Written Report - Final
Written Report - Final
Written Report - Final
ASHLEE FARRELL
OCTOBER 2019
1. introduction
The setting of this inquiry project was conducted in a category 4 Government school in the Northern
Suburbs; this school maintains high expectations of both student behaviour and academic achievement
with the school values of respect, honesty and responsibility underpinning all of their relationships. The
annual report stated that the school has a priority on Numeracy development along with Student
Wellbeing and Engagement. To aid in this priority the site has constructed a coaching program for all staff
to assist in this; each staff member is allocated to a member of leadership to meet with once a fortnight to
consider pedagogical decisions and assist teacher’s in reflecting on their student learning outcomes. A
majority of students within this case study classroom are below Year 7 standard for basic maths and
numeracy understanding and the two case studies identified are regularly disengaged from their learning
in very different ways. My planning aimed to develop the four operations of mathematical thinking for the
entire co-hort, through the introduction of a daily mental routine in conjunction with the strategy of visible
learning (Hattie & Zierer, 2019); where children are able to witness their progress on an individualised
goals board. Delivery of curriculum content was constantly evolving considering the two case studies and
reflections on their engagement with lessons, eventually lessons were delivered with multiple entry points,
to allow both case studies to operate in their different zones of proximal development (Roth & Jornet,
2017).
2. Literature review
Student responses to mathematics in regards to their beliefs, attitudes and feelings are grounded in their
experiences; and these experiences are generally confined to the classroom. Middle school is when many
students develop negative and debilitating views of maths (Grootenboer & Marshman, 2016), or otherwise
termed ‘Math Anxiety’. This is associated with an initial, rapid aversion to seeing a problem in maths, even
before beginning to solve it. A major challenge to students’ interest and success in math is because of the
negative and anxious emotions associated with the anticipation and performance of mathematics. In the
long-term, math anxious individuals show avoidance of math computations, and given the two case studies
for this report are already showing signs of class disengagement and are about to embark on their high
school journeys, it is important that some interventions are explored to make maths engaging, creative
and unique to help overcome this aversion before anxiety settles in (Pizzie & Kraemer, 2017). Students
have reported that teachers who made a difference in their lives were those that were passionate,
prepared and able to show different ways of doing things (Grootenboer & Marshman, 2016). By integrating
instructional adjustments and task variations ‘at risk’ or ‘low achieving’ students are able to find
satisfaction and success in curriculum content as well as a decrease in boredom (Werner, 2001). Both
teaching and assessment of learning should place less emphasis on memorisation (lower-order thinking)
(Gordon, 2016), and focus more on providing opportunities for creative learning through a hands-on
experience; making maths lessons more meaningful and leading to improved educational performance
(Janes, 2014). High quality learning experiences result from teaching approaches that promote
experimentation and inquisitiveness. By incorporating visual strategies into the curriculum, deep
engagement is supported with limitless possible benefits for developing social and personal skills that
make learning more meaningful and engaging.
A constructivist approach will form the basis of the planning and practice throughout this inquiry, as it will
support the case studies in generating knowledge through their own experiences (Encyclopaedia of the
sciences of learning, 2012). Blooms taxonomy states that there are six levels of a learner's development;
the first three skills are considered to be ‘lower-order thinking’ skills which are remembering,
understanding and application. These skills will form the beginning phases of lesson development to help
with explicit teaching and connections to prior knowledge. When a students’ zone of proximal
development extends beyond these skills it can move into the ‘higher-order thinking’ skills of, analysis,
evaluation and creation (Samo, 2017) with unstructured or open-ended problems (Brookhart, 2010). It is
expected that by incorporating visual and interactive strategies within the classroom along with a number
of instructional adjustments the case studies will have the right environment to operate in their individual
zones of proximal development (Roth & Jornet, 2017).
Given the diversity of both case studies, planning will consider the challenge that linking fun and creatively
based ways to do maths is not always possible when working with definitive content descriptors and
differentiated learning. The aim of this inquiry is to encourage informed professional decisions (Menter et
al, 2011) and work with the case studies rather than aiming to gather information about them
(Groundwater-Smith, 2015) so at times lessons will be informed mainly by proficiency strands and general
capabilities (ACARA, 2016) to ensure the emphasis of learning lies with individual engagement rather than
a focus on content that may be too difficult to grasp, in turn facilitating the development of math anxiety
(Prescott, 2015).
3. Methodology
3.1 Action research
Research engaged teachers have a better understanding of their practice and ways to improve it (Menter,
2011), and action research is the only research approach whose primary purpose is to improve practice
(McAteer, 2013). An action research study considering a number of different strategies that aim to engage
two very different case studies in their mathematics learning initiates a pedagogical process of exploration
and analysis of data collection that educators or teams of educators can then use to theorise the
effectiveness of their own practice (McAteer, 2013).
3.4 Participants
Children who have suffered physical or emotional abuse are often scarred for life; the adverse affects of
trauma on student’s and their learning has become a public health crisis. If a child is exposed to a
combination of a low-income community, neglect, single parent homes, or violence and abuse they are 32
times more likely to have learning and behavioural problems in school than a child who had no adverse
childhood experiences. Although a school has little control over the stability of a child’s family there are
ways schools and teachers can help children cope with the stressors in their lives. Mainly it is important
that the the impact trauma has on learning is recognised and strategies are considered to help the child
feel safe secure and supported while they are at school (Garrett, 2014).
Both case studies for this research have been exposed to a number of individual challenges that affect their
engagement in class; the implications for them now and for their impending graduation to high school are
significant in today’s modern global society. Developing effective interventions for older low-progress
students is a challenging task for researchers but can enable significant academic gains (Whithear, 2009).
3.5.2 Analysis
The analysis of the effectiveness of this research will be founded in the case study responses to their
learning during maths lessons. Given that, case study 1 is frequently out of the class and case study 2
frequently has his attention directed away from curriculum content, the initial aim was to keep them
focused on the work at hand for progressively longer periods of time with the intention of case study 1
showing signs of connection to her learning and case study 2 showing signs of interest in his learning. I
considered non-verbal and visual cues of engagement (Turner et al, 2014) to guide my assessment of their
interaction both during a lesson and after, and then analysed work samples at the end of each lesson to
show in a concrete form, evidence of engagement (Menter et al 2011). I considered the support I was
either able or unable to give when deciding upon the effectiveness of the strategy used. By the end of
placement it was anticipated that observations of engagement increased from those in the beginning and
the amount of concrete work completed per lesson had also increased.
4 Findings
On my lead in day, I participated in a game of times table bingo with the students and was shocked to see a
majority of the year 7 co-hort answering the sum of 3X4 with the assistance of a calculator. I decided that
for the beginning of each maths lesson I would implement a program that focused on the development of
student capabilities in the four operations through a drill exercise (Van de Walle, Karp & Bay-Williams,
2013) before moving on with unit plans that were aimed at covering curriculum content. The program I
used for these drill operations was ‘Beat the Clock’. Beat the clock books had four pages dedicated to each
operation and were constructed in rows of ten sums. To assist with differentiation, the books came in
three levels, each progressively more challenging than the next. Children were given levelled books that
suited their capabilities as decided by my mentor teacher and had the choice of beginning on an operation
they were comfortable with completing a row of sums in 5 minutes. Each student then identified a
personal goal to work towards (usually it was to complete a row 20 seconds faster than they previously
had); to keep motivation high it was known that if the entire class was able to achieve their goal by the end
of my placement we would have a class party (See appendix I).
My unit plan began by finishing off a previous unit on 3D shapes with just two lessons before moving into
measurement- length conversions and types of measurement were covered prior to perimeter, and then
the large focus was on area of basic shapes, irregular shapes and triangles. For my final week I then wanted
to build on their drill exercises from beat the clock and encourage peer interactions mainly for case study
2, so we played maths games, such as Yahtzee and times table bingo.
My observations of case study 2 suggested that learning needed to be hands-on and creatively based to
get him to engage with the lessons (See appendix C) and I had thought this was a strategy that was also
going to benefit all students. Although I saw instant success with case study 2, I had completely lost the
engagement of case study 1; she needed more of a challenge (See appendix G.1). This was when I
implemented the strategy of multiple entry and exit points (Van de Walle, Karp & Bay-Williams, 2013) to
lesson plans (See appendix I). This worked instantly for both case studies; Case study 2 was not
overwhelmed by confusing content and a standard worksheet and Case study 1 had opportunities to
extend herself beyond the base curriculum. As an acceleration to this lesson structure I explored
alternative strategies within the classroom environment that would help case study 1 remain on task (See
appendix C), and case study 1 to interact more regularly with peers (See appendix C).
4.1 Case study 1
As a summary to case study 1’s interaction with the program ‘Beat the clock’, she had a level 3 book and
started with addition but was able to complete this in 50 seconds, she soon moved to subtraction which
was also easy; so her true beginning point of development was on multiplication- completing a row in 2
minutes and 5 seconds. We identified a goal of 1:45. When seating arrangements were moved to provide
case study 1 with more positive interactions and be surrounded by like-minded peers (Van de Walle, Karp
& Bay-Williams, 2013) her self-determination developed. She showed signs of being very competitive and
wanting to keep her achievement at the same level as the higher students she was around. There were
times where she sensed she may fail so gave up before this could happen(See appendix G.2); but for
majority of the time she was very determined and ended up completing a row of division sums in just 2
minutes (See Appendix I).
The arts-based strategy was not effective for case study 1, it was too simplified for her and she needed to
feel extended if she was to engage in her work (See appendix G.1). When I introduced the multiple entry
points to the lesson structure, I still failed to see success in her engagement; she remained regularly
distracted and work samples had her operating in the lower-level thinking phase (See appendix G.3) this
was a challenge because I knew she could be attempting the higher-order thinking problems (yellow and
red questions, See appendix I.2). I realised that a big factor in case study 1’s engagement was her
interactions with her peers (See appendix C). So, I considered the environment, my mentor teacher had
the class sitting in rows facing the front with one table group who often worked independently on
extension work while he addressed the rest of the class. Given Case study 1’s potential (See appendix C) I
thought she would benefit from joining this group and being moved away from distractive peers; as a
result I moved the entire class into group seating and strategically placed the students. This was a
successful strategy for case study 1’s engagement (See appendix G.4).
5. Discussion
The strategies used to assess student engagement were mostly formative; the aim was to inform an
educative process that was based on a critical pedagogy of the learning environment with the practitioner
questioning the purpose of their practice and considering alternatives (Blackmore, 1988). I was then able
to use the evidence gathered to adapt my teaching to meet student needs (Black & Wiliam, 1998). It is said
that there are three basic methods for using formative assessment to evaluate students’ understanding:
observation, interviews-discussions and tasks-work samples (Piaget, 1976) so these methods formed the
basis of data collection. Observations make information that may have gone unnoticed, visible and
important; and this data can be gathered and added to other data to use for planning lessons and
providing feedback to students (Van de Walle, Karp & Bay-Williams, 2013).
The decision to implement ‘Beat the clock’ came from the idea that effective teaching of basic facts
focuses on self-improvement. Students should only be in competition with themselves and monitor their
growth regularly. Drills in short time segments (ten minutes or less) are more productive than longer
periods (Van de Walle, Karp & Bay-Williams, 2013). Just five minutes on fact development provided
continued support without taking up maths instructional time and was reinforced with class enjoyment as
they were all working towards a common goal in the end- a class party. The use of multiple entry and exit
points was implemented because of the varied scope of case study 1 and 2’s mathematical
comprehension. It was important to use lessons that had varying degrees of challenge within them which
catered to different levels of cognitive demand (Van de Walle, Karp & Bay-Williams, 2013). Case study 1
needed opportunities to explore higher-order thinking skills (Samo, 2017) to develop deeper levels of
understanding of mathematical concepts and utilise complex and nonalgorithmic thinking. Case study 2
was not ready for higher-order thinking so he operated on lower-level thinking tasks that were
straightforward and involved routines and producing previously learned facts (Van de Walle, Karp & Bay-
Williams, 2013). Given that schools need to make sure there is an environment and culture in which
meaningful learning can take place (Brady & Kennedy, 2018), and case study 1 was not engaging at her full
potential due to her peers I considered the strategy of adjusting the environment to enhance her learning
experiences. This way, she was engaging with others working on the same ideas. Through these
interactions she was able internalise concepts that may have been out of reach without the input from
like-minded peers and expand on her existing network of concepts (Van de Walle, Karp & Bay-Williams,
2013).
Every day after class I was engaged in discussions with my mentor teacher and SSO correlating our
observations and personally assessing work samples to inform my pedagogical approach for the next day. I
was regularly updating beat the clock goals because the class’s development was constant and making lists
of children who needed misconceptions addressed. Lesson progression of curriculum content was only
planned once a combination of collected data suggested that majority of the co-hort was ready to move
forward (Brady & Kennedy, 2018).
6 Conclusion
The use of a visual stimulus to celebrate student progress in the four operations was a powerful strategy in
making growth evident to all students, in particular the case studies. Appendix H.3 suggested I began on
the right path to effectively engaging case study 2 but I just needed to modify my approach a little to also
engage case study 1. Appendix H.5 proved to be a strategy that included case study 2 in interactions with
peers and gave him a sense of joy by moving educational expectations away from having to write. The
progressive development of my knowledge of case study 1 as seen in appendix C assisted me in
considering appropriate strategies to best engage her. As seen in appendices G.2 and G.3 there were
challenges in critically reflecting on which strategies were going to work best for her. A pinnacle moment in
extending her capabilities was seen in appendix G.4. From here she was given opportunities to show
autonomy and independence for her work by being allowed to work outside of the classroom in small
extension groups empowering her with the responsibility of her own engagement in her learning. I will
consider the strategies used throughout this action research for my future practice, however it is
important to remember that these were effective because they were context and participant specific.
Educators must always consider the context of their site and dynamics of their learners before deeming a
strategy to be effective or worthwhile in implementing.
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appendices
Appendix A: Map of the school
Case Study
Classroom
Appendix B: Class environment (after I moved it into group seating)
Case 1:
Birthdate: 11/06/06
Significant learning information: trauma background, running record level V, expected to be at level by end
of year, high spelling and maths perceptions.
Significant information gained: escapism, enjoys taking work home and completing it there instead of class,
needs continual check ins to stay on task, easily distracted, constantly out of her seat- wants a drink, to go
to the library, toilet, complete a job, see what a friend is doing, mediating in peer relationship concerns,
needs to feel extended to complete work, seeks attention, low self-belief, comparative to ‘higher
achieving’ peers.
Potential focus for learning/teaching: maintain engagement beyond 10 minutes to help achieve her
potential (trauma affected)
Related teaching strategies: open ended learning activities, minimise distractions, surround with
educationally focused peers, extension opportunities requiring higher-order thinking.
Case 2:
Birthdate: 27/10/06
Significant learning information: verified intellectual disability – severe receptive language understanding,
Oxford 307 words completed, Running record level T(below level).
Significant information gained: has opportunities to participate in school projects but chooses to stay in the
class, if not monitored regularly will read and ignore work, growls, shuts down or cries when pushed past
his capabilities or interests, reluctant to write anything- SSO completes a lot of his work with constant
dialogue with him, no peer interactions initiated- often has issues in break times with peers that has
effects upon re-entry to the classroom, possesses repetitive/obsessive traits, likes comic books, drawing,
sonic and pacman.
Potential focus for learning/teaching: maintain engagement, increase intrinsic motivation, incorporate his
interests into learning, facilitate peer interactions.
Related teaching strategies: continual check in, utilise SSO support to the fullest (only allocated 3 hours a
week but SSO time is borrowed/shared from other students and in the class for 20 out of 26 lessons a
week), maintain vigilance on his in class activities, link to his personal interests, drawing, visual and
modelled instruction, adult conferencing, clear explicit instructions, opportunities to experience success.
Date: Time:
Visual cues:
Verbal interactions:
2. Discussion
Date: Time:
My comments:
Mentor comments:
SSO comments:
3. Work sample
Date: Time:
Learning environment:
Appendix F: Time-line
Data Collection Data Analysis Reflection on Reflection on
Week 1 children/student practice
learning
Who will be Observation- Case Reflection and Disengaged How can I keep
involved and what study 1 discussion on differentiated
action will they Work sample- Case outcomes Engaged learning with
take? study 2 extension
opportunities?
When will this take During lesson After class During lesson After class
place?
Where will this Classroom Classroom Classroom Classroom
happen?
Data Collection Data Analysis Reflection on Reflection on
Week 2 children/student practice
learning
Who will be Observation and
involved and what work samples Reflection on Is beat the clock
action will they observations made Competitive nature going to be
take? Case study 1 with peers is effective if I persist
detrimental to with it or
engagement detrimental to
engagement?
Case study 2 Becoming frustrated
with himself
When will this take During lesson After class During lesson After class
place?
Where will this Classroom Classroom Classroom Classroom
happen?
Visual cues: Slumped in chair. Looking at the blocks with disinterest. Beginning conversations with her friend.
Made no attempt to record or build the city.
Verbal interactions: I kept reminding her to write in learning intention and success criteria. Wrote only the
date and learning intention in her work-book.
What does this mean for future planning: this task was not stimulating. Need a lesson that will challenge her
more mentally.
Visual cues: Frustrated. Disengaged once she noticed the time on the board was at 2 minutes.
Non-verbal interactions: completed 4 sums in the row then scribbled them out and left a note in her book
‘didn’t even try’
What does this mean for future planning: time constraint can be an un-motivator for case study if she isn’t
in the right mindframe to challenge herself.
This was the ‘green’ expectation for the lesson. Case study is
perhaps not aware of her potential to operate in the yellow
and red sections, fell into her normal habits of leaving the
room, getting distracted and not challenging herself.
4. Response to multileveled lesson after moved to group seating - Good
My comments: Talked about how case study tried to distract peers but because they were more educationally
focused as opposed to ‘the dramas of the school yard’ or silly comments these distractions were not able to go
anywhere. She seemed to enjoy the sense of ‘extension’ and being seen as a member of the children able to
work in the corridor on more challenging work in her stride.
Mentor comments: Was always apprehensive about moving children into group seating because he liked the
sense of control in being able to see everyone sat in their rows at all times, but commended and assisted in the
new seating arrangement and was happy that we were able to face backs of key distractors to the case study so
she could not interact with them during learning times.
Appendix H case study 2:
Visual cues: would not pick up pencil. Refusal to try. Didn’t seem to understand why the timer was
on the board and why he had to ‘hurry’
Verbal interactions: I approached and tried to instill some urgency, SSO joined in and tried to give
him the pencil with lots of encouragement.
What does this mean for future planning: Is the sense of a timer too much pressure for him to
handle?
Visual cues: approached me at the front of the class before lunch break. Held out his work in his
hands proudly awaiting praise.
Verbal interactions: I pretended not to believe he really got it done in such a short time. He loved
the argument that he did in fact achieve this. I praised him on his efforts and said that 1:20 is a
really short period of time and it may be time to learn subtraction. He laughed it off saying no.
What does this mean for future planning: I rubbed off his goal and moved a blank goal into the
subtraction section and asked the case study to learn subtraction with me during another lesson.
He refused to do so and continued to work on addition for the remainder of my placement.
3. First lesson- hands on learning MA blocks
Visual cues: built a complex city. Particular about counting out 20 blocks. Came to the front of the class to
participate in this. Drew the views with ease. Did not progress to the 3D view option, instead continued to
play with blocks after having done the two drawings.
Verbal interactions: Would not write Learning intention and success criteria so SSO did this for him.
What does this mean for future planning: incorporating his interest for artistic exploration and minimising
writing expectations is going to engage him.
My comments: I was disappointed in how the lesson went because it was a bit chaotic with lots of blocks every
where. Case study 1 was completely disengaged and a number of children constructed very simply cities so did
not extend their thinking for the drawing section.
Mentor comments: Commended the use of the MA blocks and was happy to hear my ideas for more arts based
lessons as he is usually stuck in his ways of referring to a text book, displaying it on the board and having
students work through the sums.
SSO comments: Commended me on the lesson plan because case study 2 ‘never attempts much at all’ so even if
it didn’t feel like a complete success I had had success with him today.
4. Responded to multiple entry points well