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Inclusive Principles and Practices in Literacy Education
Examining the Literacy within Numeracy to Provide Access to the Curriculum for All
David Evans,
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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
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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
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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
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DAVID EVANS
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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)
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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
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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).
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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
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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
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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
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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
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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
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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
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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.
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