Report: MA Teaching (Secondary) - Numeracy and Professional Practice

This report, prepared for a MA in Teaching (Secondary) program, delves into the multifaceted aspects of numeracy education and professional practice. It explores professional knowledge areas, including understanding diversity and inclusion, and the application of behaviorism theory in numeracy instruction. The report outlines the Australian curriculum's numeracy continuum, detailing key concepts such as estimation, patterns, decimals, spatial reasoning, and statistical interpretation. Furthermore, it examines professional practice, focusing on effective classroom communication strategies, the importance of the learning environment, and motivational theories, including behaviorist and humanist approaches. It also analyzes the impact of assessment processes on student learning. The report provides a comprehensive overview of the critical elements of numeracy instruction and the professional responsibilities of educators, offering valuable insights for teachers and educational researchers.

Running head: MA OF TEACHING (SECONDARY)
MA of Teaching (Secondary)
Student’s Name
University Name
Author’s Name

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Table of Contents
1. Professional Knowledge.........................................................................................................3
1.1 Understanding the Complex nature of diversity and inclusion........................................3
1.2 Behaviourism theory........................................................................................................3
Estimation with whole numbers.........................................................................................4
Patterns and relationships involved in patterns...................................................................5
Usage of decimals, percentage and fractions......................................................................5
Spatial reasoning.................................................................................................................5
Interpretation of statistical Diagram...................................................................................6
2. Professional Practice..............................................................................................................7
2.1 Effective Classroom communication strategies...............................................................7
2.2 importance of the learning environment...........................................................................8
1. Encouragement to undertake risks..................................................................................8
2. Elimination of discomforts that students face in a classroom........................................8
3. Meaning of the classroom session..................................................................................8
5. Usefulness.......................................................................................................................9
2.3.1 Motivational theories...............................................................................................10
Behaviourist view of motivation.......................................................................................10
The humanist approach of motivation..............................................................................10
2.4 Impact of the assessment process...................................................................................11
Homework........................................................................................................................11

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Standardised testing..........................................................................................................12
Professional Learning Plan......................................................................................................13
Reference List..........................................................................................................................16

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1. Professional Knowledge
1.1 Understanding the Complex nature of diversity and inclusion
Inclusive schooling is the foundation behind democratic involvement in a classroom. In many
of the conventional classrooms, the students face alienation, and not only them, but the
teachers at times are forced to work under subordination of the hegemonic education system.
The prime focus of schooling involves fulfilment of the criteria of the students’ becoming
informed, professionally active and democratic civilians (Allen et al. 2018). The democratic
authority in a school should lead students with persuasion as well as negotiation. Teachers
would be unable to substantiate the worth of the subjects taught, if they are unable to solve
minimum amount of persuasive cases. A classroom might be called inclusive as well as
socially inclusive from the context which values each of the students as valuable counterparts
of the school community (Burrows et al. 2017).
1.2 Behaviourism theory
The behavioural approach of education of numeracy relies on the external events which cause
perceptible changes in the behaviour of students. Imparting education on numeracy have been
an area of concern for the practitioners. In the educational context, there have never been a
real agreement between the position and the role that numeracy plays in the societal context
and the foundation of numeracy that the students gain in secondary end higher education.
Students come up with a lots of difficulties varying from gap in their learning from schools,
through to further-more fundamental numeracy topics. Students who have poor
understanding of numeracy, openly despise the subject, not realising the necessity of real
application of the subject matter. Further alarming is that students seeking assistance have
absolutely feeble or no sense of numbers or estimation skills at all. Studies have revealed that

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application of potentially low methods of learning have given rise if such a situation where
the straightforward addition and/or subtraction facts are not clear to them.
1.3 General Teaching capabilities and disciplines (specifically numeracy)
The continuum of numeracy learning in the Australian curriculum is focused upon the
following aspects.
Numeracy Continuum Mathematical Context in Australia
Learning calculation with whole numbers 1. General numbers and basic knowledge of
algebra
2. Symmetrical measurement and Geometry
Recognising numeric patterns and
understanding the numeric relationships
1. Number and applied algebra
2. statistics
3. Probability
Calculating with fractions, percentages,
ratings and ratios
1. Algebra
2. Geometry
Interpretation of statistical information 1. Statistics
2. Probability
Using metrics of measurement Metrics and geometry
Table 1: Numeracy in Australian curriculum
(Source: Clark and Goddard, 2016)
Estimation with whole numbers
This lesson requires the students to deal with numbers for multiple purposes. His strategies
that teachers mainly teach the students to deal with whole numbers are mental, written and at
times digital (Correa-Velez, Gifford, McMichael & Sampson, 2017). In an open end teaching
platform the students of numeracy learn from their teachers how to

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1. Understand and learn the application of numbers in life time contexts
2. Make numerical reference, calculation and reference
3. Handle liquid currency notes and keep monetary record
Patterns and relationships involved in patterns
In this related raining the students learn how to identify trends and describe them using a
variegated range of rules and relationships. Example of an authentic context might be
provided in this context. A students might be given to describe the numerical significance
of a price tag that stares 20% discount on a price of AUD $175 (Daniel, 2015). A student
will apply his or her understanding of the metrics of measurement and resolve the exact
sum of discount.
Usage of decimals, percentage and fractions
The students learn the practical implication of these representation and how they might be
applied in the real life. Teachers make the students visualise, arrange and describe various
proportions and learn the breakdown of relationships in ratios, rates and percentage
(Forgasz, Leder & Hall, 2017). The two primary knowledge that students apply in this
context are:
 Interpretability of proportional reasoning
 Application of proportional reasoning
Spatial reasoning
This element of numeracy requires students to substantiate the knowledge of space around
them in mathematical terms. Students in the class make a visual analysis of the shapes and
objects and describe their understanding of the key features of the shapes in the surrounding
environment (Goos, Vale, & Stillman, 2017). Other than shapes, symmetry and angular

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dimensions are used by students to solve the problems presented to them. In lieu of this
knowledge the teachers of numeracy in the classes interpret maps and engineering diagrams
with the use of scale and legends in syntax of directional language. This knowledge is of
profound help in anticipating routes and locations. In the context of these topics the students
also develop a knowledge of the following facts
 Visualisation of the two dimensional and three dimensional objects
 Interpretation of maps and diagram
Figure: Visualisation of 2-D and 3-D figures (Grasby et al. 2017)
Interpretation of statistical Diagram
Statistical information is represented through problem solving in original contexts. This
includes comparison and evaluation of data portrayal of various types. Such numerical
representations helps to explain the outcome of various kind of chance events. The primary
activities of students in this case are and interpretation of chance events.

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Figure interpretation of Statistical Diagram 3:
(Source: Hancock et al. 2016)
2. Professional Practice
2.1 Effective Classroom communication strategies
Effective communication between the students and the teachers is responsible for reflective
learning of the students. In order to ensure that, the students should have profound knowledge
of the numeracy demands and learning opportunities inherent in their teaching techniques.
Moreover, the students should be also aware of the numeracy learning needs of the student
and particularly the students who are weak at perceiving the numeracy concepts owing to
their limited knowledge (Hardy, 2015). In order to endorse the learning of those students the
education foundations of Australia should promote assessment programs that are multi-
faceted. The assessment programs are to be deemed valid only when they cover all the
domains of the mathematics as required for raising the proficiency level of the students
(Harris et al. 2018).
interpretation of data
displays
interpretation of
chance events

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2.2 importance of the learning environment
Democratic education is most preferred because democracy in the classroom influences the
students to achieve their targets in life to the best of their potential. Democratic education
system brings within its scope, a number of encouragements in a coherent and integrated
manner. These are:
1. Encouragement to undertake risks
In least cases it has been observed that the students min the conventional secondary education
system in Australia take chances. In case if the students risk to flaunt their own opinion
challenging the decision of the authority in some instance, there are high penalty awaiting
him or her, on the ground of breach of conduct in school (Heldsinger & Humphry, 2013). The
definition of standards for the students are only strategies to lessen their participation in
discouragement of undertaking risk.
2. Elimination of discomforts that students face in a classroom
Some of the discomforts that students face in the classroom are unavoidable. However, here
are some instances where the level of discomfort can be minimised. Some such discomforts
are public discomfort, boredom with the teaching process and loneliness in the class (Luke,
2018).
3. Meaning of the classroom session
The education imparted in the class to the students have two meanings l one is what is
expected of the4 student form the teachers and the school authority and the other is how may
a student’s utilise that which is being taught in the class. In the present condition it might be
commented that the utility of the knowledge acquired form the schools is perfunctory as well
as unpersuasive (Miškolci, Armstrong and Spandagou, 2016). This is chiefly applicable for

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those who are distinctively discouraged form promoting themselves to higher education
owing to the lack of intellect.
4. A mentality of competency
The schools instils in the students a sense of competency in attempting the rate race of
ranking. However this competence is narrowly exhibited by the teachers and authority. In fact
the competence is tangentially inclined to the yardstick of academic performance.
5. Usefulness
Schools are organisations that aim at promulgating future excellence. However in a school
classroom, students learn to fulfil immediate utility. Students in a democratic classroom deal
with problems that are real time and relevant in the context of the present society (Parnis &
Petocz, 2016). An environment of cross age tutoring is very important in a democratic
classroom.
2.4 Impact of the motivation process
Neuroscience is being utilised to improve educational standards. The Fast Forward Program
is the first education program based on neuroplasticity. Teachers of neuroplasticity needs to
carefully consider the impact of motivation in better learning. In the digital world, it is
invaluable in complain students’ less concentration. Frequently it has been found that young
learners’ minds are highly impacted by television (Polesel, Dulfer and Turnbull, 2013). It
exhibits that the mode of learning things that television has obtained has a casting impact on
the minds of learners, therefore, in this digital age, students’ needs to be taught through the
means of digital tools that make understanding of facts very easy. Such learning is called
physical learning. Moreover, neurone surveys show that students who learn from the digital
medium have developed grey matter in their brain, compared to students who learn through
traditional methods (White, 2017).

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2.3.1 Motivational theories
Behaviourist view of motivation
Students learn better when they receive appraisals. Rewards evoke high level of positivity in
their minds. Students tend to learn better because they keep on looking for future
opportunities of getting appraisal. Such extrinsic reinforcements have a high level of impacts
on the learners. In order to eradicate unwanted learning habits from the habits the teacher
might often pertain to punishments also (Won, Hackling & Treagust, 2017). However the rate
of positive appraisal should be less than negative punishments.
The Cognitivist view of education
The cognitivists have a conception that children are inherently active learners. Generally they
do not need rewards for better performance in the classroom. However, they might often
require motivation and skill up gradation. Motivations that are goal directed are more
admirable for the cognitivists. An instance can be provided. Students should be motivated to
believe on their self-potential. They should not be influenced by extrinsic influences on many
occasions. That would make them, believe that they cannot accomplish any learning program
without the appraisal of a teacher (Hardy, 2015). Cognitivists believe that students undergo a
learning program in order to produce positive consequences such as competency or
knowledge or gradual development of the ability to accomplish a task without the aid of the
teacher.
The humanist approach of motivation
The hierarchy of needs have been given optimum prominence in motivating student, in view
of the Maslow’s theory. Human behaviour and approach are contingent on fulfilling those
needs. The prime reason why a student needs a motivation is that at a tender age he or she is
not able to identify his or her basic needs. A beginning learner cannot differentiate between

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the importance level of an animation series in television and his mathematics class.
According to the humanists the above discussed theories are all aligned to elevate the level of
the student’s level of realisation of personal achievements. Imbibing self-confidence and
developing sense of independence while performing the task assigned to him or her, is also
essential. Hence, according to the humanist’s conception, any of the conceptions of
motivation are applicable based on the current need of the student.
2.4 Impact of the assessment process
The efficiency testing of the students in Australia is by two standard ways. They are
hime3work and standard tests. The three things are tested in assessment program, namely the
intent, efficiency and the output produced by the student.
Homework
One of the most predicted aspect of schooling is homework. Homework’s can be most
proficiently defined as task that have been assigned to the students to be performed by their
own during the non-school hours and without the guidance of the teachers. However, the
efficiency of homework in analysing a students’ merit is subjected to debate quite often. At
times the parents judge the level of schooling in an educational institution from the standard
of homework that is being provide to the students in the class. However, educators often
utilise the homework as a meter to judge the scholastic achievement of a learner (Hardy,
2015). Moreover the teachers assume that by completing homework would also learn another
impoer6tnat life skill that is time management. Again, homework also helps the learners to
analyse and revise the things that they learn in the class. Hence, they would be able to be
analyse the loopholes in the learning and the areas of learning that is unclear to them.
Although the perspective of homework is different for parents, learners and teachers.

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However, homework might also be a source of conflict and confusion between the educators
and the parents.
Often it is visible that there is a mismatch between the execution level of the teachers and the
parental input that goes in the completion of the homework. Again, when it is revealed that
the students’ homework have been solved by the parents, the educators condemn such
behaviour (Heldsinger & Humphry, 2013). Therefore it can be concluded that homework
should not be assumed as the ultimate parameter of judging the learning potential and the
efficiency of the students.
Standardised testing
Spreading across an array of educators and parents, the process of standard testing is also a
popular method of assessment. In 63% of the primary schools of Australia, the standard
testing have been acclaimed as the best method of testing the credibility of the student.
However in secondary school level, the various; level of test have been used by the schools as
a means of evaluating the level of education that has been achieved by the students. Moreover
future study options of the students are also decided by standard test in many Australian
schools. However like homework, the way the schools perceive the value of output in
standardised tests is a subject of debate. One of the most potential challenges is that standard
tests are not able to evaluate the entire circumference of the learning of the students (Polesel,
Dulfer, and Turnbull, 2013). It only tests the students based on a certain set of questionnaire
that represents certain fragments of his learning domain.
4. Professional Engagement
Numeracy education in Australia is imparted by specialist practitioners who possess TESOL
qualifications. WELL practitioners as well as vocational trainers can also act as numeracy
tutors in Australia. Majority of the primary numeracy educators in Australia are female

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(about 81%) and almost 70% of them are above 45 years of age (Parnis & Petocz, 2016). The
AAMT ensured that the teachers associated with teaching of primary level numeracy, should
have the knowledge of real life numeracy demands and opportunities related to numeracy.
The teachers should also be able to respond properly to the learning needs of the individual
students. The AAMT also ensures that the teachers take special care of the students who have
limited numeracy skills.
The mathematics teacher s registered under the AAMT are liable to make sure that the
students develop a consolidated understanding of the mathematical concepts, and are able to
address the application of mathematics in the social context (White, 2017). The current
propensity of the large scale numeracy teachers of Australia is to rely on systemic assessment
programs for reporting the students’ achievements within the curriculum of mathematics.
Professional Learning Plan
The professional learning plan is aimed at building the capacity of the school authorities to
work in association with the numeracy teachers. The greater aim of this learning plan is to
bring about sustainable development in the outcomes of the numeracy students. The primary
liabilities of the teachers as per the scope of this learning plan are:
1. Reviewing the current outcomes of the numeracy students and fostering instructional
practices for establishment of a renewed numeracy improvement planning.
2. Identification of the stages of numeracy development of the students and related evidence
based implications in order to scaffold students’ learning of numeracy.
3. Implementation of the learning models that foster collaborative learning of the teachers to
enhance their capacity in analysing student assessment data along with implementation of
differentiated numeracy instruction.

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Five postulates if the learning plan have been identified each of which stress on the particular
learning outcomes of the participants.
My Professional Learning Plan 2018
Nature of Gap in
Professional Learning
Learning objective to
address this learning gap
Success Criteria
I have a potential
nervousness in reviewing
the current outcomes of the
numeracy learners in
interactive sessions. There is
also a lapse in my
instructional implementation
in the lecture sessions
according to the views of
my mentor
Before the commencement
of the year I will learn to
commendably analyse the
outcome of numeracy
learners
Within this year, I would
also mitigate the dearth in
my skills of structural
implementation
1. By the end of June, I
would review my
marking of the recent
performance of the
students in numeracy
learning programs
using indicators of
the numeracy
learning outcomes.
2. By the end of
September I would
create a whole
school approach
towards an integrated
numeracy
assessment that
would be able to
provide me accurate
evidence of the

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correctness of my
employed numeracy
learning and the
classroom instruction
method and quality.
Furthermore I have some
issues in identification of the
stages of numeracy
development of the students
and related evidence based
implications in order to
scaffold students’ learning
of numeracy.
Within this year I would
revise the stages of
numeracy stages (agewise)
that students needs to learn
By the end of the year I
would also learn how to
implement the outcomes of
my revision in scaffolding
students’ numeracy learning
1. By the end of
September, I would
learn to create a
sustainable whole
school approach
towards numeracy
assessments which
provides proper
evidence for
informing the
improvements in
numeracy learning
along with classroom
instructions.
I also have some difficulties
in implementation of the
learning models that foster
collaborative learning of the
By the end of this year I
would have achieved a
better understanding of the
learning models that foster
1. By the end of this
year, I would strictly
learn using strategic
knowledge of the

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teachers to enhance their
capacity in analysing student
assessment data along with
implementation of
differentiated numeracy
instruction. In fact my
mentor also addresses that.
collaborative learning. numeracy level of
the students in order
to develop a plan for
effective numeracy
education
Table 1: Professional Learning Plan
(Source: Wyatt, 2017, p.14)

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Reference List
Allen, J.M., Wright, S., Cranston, N., Watson, J., Beswick, K. and Hay, I., 2018. Raising
levels of school student engagement and retention in rural, regional and disadvantaged areas:
is it a lost cause?. International Journal of Inclusive Education, 22(4), pp.409-425.
Burrows, T., Goldman, S., Olson, R.K., Byrne, B. and Coventry, W.L., 2017. Associations
between selected dietary behaviours and academic achievement: A study of Australian school
aged children. Appetite, 116, pp.372-380.
Butterworth, B., 2018. Low Numeracy: From brain to education. In Building the Foundation:
Whole Numbers in the Primary Grades (pp. 477-488). Springer, Cham.
Clark, T.F. and Goddard, R., 2016. A School Staff Opinion Survey Predicts Student
Achievement in Victoria, Australia: Evidence from a Structural Equation Modeling
Analysis. Society for Research on Educational Effectiveness.
Correa-Velez, I., Gifford, S.M., McMichael, C. and Sampson, R., 2017. Predictors of
secondary school completion among refugee youth 8 to 9 years after resettlement in
Melbourne, Australia. Journal of International Migration and Integration, 18(3), pp.791-805.
Daniel, G., 2015. Patterns of parent involvement: A longitudinal analysis of family-school
partnerships in the early years of school in Australia. Australasian Journal of Early
Childhood, 40(1), p.119.
Forgasz, H.J., Leder, G. and Hall, J., 2017. Numeracy Across the Curriculum in Australian
Schools: Teacher Education Students’ and Practicing Teachers’ Views and Understandings of
Numeracy. Numeracy, 10(2), p.2.
Goos, M., Vale, C. and Stillman, G., 2017. Teaching secondary school mathematics:
Research and practice for the 21st century. Allen & Unwin.

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Grasby, K.L., Coventry, W.L., Byrne, B. and Olson, R.K., 2017. Little Evidence That
Socioeconomic Status Modifies Heritability of Literacy and Numeracy in Australia. Child
development.
Hancock, K., Mitrou, F., Povey, J., Campbell, A. and Zubrick, S.R., 2016. Three-generation
education patterns among grandparents, parents and grandchildren: Evidence of
grandparent effects from Australia (No. 2016-08).
Hardy, I., 2015. A logic of enumeration: The nature and effects of national literacy and
numeracy testing in Australia. Journal of Education Policy, 30(3), pp.335-362.
Harris, F., Smith, M., Laurens, K.R., Green, M.J., Tzoumakis, S., Kariuki, M. and Carr, V.J.,
2018. Validation of a two-factor model of the Best Start Kindergarten Assessment of literacy
and numeracy. Australian Journal of Education, p.0004944118761381.
Heldsinger, S. and Humphry, S., 2013. Using the method of pairwise comparison to obtain
reliable teacher assessments. The Australian Educational Researcher, 37(2), pp.1-19.
Luke, A., 2018. Critical literacy in Australia: A matter of context and standpoint. In Critical
Literacy, Schooling, and Social Justice (pp. 168-188).
Miškolci, J., Armstrong, D. and Spandagou, I., 2016. Teachers’ Perceptions of the
Relationship between Inclusive Education and Distributed Leadership in two Primary
Schools in Slovakia and New South Wales (Australia). Journal of Teacher Education for
Sustainability, 18(2), pp.53-65.
Parnis, A.J. and Petocz, P., 2016. Secondary school students’ attitudes towards numeracy: an
Australian investigation based on the National Assessment Program—Literacy and
Numeracy (NAPLAN). The Australian Educational Researcher, 43(5), pp.551-566.

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Polesel, J., Dulfer, N. and Turnbull, M., 2013. The experience of education: The impacts of
high stakes testing on school students and their families. Literature Review prepared for the
Whitlam Institute, Melbourne Graduate School of Education, and the Foundation for Young
Australians. Available online at: http://www. whitlam.
org/__data/assets/pdf_file/0008/276191/High_Stakes_Testing_Literature_Review.pdf
(accessed 20 september 2012).
White, M.A., 2017. Welfare to wellbeing: Australian education's greatest
challenge. Australian Educational Leader, 39(1), p.18.
Won, M., Hackling, M. and Treagust, D., 2017. Secondary science teacher education in
Australia. Model Science Teacher Preparation Programs: An International Comparison of
What Works, p.229.
Wyatt, T., 2017. Enhancing instructional leadership: Lessons from the NSW Literacy and
Numeracy Action Plan.