or opt for a general mathematics option (Quinnell, Thompson, & LeBard, 2013). The decline in the number of students completing higher-level mathematics is a concern in an era of STEM and building social capital. Yet the use of mathematical literacy is needed across all curriculum areas, and within everyday society. The Australian Government’s National STEM School Education Strategy comprises five domains for action. One of these areas involves ‘[extending] the national literacy and numeracy continuum to better assist teachers to identify and individual student needs …’ (Education Council, 2015, p. 9). This development reflects an ongoing concern about declining numeracy levels amongst students, reduction in number of students taking higher-level mathematics, as well as the need to develop this knowledge base in today’s students as part of building tomorrow’s social capital within the science and engineering domains. Quinnell et al. (2013) illustrate the role mathematical knowledge in working with scientific content, and its implications for science teachers. Science teachers need to: ‘explicitly reveal to students that quantitative skills (what they deem to be ‘maths’) are interwoven within the sciences, and that the ability to use these skills fluidly and confidently by scientists is an essential part of practicing the discipline’ (p. 814). This example from science can be replicated across other curriculum areas where mathematical knowledge is required to demonstrate understanding of key ideas (National Academies of Sciences, Engineering, and Medicine, 2016). In secondary history, for example, the use of timelines requires students to understand, structure and discuss the chronology of events using Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) 44 DAVID EVANS language concepts that many take for granted (e.g. now, later, before) (Blow, Lee, & Shemilt, 2012). The use of this mathematical literacy is used to understand complex sequences of events, argue differences in understanding historical circumstances, and justify conclusions drawn. The use of mathematical knowledge, that is numeracy or mathematical literacy, empowers students to better understand differing curriculum content with a range of contexts. As a result, teachers need to ‘have appropriate knowledge (mathematical, pedagogical and curriculum), a rich personal conception of numeracy, and a belief that numeracy is an integral part of the subjects they teach’ (Bennison, 2015, p. 572). Math language and development of numeracy requires a deliberate focus by teachers from across all curriculum areas (Harmon, Hedrick, & Wood, 2005). In primary school settings where the same teacher usually delivers the majority of curriculum areas to one group of students this aim could be structurally easier. In the secondary school setting, where students have differing curriculum specialists the task may be harder. Hence, all teachers need to be teachers of numeracy. Goos, Geiger, and Dole (2014) provide a model for developing numeracy across curriculum areas. This model comprises five elements: mathematical knowledge, contexts, dispositions, tools and critical orientation. The Goos et al. model reinforces a number of elements from the Nation Research Council for mathematical proficiency (e.g. disposition, procedural proficiency and conceptual understanding, strategic disposition). This model also highlights the importance the role tools play in being numerate (e.g. use of representations, technology to facilitate use of mathematical knowledge). Finally, this model gives a specific focus to a critical orientation: ‘Use of mathematical information to make decisions and judgments, add support to arguments, and challenge an argument or position’ (p. 84). While this latter element could be applied to formal mathematical knowledge, its use to make judgments in everyday contexts underpins it. This critical element involves making sense of ones’ world, often through proficient use of mathematical knowledge and language (e.g. number sense skills). Enhancing Access to the Curriculum through Numeracy In an era where all students have the right to access a quality schooling experience, teachers are continually challenged as to how to cater for the diverse range of student need in their classroom. In developing the Australian Curriculum, all students were considered as part of its design, and this is reflected in the three-dimensional design of the curriculum today. Providing access to the curriculum for all students required a curriculum that was flexible, meaningful and dignified for all. This has been achieved to a large extent through using the differing dimensions of the curriculum flexibly. In many Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) Examining the Literacy within Numeracy 45 circumstances, students enrich their access to the curriculum through focusing on all strands of content, using a rich array of the general capabilities and cross-curriculum priorities. In catering for the range of student needs in the classroom, teachers will need to give specific attention to how the curriculum they design and implement may pose barriers to student access. The language of mathematics, and the mathematical literacy within differing curriculum areas, is a potential barrier. While often literacy is seen as the primary barrier, mathematical literacy can also pose such frustrations for students. In planning to meet the range of student needs, the starting point is the age appropriate content listed in the curriculum framework. Through starting at this point, high expectations are established for all students. When teachers judge that students are unable to access the content, reflecting on the barriers within the curriculum design, materials and assessments could be considered (if this has not already been done). If with strong design features students cannot access the curriculum, adjustments may be considered (e.g. curriculum, instruction, environment and resources). Even with adjustments, if students are still continuing to experience difficulties accessing grade level content, teachers may draw on content from lower levels. In undertaking this process, teachers can also reduce the focus of the curriculum for some students. By reducing the amount of content they are working towards, teachers can teachers strengthen core mathematical understanding and numeracy. They can achieve this by also promoting personal needs and motivations, and everyday skills. Personalising Learning through Numeracy Over 150 countries have ratified the Convention on the Rights of Persons with Disabilities (United Nations, 2006). In the domain of education, it commits countries to providing the opportunity for students with disability to participate in education on the same basis as students without disability. Promoting numeracy is one way to support the intent of the Convention, and to personalise learning. Personalised learning has developed through endeavours to enhance the learning opportunities for all learners, in particular, persons with disability. The Australian Government, for example, in addressing its commitment to the Convention has provided guidance to education providers on developing personalised learning (Australian Government, n.d.). The process includes gathering information on a student and their background, examining available resources, establishing goals in collaboration with students with long-term benefits in mind, and developing processes to assess and monitor progress towards goals. This process provides a basis on which to establish the numeracy goals that Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) 46 DAVID EVANS may provide short-term access to curriculum areas, as well as providing access to outcomes that will have lifelong impact (e.g. personal care, employment, leisure interests). This process reinforces the notion that numeracy is context based (Goos et al., 2014; Jablonka, 2003; OECD, 2014). In examining the numeracy demands within regards to personal goals, understanding a student’s background knowledge is important. This requires consultation with the student to plan long-term goals. For example, in planning transition from secondary school to post school opportunities, the interests and personal motivations may be considered in regards to possible employment opportunities. Working as an apprentice, within an office or supermarket all require skills and knowledge of mathematical literacy; living independently and taking responsibility for personal care involves a strong sense of numeracy. In many cases these numeracy demands will need to be operationalised quickly (e.g. retrieving more of an item, requesting that an item be shifted so that another can be fitted in, providing cash for payment of an item), so mastery of skills and knowledge is an important of planning and supporting learning. Having this over the horizon view of the benefits of teaching robust mathematical knowledge alongside its use within genuine and meaningful contexts is essential for all classroom teachers. Not to have this over the horizon vision can lower expectations; to achieve this vision requires careful planning where students are given the chance to access the general curriculum on the same basis as their peers without disabilities. Yet there is evidence that suggest students with extensive educational needs do not receive quality instruction in early mathematics skills, or the opportunity to develop and practice early mathematical skills. Towles-Reeves, Kearns, Kleinert, and Kleinert (2009) reported that only 7.7% of students could rote count to 5. In a later study, Kearns, Towles-Reeves, Kleinert, Kleinert, and Thomas (2011) reported that 4% of elementary school students taking alternate assessments could use computational processes to solve simple real-world problems (i.e. use early number sense skills to solve everyday problems). In an enquiry into education programs for students with disability, an Australian Senate Committee reported that parents and carers considered the education programs that students with extensive support needs received was tantamount to ‘baby sitting’ (Commonwealth of Australia, 2016, p. 23). In one deposition a parent commented: He has got significant developmental delay I know that but he has functional literacy and numeracy. I do not need to justify why he should be able to learn how to read and write. His world is greatly enriched through his learning but he was denied the opportunity because of these assumptions that someone with a cognitive impairment should not learn. (p. 23) In a recent workshop with teachers, they reported teaching probability to group of Year 9 students with complex education needs. Video evidence highlighted the use of early communication skills to permit students to Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) Examining the Literacy within Numeracy 47 communicate their learning, and justify their choice. This example is contextualised within the student’s learning environment, and current interests and motivations. This anecdotal evidence exemplifies how high expectations, knowledge of age equivalent content, and the general capabilities (i.e. mathematical literacy) can maximise the inclusion of students with disabilities in the curriculum on the same basis as their peers without disabilities. Juxtapose this example with evidence where students with complex needs are provided access to an alternate curriculum on the basis they have a disability (Commonwealth of Australia, 2016). Promoting literacy, including mathematical literacy, empowers all students no matter their learning background or assumed ‘ability’. Providing the opportunity for students with complex support needs to access the same opportunity to participate in numeracy programs can have a long-term impact their quality of life. It can also impact on the social and financial welfare of their society. CONCLUSION Numeracy, or mathematical literacy, is the use of mathematical knowledge to navigate through and engage with our world. In discussing the importance of numeracy within the context of inclusive literacy practices, it is important to examine the broader benefits of numeracy. Often the focus is on developing higher-order mathematical knowledge (e.g. algebra, trigonometry), and using this knowledge to resolve today’s problems, or to underpin tomorrow’s great finding. Numeracy has an important place in everyday life for all of us. A key focus, therefore, should be on developing and using numeracy skills within a range of contexts that are important to each one of us (Steen, 2001). In designing inclusive education programs, mathematical literacy is foundational for all students across all domains of learning (National Academies of Sciences, Engineering, and Medicine, 2016). For students with disability, it is equally as important; but it needs to be tailored to their needs. Through designing curriculum that considers the demands of mathematical literacy, and the personal needs of students, teachers can address learning in a dignified and meaningful manner. Many of the numeracy skills are ones that commonly develop in the early years of life, but they are ones that we all use to navigate our own worlds (e.g. subitising, magnitude, position, patterns, estimating) and engage with higher-order everyday skills (e.g. positional strategies in using gaming console, problem-solving when constructing a household item). Each of these early numeracy skills is key for us all, and can be used to support learning across the curriculum and support us achieve our personal goals. Being numerate within your own context strengthens community and person. Being able to critically examine quantity through the use of flexible and efficient mathematical skills can prevent personal dramas, as well as allow one 48 DAVID EVANS to function efficiently in society. The language in using this mathematical knowledge in real-world situations is what opens doors in our lives. Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) REFERENCES Aunio, P., Hautamaki, J., & Van Luit, J. (2005). Mathematical thinking intervention programmes for preschool children with normal and low number sense. European Journal of Special Needs Education, 20, 131 146. Australian Curriculum, Assessment and Reporting Authority. (2016a). Australian curriculum: General capabilities. Retrieved from http://v7-5.australiancurriculum.edu.au/generalcapabilities/overview/general-capabilities-in-the-australian-curriculum Australian Curriculum, Assessment and Reporting Authority. (2016b). Australian curriculum: Numeracy - Introduction. Retrieved from http://v7-5.australiancurriculum.edu.au/generalcapabilities/numeracy/introduction/introduction Australian Curriculum, Assessment and Reporting Authority. (2017). Australian curriculum: Meeting diverse learning needs. Retrieved from http://www.australiancurriculum.edu.au/studentdiversity/meeting-diverse-learning-needs Australian Government (2014). Review of the Australian curriculum: Final report. Canberra: Author. Retrieved from https://docs.education.gov.au/system/files/doc/other/review_of_the_national_ curriculum_final_report.pdf Australian Government (n.d.). Planning for personalised learning and support: A national resource. Canberra: Department of Education and Training. Retrieved from https://docs.education. gov.au/system/files/doc/other/planningforpersonalisedlearningandsupportnationalresource. pdf Ayres, K., Lowrey, A., Douglas, K., & Sievers, C. (2011). I can identify Saturn but I can’t brush my teeth: What happened when the curricular focus for students with severe disabilities shifts. Education and Training in Autism and Developmental Disabilities, 46, 11 21. Baroody, A., Eiland, M., & Thompson, B. (2009). Fostering at-risk preschoolers’ number sense. Early Education and Development, 20, 80 128. Barth, H., La Mont, K., Lipton, J., & Spelke, E. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences of the United States of America, 102, 14116 14121. Bennison, A. (2015). Supporting teacher to embed numeracy across the curriculum: A sociocultural approach. ZDM Mathematics Education, 47, 561 573. Berch, D. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333 339. Blow, F., Lee, P., & Shemilt, D. (2012). Time and chronology: Conjoined twins or distant cousins? Teaching History, 147, 26 34. Browder, D., & Spooner, F. (2011). Teaching students with moderate and severe disabilities. New York, NY: Guilford. Cheong, J., Walker, Z., & Rosenblatt, K. (2016). Numeracy abilities of children in grades 4 to 6 with mild intellectual disability in Singapore. International Journal of Disability, Development and Education. doi:10.1080/1034912X.2016.1188891 Commonwealth of Australia. (2008). National numeracy review report. Canberra: Department of Works, Education Workplace Relations. Commonwealth of Australia. (2016). Education and employment reference committee: Access to real learning - The impact of policy, funding and culture on students with disability. Canberra: Author. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press. Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) Examining the Literacy within Numeracy 49 Duncan, G., Dowsett, C., Claessens, A., Magnuson, K., Huston, A., Klebanov, P., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428 1446. Dyson, N., Jordan, N., & Glutting, J. (2013). A number sense intervention for low-income kindergartners at risk for mathematics difficulties. Journal of Learning Disabilities, 46, 166 181. Education Council (2015). National STEM school education strategy: A comprehensive plan for science, technology, engineering and mathematics education in Australia. Retrieved from http:// www.educationcouncil.edu.au/site/DefaultSite/filesystem/documents/National%20STEM% 20School%20Education%20Strategy.pdf Frye, D., Baroody, A., Burchinal, M., Carver, S., Jordan, N., & McDowell, J. (2013). Teaching math to young children: A practice guide (NCEE 2014-4005). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from the NCEE website: http://whatworks.ed.gov Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J., … Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc/publications/ practiceguides/ Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. Journal of Special Education, 33, 18 28. Goos, M., Geiger, V., & Dole, S. (2014). Transforming professional practice in numeracy teaching. In Y. Li, E. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 81 102). New York, NY: Springer. Gray, S., & Reeve, R. (2016). Number-specific and general cognitive markers of preschoolers’ math ability profiles. Journal of Experimental Child Psychology, 147, 1 23. Griffin, S. (2004). Building number sense with whole numbers: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173 180. Harmon, J., Hedrick, W., & Wood, K. (2005). Research on vocabulary instruction in the content areas: Implications for struggling readers. Reading and Writing Quarterly, 21, 261 280. Hoppey, D., & McLeskey, J. (2013). A case study of principal leadership in an effective inclusive school. Journal of Special Education, 46, 245 256. Hoppey, D., & McLeskey, J. (2014). What are qualities of effective inclusive schools? In J. McLeskey, N. L. Waldron, F. Spooner, & B. Algozzine (Eds.). Handbook of effective inclusive schools (pp. 17 29). New York, NY: Routledge. Huntsinger, C., Jose, P., & Luo, Z. (2016). Parental facilitation of early mathematics and reading knowledge through encouragement of home-based activities. Early Childhood Research Quarterly, 37, 1 15. Jablonka, E. (2003). Mathematical literacy. In A. Bishop, M. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education. Kluwer Academic. Jordan, N., Kaplan, D., Olah, L., & Locuniak, M. (2006). Number sense growth in Kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153 175. Kamil, M. L., Borman, G. D., Dole, J., Kral, C. C., Salinger, T., & Torgesen, J. (2008). Improving adolescent literacy: Effective classroom and intervention practices: A practice guide (NCEE #2008-4027). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc Kearns, J., Towles-Reeves, E., Kleinert, H., Kleinert, J., & Thomas, M. (2011). Characteristics of and implications for students participating in alternate assessments based on alternate academic achievement standards. Journal of Special Education, 45, 3 14. Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) 50 DAVID EVANS Kozleski, E., & Waitoller, F. (2010). Teacher learning for inclusive education: Understanding teaching as a cultural and political practice. International Journal of Inclusive Education, 14, 655 666. MacFarlane, K., & Woolfosn, L. (2013). Teacher attitudes and behavior toward the inclusion of children with social, emotional and behavioral difficulties in mainstream schools: An application of the theory of planned behavior. Teaching and Teacher Education, 29, 46 52. Moore, A., vanMarle, K., & Geary, D. (2016). Kindergartner’s fluent processing of symbolic numerical magnitude is predicted by their cardinal knowledge and implicit understanding of arithmetic 2 years earlier. Journal of Experiential Child Psychology, 150, 31 47. Morgan, P., Farkas, G., Hillemeier, M., Hammer, C., & Maczuga, S. (2015). 24 month-old children with larger oral vocabularies display greater academic and behavioral functioning at kindergarten entry. Child Development, 86, 1351 1370. National Academies of Sciences, Engineering, and Medicine. (2016). Science literacy: Concepts, contexts, and consequences. Washington, DC: The National Academies Press. doi:10.17226/ 23595 National Numeracy. (2016). What’s the issue? Retrieved from https://www.nationalnumeracy.org.uk/ what-issue National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Mathematics learning study committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. OECD. (2014, February). PISA 2012 results: What students know and can do Student performance in mathematics, reading and science (Vol. 1, Revised ed.). Paris: OECD Publishing. Quinnell, R., Thompson, R., & LeBard, R. (2013). It’s not maths; it’s science: Exploring thinking disposition, learning thresholds and mindfulness in science learning. International Journal of Mathematics Education in Science and Technology, 44, 808 816. Riccomini, P., Smith, G., Hughes, E., & Fries, K. (2015). The language of mathematics: The importance of teaching and learning mathematical vocabulary. Reading and Writing Quarterly, 31, 235 251. Riccomini, P., & Witzel, B. (2010). Response to intervention in mathematics. Thousand Oaks, CA: Corwin Press. Ryndak, D., Moore, M., Orlando, A., & Delano, M. (2008 2009). Research-based practice for students with extensive support needs. Research & practice for persons with severe disabilities, 33 34, 199 213. Slee, R. (2013). How do we make inclusive education happen when exclusion is a political predisposition? International Journal of Inclusive Education, 17, 895 907. Spooner, F., McKissick, B., Hudson, M., & Browder, D. (2014). Access to the general education curriculum in general education classes. In M. Agran, F. Brown, C. Hughes, C. Quirk, & D. Ryndak (Eds.), Equity and full participation for individuals with severe disabilities: A vision for the future (pp. 217 234). Baltimore, MD: Paul H. Brookes. Steen, L. (2001). The case for quantitative literacy. In L. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. 1 22). Princeton, NJ: National Council on Education and the Disciplines. Thomas, C., Garderen, D., Scheurmann, A., & Lee, E. (2015). Applying a universal design for learning framework to mediate the language demands of mathematics. Reading and Writing Quarterly, 31, 207 234. Thompson, D., & Rubinstein, R. (2000). Learning mathematics vocabulary: Potential pitfalls and instructional strategies. Mathematics Teacher, 93, 568 573. Toll, S., & Van Luit, J. (2014). The developmental relationship between language and low early numeracy skill throughout kindergarten. Exceptional Children, 81, 64 78. Torbeyns, J., Gilmore, C., Verschaffel, L. (2015). The acquisition of preschool mathematical abilities: Theoretical, methodological and education considerations. Mathematical Thinking and Learning, 17, 99 115. Downloaded by Australian Catholic University At 23:01 25 October 2017 (PT) Examining the Literacy within Numeracy 51 Towles-Reeves, E., Kearns, J., Kleinert, H., & Kleinert, J. (2009). An analysis of the learning characteristics of students taking alternate assessment based on alternate achievement standards. Journal of Special Education, 42, 241 254. Tsakiridou, H., & Polyzopoulou, K. (2014). Greek teachers’ attitudes toward the inclusion of students with special educational needs. America Journal of Educational Research, 2, 208 218. UNESCO. (1994). The world conference on special needs education: Access and quality. Final report. Salamanca, Spain: Ministry of Education and Science, Madrid; UNESCO. Retrieved from http://www.unesco.org/education/pdf/SALAMA_E.PDF United Nations. (2006). Convention on the rights of persons with disability. Retrieved from http:// www.un.org/disabilities/convention/conventionfull.shtml van der Walt, M., Maree, K., & Ellis, S. (2008). A mathematics vocabulary questionnaire for immediate use in the intermediate phase. South African Journal of Education, 28, 489 504. van Garderen, D., Poch, A., Jackson, C., & Roberts, S. (2017). Teaching mathematics to students with disabilities from diverse background. In M. Hughes & E. Talbott (Eds.), The Wiley handbook of diversity in special education (pp. 209 230). Hoboken, NJ: Wiley. Watts, T., Duncan, G., Chen, M., Claessens, A., Davis-Kean, P., Duckworth, R., … Susperreguy, M. (2015). The role of mediators in the development of longitudinal mathematics achievement associations. Child Development, 96, 1892 1907. Wehmeyer, M. (2014). Disability in the 21st century: Seeking a future of equity and full participation. In M. Agran, F. Brown, C. Hughes, C. Quirk, & D. Ryndak (Eds.), Equity and full participation for individuals with severe disabilities: A vision for the future (pp. 3 23). Baltimore, MD: Paul H. Brookes.

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