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Diversity issues in mathematics classrooms can provide great challenge for

teachers, who must identify these students and understand their special

mathematical needs. There is a complex mix of educational and ethical demands on

the teacher in mathematically empowering students for success in the classroom

and the ‘real world’.

This essay will seek to outline three different groupings of students, common on the Mid

North Coast of NSW, that demand differentiation of the mathematics curriculum in

order to succeed in the classroom and real world. The author will explore common

assessment tools, some strategies useful in fostering mathematical interest will be

highlighted as will teacher responsibility in successful curriculum delivery. At the core

of this essay will be the notion that all learning, particularly mathematics, must be

delivered equitably and that hidden amongst curriculum documents, policies and

ultimately a teachers own pedagogy is the political and sociological aspects that shape

and colour the final product identifying that all learning is ultimately an invention of

political and social expectation within the context of the student, their family and

community. With this knowledge it is imperative that the educator create authentic and

meaningful tasks that make real world connections to all students’ mathematical

learning.

The nature of the Australian classroom has shifted rapidly, especially in regional NSW,

where high populations of refugee families now exist who have children needing to be

educated in regular English speaking classrooms (Coffs Harbour City Council, 2009;

Hickey, Nicholls, Hayes, Firkins, & Parry, 2011). This challenge is also compounded with

high proportions of Indigenous students and mounting enrolments of students with

varying diagnosis or additional needs. Then there are regular, talented and gifted

students ultimately making exceptional demands on a teachers’ ability to deliver a

quality curriculum that is inclusive, rigorous and meets the learning needs of all

students (Churchill et al., 2011; Conway, 2008; Groundwater-Smith, Brennan,

McFadden, Mitchell, & Munns, 2009).

The NSW Mathematics syllabus states that in order for a student to “make connections

and develop richer understanding of mathematical concepts” they need to be ‘working

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mathematically’ (Board of Studies NSW, 2002). They need to question, apply decoding

strategies, communicate, reason and reflect upon their learning (Board of Studies NSW,

2002). The Australian curriculum asks for students to problem solve, demonstrate

understanding and fluency in their mathematical learning (ACARA, 2010). Both these

curriculums are driven by national and state policies that reflect the core beliefs and

values of the current political party in office and therefore the curriculum will always be

birthed from government drivers towards what is deemed valuable to the nation.

Whatever system you could work in or whatever government is in power at the time,

will be incidental as it will be the educators informed choices and decisions about the

relevance of the curriculum for their students that will determine the actual curriculum

reality (Groundwater-Smith et al., 2009). The educator wields great power in the

classroom and mathematics is inherently the most challenging of key learning areas

(KLA’s) for the child; how that educator chooses to deliver maths will be significant in

either empowering or disempowering the student.

When designing and creating a maths program for the classroom the educator must

ensure that it is an equitable living document that allows all students in her class the

same opportunities to succeed in their mathematical outcomes. Being aware of the

“interests and experiences” (Gojak, 2012) of students in the classroom will allow

teachers to shape mathematical learning practices authentically in order for students to

make sense of their learning and be able to apply it to real world contexts meaningfully

(Gojak, 2012; Nasir & Cobb, 2002). A relationship must be fostered between the learner

and educator that allows for shared ownership of learning experiences. This enables the

learner to become empowered through the teacher valuing their voice and input. The

classroom becomes a safe place to take mathematical risks, question and apply new

learning through mathematical enquiry and reasoning (Ayers, 2004; Crawford &

Rossiter, 2006; Foreman, 2008).

Before a maths program can be created assessment must occur. One cannot exist

without the other. It is imperative that the teacher know where their students are

exactly in order to map future learning. Self-assessment by the student also creates

ownership and responsibility for their learning (Koshy & Jackson-Stevens, 2011; Van De

Walle, Karp, & Bay-Williams, 2010) and can be accessed through rubrics or using maths

journal activities (Runde, 2012), for instance, where the student applies the traffic light

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comprehension dot i.e. green = good to go on, yellow = proceed with caution – check for

understanding before moving on and red = stop – must have extra practice with the

concept before moving on. Self-assessment allows the educator a window into how their

student sees and constructs their own learning (Van De Walle et al., 2010) and this then

affords deeper understanding into a student’s understanding of a topic. There is an

element of risk with self-assessment as new learning will challenge the students

thought processes within their social constructs and the teacher must be sensitive in

order to expand students’ knowledge base and construct new realities (Shipway, 2011).

Self-assessment also nurtures agency for the child as they develop understanding

through mathematical endeavour. This is highly empowering for a student of all abilities

as they are able to critically evaluate, make assumptions and share their finding with

their teacher and peers (Stinson, Bidwell, & Powell, 2012).

Assessment must be fair, reliable and transparent in order to be equitable and must be

used as a tool to enrich learning and not be tacked to the end of a learning topic (Killen,

2005) simply to tick a box. It should also align with the quality teaching model (Hinde-

McLeod & Reynolds, 2006; NSW Department of Education and Training, 2003) which in

turn encourages the development of richer tasks that foster deep knowledge,

problematic and higher order thinking whilst demanding high expectations that are

significant and incorporate inclusivity and connectedness for all learners (Hinde-

Mcleod & Reynolds, 2007; Killen, 2005).

Much research defines what quality or rich assessment tasks are and they can take

many forms, for example, the most common assessment formats that are used in the

NSW maths classroom are: Diagnostic: NAPLAN, Best Start, SENA, Newman’s Analysis,

TENS; Summative: Tests, quizzes, presentations, group projects, portfolios; Formative:

Observation, anecdotal note taking, self-assessment, peer-assessment, discussion,

strategic questioning. It is up to the teacher to ensure that her students are equally

prepared and have the skills necessary to complete a particular assessment fairly as

many of the above examples require specific skills, particularly lingual and literacy, in

order to be successful.

Consequently by adopting the above tools and strategies the educator should be able to

gain an understanding into how their students have “understood mathematical facts

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and language, acquired mathematical skills with understanding, appreciated the

interconnectedness of mathematical ideas, developed robust conceptual understanding

of ideas, employed effective strategies for problem solving and developed a positive

attitude towards the subject” (Koshy & Jackson-Stevens, 2011, p. 152).

Notably, this is no more important than when dealing with Indigenous students.

Howard and Perry stipulate that prior knowledge of Indigenous students’ abilities and

interests is critical alongside developing relationships with their families and

community (2011). Many of these students arrive in the classroom with great

mathematical knowledge but the importance is to recognise that it has been acquired

differently from the traditional structured manner (Howard & Perry, 2011; Wyatt,

Carbines, & Robb, 2007) that is often found in the Western classroom. What these

students learn must be relevant to them and their real world. The Indigenous student

needs to work mathematically and develop understanding that is purposeful to them.

The educator must create experiences that are connected to the Indigenous child’s

world, for example an excursion to the Arrawarra fish traps might also involve students

mapping the area, identifying fish species, and looking at the tides and their connection

to the lunar cycle. Additionally Howard and Perry identify three components that they

believe will ‘close the gap’ for Indigenous and non-Indigenous students and these are:

Mathematisation: Creating mathematical problems from real world issues and

using mathematical strategies to solve them.

Argumentation: This is the reasoning where the student explains and justifies

their learning whilst also applying understanding to other students’ rationales.

Connection: Allowing the student to see the connections their learning in a

mathematical area has to other areas of mathematics and their own life.

(Howard & Perry, 2011, pp. 135-136)

Vygotsky identified the inherent role of social interaction upon the child’s cognitive

development and the context which defines it (Berk, 2006) and this knowledge

preceded further research that also recognises that mathematics is ‘embedded in

certain cultural contexts’ (Wyatt et al., 2007). The difference between western

mathematics and the Indigenous people’s relationships with mathematics is expansive.

Acknowledging and embracing this difference as potential for rich learning is vital. As

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Noel Pearson writes “if you are black in this country, you start with a great and crushing

burden” (Pearson, 2009, p. 25) therefore it is crucial that educators do not bow down

and lower their expectations for Indigenous students in their class. These students are

mathematically empowered and by recognising their skills, adapting lesson content and

language, and involving their community and them in the creation of meaningful maths

experiences, learning outcomes should be successful for all stakeholders.

Similarly for the gifted and talented (GAT) students the maths classroom can be a

daunting or uninspiring place. Identification of these students early is critical in order to

provide opportunities to develop talent further. If the educator provides diverse

learning strategies in her classroom these can help to identify these students, but if

teaching is delivered in a one size fits all box these students will often slip under the

radar or off it altogether (Casey, 2011; Norris & Dixon, 2011; Van De Walle et al., 2010;

Watters & Diezmann, 2003). Koshy, Ernest and Casey suggest that there is no one

definition of mathematical giftedness and rather it is the “quality of being able to do

mathematical tasks and utilise knowledge effectively” (as cited in Casey, 2011, p. 126).

They add that there is another dimension to this talent and that is the ability to solve

“novel and non-routine problems” (Casey, 2011, p. 126). This opens the door to the

educator and challenges them to throw out the extension worksheets and provide these

students with richer challenging tasks such as personal learning projects (PLP’s) or

challenges selected by the students, created in collaboration with the educator, and

constructed within the Gardiner and Blooms learning matrix (Bloom, 1956; Gardner,

2012). These PLP’s can incorporate objectives across the curriculum and therefore are a

powerful and authentic activity that allows the student to ‘dig the learning hole deeper

not wider’- the student is motivated and can work at a higher pace autonomously. An

example could be to connect the HSIE unit Antarctica to maths outcomes i.e. looking at

temperatures, wind speeds, seasons and solar rotations, animals heights and weights,

construction of Antarctic bases, the list is endless and the mathematical applications

also unlimited. The author is currently working on a project with a Stage 3 class on the

Mid North Coast and the students are utilising virtual technology to build Antarctic

bases and environments. The virtual program is highly mathematical utilising 3D space

and mapping/size grids which is highly engaging especially for the more able students

in the class.

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Gifted students can also be very creative and mathematics lends itself beautifully to the

creative arts. Allowing students to integrate their mathematical learning into artistic

projects by looking at art from a mathematicians eye and seeing maths in the wider

world whether through music, architecture, the seasons, flora and fauna etc, can tap into

those intelligences that will result in further mathematical interest, success and

achievement (Banffy, 2012; Casey, 2011).

A final group of students that will often appear in the classroom with diverse and

varying English spoken and written skills are those who have arrived with refugee,

migrant or international student status, commonly called English as secondary language

students (ESL). This creates difficulties in the maths classroom as mathematical

language is defined as “academic language” and therefore takes considerable time, often

years, to master (Van De Walle et al., 2010, p. 103). Of primary importance is that these

students are enrolled into an intensive English program in consultation with the

parents, ESL teachers and numeracy and literacy consultants. Diagnostic testing is

critical to identify the exact starting point for learning (ACARA, 2012). Some maths

dictionaries are available that offer translations to the students own dialect, for

example, Coffs Harbour Public School uses a Farsi and Swahili maths dictionary for its

students from Afghanistan and Africa. Another strategy is to be explicit in instruction,

concentrate on using concrete materials the students can touch and manipulate and link

mathematical activities to the ESL students’ real life experiences (Buchanan & Helman,

1997). All maths assessment tasks should be checked for “wording that does not

introduce additional comprehension hurdles over and above required content” (Shaftel,

Belton-Kocher, Glasnapp, & Poggio, 2006, pp. 121-122). Working maths groups of

students’ whose first language is the same as the new ESL student also works well as it

draws out the students confidence as they work alongside their peers and this also

enables the teacher to glean more information about the students in a non-threatening

and safe environment. Van De Walle et all writes this strategy also identifies to the ESL

student that their language and culture is valued as something to be utilised in the

classroom meaningfully rather than to be seen as an obstacle to overcome (Van De

Walle et al., 2010, p. 105).

In conclusion diversity is challenging for the maths teacher when it takes so many

different forms. Educators have to become adept at harnessing strategies that are

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equitable and foster inclusion for all the students in their class. Mathematics being

characteristically problematic due to complex language and symbol barriers sets the

challenge for educators to design meaningful experiences for students through learning

plans that reach and extend each student’s specific mathematical needs. Throughout

this essay the common theme has been connecting through relationships and valuing

each student’s identity in order to achieve success in learning. Research further

underpins this concept by stating that “identity plays a significant role” (Nasir & Cobb,

2002, p. 99) in the equitable delivery of learning as the two are intertwined; and if the

educator can embrace this concept richer learning experiences will eventuate and

deeper understanding of mathematics and it place in the many different worlds of the

students will eventuate (Nasir & Cobb, 2002).

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