GENDER

Evidence suggests that there are fewer females entering scientific and

mathematical vocations (Tytler, Osborne, Williams, Tytler & Cripps-Clark,

2008), which appears associated with engagements levels with these subjects in

middle school (Carmichael & Hay, 2009, p. 97). Students with an interest in maths in middle

school gravitate toward mathematical subjects in secondary school (Forgasz,

2006 cited by Carmichael & Hay, 2009).

It could therefore be inferred that boys are more interested in maths in

primary school.

Many theories attempt to explain this gender differences, from context

or topics chosen and strategies employed by teachers (Carmichael & Hay,

2009), to student self-efficacy, cultural identity and academic achievement (O’brien, Martinez-pons, & Kopala, 1999).

Tytler et al. (2008) identify several strategies to assist teachers to

address student interest, including creating “contextual and socially

responsive” (p. 136) maths lessons to meet curriculum outcomes, as well as

suggesting that teachers vary the pedagogies used to ensure student engagement

is maintained and “to build students’ resilience and self efficacy through

pedagogies that provide encouragement and stimulate intellectual engagement

that can lead to successes for all students and do not support premature

judgments, or send the message to students that they are not capable of success

in STEM” (p. 136).

Albeit in a statistics context, Carmichael & Hay (2009) suggest

that boys interests favoured outcome driven topics such as sports, whereas

process driven tasks such as surveys maintained the interest of female

students. Eccles (1987) also reports

that female students prefer cooperative tasks as opposed to competitive ones

(cited by Carmichael & Hay, 2009).

Lowrie, Diezmann & Logan (2009) cite Silverman & Choi (2006)

who suggest that boys are better at mapping tasks than girls, perhaps due to

their confidence from increasing “exposure to technology-based

entertainment games” (p. 2).

Having said this, Else-Quest, Hyde & Linn (2010) suggest that

gender differences in mathematics performance by students in the USA is

diminishing or has been eliminated.

Similarly, Marks (2008) reported the results from studies such as Husen

(1967, p. 240) who reported that “boys outperformed girls in mathematics

in most countries” (p. 91) to the 1990 where Baker and Jones (1993) found

that “gender differences in mathematics declined in all but two of the

nine countries where comparisons could be made” (p. 91). With regard to gender performance in

mathematics in Australia, National Assessment Program Literacy and Numeracy

(NAPLAN, 2017) results for 2016 show that there is a higher percentage of

female Year 3 students at or above national minimum standard than male students

in all states and territories, and this result is replicated in Year 5 and Year

7. It is only in Year 9 that male students

in Tasmania outperform female students.

Despite the narrowing or closure of the gender gap in mathematics, it

is still worth noting the ways in which the interest and motivation of both

genders can be accommodated in the classroom during mathematics lessons.

The literature review suggests that the teacher’s selection of context

for their math lesson is imperative to gaining and maintaining the interest of

their students. It is for this reason

that a group cooperative learning strategy using role cards will be employed to

engage students in the MA2-12MG outcome focussing on measuring, recording and

comparing the mass of classroom objects.

Students will be required to use appropriate terminology and symbols

when recording results (MA2-1WM).

Mixed ability and mixed gender groups will be established by the

teacher. Roles appropriate to the

individual’s abilities and interest will be assigned by the teacher. Refer to Appendix 1 for an outline of the

available roles. The goal-orientation of

the boys will be addressed via competition linked to accuracy of results. The focus for the girls will be on the

collection process, verification of findings and displaying the group’s

results. Differentiation in roles each

student assumes is designed to maintaining interest of both gender groups. A group task where both competition as well

as cooperation are created.

INDIGENOUS

Indigenous students perform lower, even up to two years behind in

mathematics than non-indigenous students, (Warren & deVries, 2009). National Assessment Program Literacy and Numeracy

(NAPLAN, 2017) results show that 15.1% of indigenous Year 3 students are below

national minimum, compared with just 1.9% of non-indigenous students. This increases to 17% in Year 5 and 17.2% in

Year 7 for indigenous students.

Matthews, Watego,

Cooper & Baturo (2005) propose that as Indigenous culture is not embedded

in Australian curriculum, Indigenous students find it hard to relate to

mathematics, and there is little confidence in their mathematical ability by

teachers.

Matthews et al. (2005) submit that the Australian education system

devalues and undermines Indigenous cultures and identities, preferring to

reflect dominant western beliefs. Siemon, Beswick, Brady, Clark, Faragher,

& Warren (2011) recommend considering the experience and opportunities that

all students, Indigenous and non-indigenous bring to the class (p. 155) to

determine appropriate pedagogy.

Despite the perceived devaluing of their

culture, in order to maximise opportunities outside of their local community, Indigenous

and Torres Strait islander children, their families, communities and elders

should consider the benefits of a Western education alongside traditional

knowledge (Siemon et al., 2011, p. 155).

Supporting this, Matthews et al. (2005) indicate that some Elders of

Indigenous communities support the need for Indigenous children to learn

mathematics as it is their desire for them to have greater opportunity. In order to support Indigenous students,

mathematics educators need to acknowledge the need for Indigenous student to

maintain connections with their home community, while prioritising the

supporting they provide for these students to transition into Australian

society (Meaney & Evans, 2012).

Students are more likely to make connections

between classroom mathematics and other areas of their life if their social or

cultural context is taken into account (Siemon et al., 2011). “A culturally responsive approach to

numeracy adopts teaching strategies and curriculum content that are adjusted so

that students can build upon their familiar, existing skills and

knowledge” (Siemon et al., 2011, 171).

Contextualisation is one way of

“incorporating aspects of Indigenous culture and Indigenous perspectives

into the pedagogical approaches to mathematics” (Matthews et al. 2005, p.

5), but caution that “it is important not to get caught up in applying

reductionism to find mathematics relevance within Indigenous culture as this

approach may lead to Western pedagogies dressed up in superficial Indigenous

motifs.” (p. 6). Perry & Howard

(2008) discuss a contextualisation project undertaken by the NSW Board of

Studies called the Mathematics in Indigenous Contexts (MIC) which enjoyed some

success in implementing inclusive pedagogies, consulting and involving local

Indigenous communities in the planning and execution of units of work.

It is important to acknowledge however, that

the home environments and cultural experience of Indigenous students are very

diverse, depending on their rural or urban location (Warren & Miller,

2013). What appears to be consistent is

that Indigenous students come to school possessing mathematical skills, albeit

not necessarily Western mathematics (Warren & Miller, 2013).

Similar to the MIC project outlined by Perry & Howard (2008), the

four Indigenous students in our class are from the local Dharawal Aboriginal

community to whom there are several sites of significance within excursion

distance of the school.

A place-based and cooperative learning activity will be undertaken whereby

students are taken out of the school to visit a local site of Aboriginal

significance. Whilst there, a member of

the Dharawal community will talk to the students about the significance of the

site and what it means to their community, calling on the Indigenous students

in the class to share some of their experiences (cross curricular synergies

with History Stage 2 Community and Remembrance outcomes). In small groups, students will then complete

activities designed to deliver MA2-9MG outcomes, focussing particularly on

recognising “the features of a three-dimensional object associated with

length that can be measured, eg length, height, width, perimeter” (NSW

Board of Studies, 2012). Students will

be required to estimate and then check the accuracy of their estimations and

explain their reasoning (MA2-3WM) for any differences in estimates and actual

measurements. Worksheets will be

provided (see Appendix 2 for an example).

MILD AUTISTIC SPECTRUM DISORDER

Children with autism display characteristics described by Autism

Spectrum Australia (Aspect) (2017) as having behavioural difficulties, and facing social and communication challenges.

Children with ASD favour routine and repetitive behaviour so as to maintain

environmental predictability, socially they “have difficulty establishing

and maintaining relationships” and with regard to communication,

“those who can speak, they will often use language in a very limited or

unusual way”. Donaldson & Zager

(2010) go so far as to suggest that high functioning ASD students have a

similar neuropsychological profile as students with non-verbal learning

disabilities (p. 41).

“With acceleration of the prevalence of autism spectrum disorder

(ASD) has come the imperative to provide effective intervention and treatment”

(Wong, Odom, Hume, Cox, Fettig, Kucharczyk, Brock, Plavnick, Fleury &

Schultz, 2015, p. 1951)

When compared with students with learning disabilities, students with

ASD demonstrate slower rates of improvement in applied mathematics and

calculation skills (Wei, Lenz, & Blackorby, 2013).

Further, King, Lemons & Davidson (2016) cite Migliore, Timmons,

Butterworth, & Lugas (2012) who claim that despite average or above-average

mathematical performance, students with ASD are less likely to attend tertiary

education than other students with a disability, and so are more susceptible to

unemployment (p. 444).

As cited by Barnett & Cleary (2015, pp. 172-173), Mayes &

Calhoun (2003) and Whitby & Mancil (2009) report that when the cognitive

complexity increases, and students with ASD are required to problem solve,

engage in higher order thinking and mathematical reasoning, students with ASD

may struggle to sustain acceptable mathematics skills, knowledge and

understanding.

Targeted direct instruction, particularly visual representation, as

seen in the results of studies conducted by Bouck, Satsangi, Dougherty, &

Courtney (2013), Cihak & Foust (2008), and Rapp, Marvin, Nystedt, Swanson,

Paananen, & Tabatt (2012) as outlined by Barnett & Cleary (2015, pp.

175-177) has achieved some success improving the mathematical performance of

students with ASD in primary school.

King et al. (2016, p. 453) also elaborate on instructional intervention

strategies, including the use of ICT via videos and computer programs, as well

as prompting, supported by a combination of positive reinforcement and concrete

manipulatives (p. 456). In addition,

many of the students in these studies were removed from the mainstream class to

either a secluded section of the classroom, or another room (Barnett &

Cleary, 2015, p. 181). This instruction

was one-on-one in a large portion of cases (King et al., 2016, p. 455).

Many of the studies cited by both Barnett & Cleary (2015) and King

et al. (2016), involved small sample groups.

While this may not seem statistically significant, it is reasonable to

consider the outcomes relevant to an inclusive classroom in which just one

student has ASD.

As discussed in the literature review, targeted one-on-one

instructional intervention using concrete manipulatives has been successful in

achieving positive results with students with ASD. It is therefore the chosen strategy to teach

the required concepts of time for Mathematics outcome MA2-13MG to our

high-functioning autistic student, focussing on matching digital and analog

times and writing them in words.

Concrete manipulatives such as the clocks used in the What is the Time?

activity on nrich.maths.org, matched with custom digital time flashcards (see

Appendix 3) will be used.

During the class math lesson, our ASD student works one-on-one with the

Special Needs Teacher in their office.

Tailored to the Mathematics MA2-13MG outcome, the Special Needs teacher

may choose to use the following concrete manipulatives: a selection of analog

clocks (refer Appendix 3) that the student can then identify using appropriate

terminology (MA2-1WM), and also write the digital time; or they may play a

matching game where flashcards (such as those in Appendix 3) are turned over to

match the digital and analog times.

While students in the mainstream class me be engaging in the same

activities, the ASD student benefits from one-on-one direct teaching to assist

and prompt where and when required.