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
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 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.
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
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
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.