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December 2012
Numeracy Strategy
Catholic schools and colleges in Tasmania are committed to providing
quality education in all learning areas.
Each school and college curriculum should have a strong emphasis on
meeting individual needs of students in a way that enhances their sense
of personal worth. Archbishop’s Charter
In the teaching of numeracy, the following Guiding Principles apply:
Numeracy is a priority in every school.
All learners are entitled to become numerate.
All teachers are competent in teaching for numeracy.
Numeracy is a priority in every school
Leadership development
The effective teacher depends foremost on an effective principal. Without
strong principal whole school achievement is rarely possible or sustainable.
(Routman, 2012). School leadership involvement in professional learning is
critical. Professional learning teams need leaders with a deep understanding
of effective professional learning and how to work with team members to
develop skills that will improve student achievement. Leaders need to assist
in evaluating the impact of the professional learning team on teacher
knowledge, classroom practice and student learning.
Numeracy is the
capacity to apply
mathematical concepts
and skills to successfully
meet the demands of
every day contexts learning, school, home,
work and community
and civic life.
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Evidence based practices
Collecting data without purpose is meaningless. Evidence should be
reviewed, talked about with colleagues, new things will be tried out
and evaluated. (Thomas & Pring 2004)
Simply collecting data, however systematically and routinely, will not
of itself improve schools. There needs to be a commitment to
scrutinise such data, to make sense of it, and to plan and act
differently as a result.(Hopkins 2001)
Whole school approach
Ongoing professional learning communities (PLCs) are the bedrock of the work that creates a whole school of
effective teachers (Routman, 2012)
Participants view, discuss, study, and reflect upon effective mathematics/numeracy practices from diverse
classrooms. They collaboratively plan, apply, and analyse those practices in their own classrooms.
The following elements can form the basis of professional learning in PLC’s:
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examining the ‘big ideas’ that underpin the main strands of the
mathematics curriculum,
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exploring the meaning of the proficiencies ACARA (2010a) and devising experiences for students that
create the possibility of all four proficiencies: understanding, fluency, problem solving and reasoning
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ways of appropriately emphasising numeracy and practical mathematics in teaching and assessment
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approaches to engaging all students
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selecting and using a range of tasks that engage students in
meaningful mathematics and numeracy and building these tasks
into lessons
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exploring the specialised content knowledge involved in
mathematical tasks, and
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examining pedagogies (Sullivan 2011)
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Home- school partnerships
Home–school partnerships enlisting parents’ support also have a critical impact on student outcomes. The
earlier that parents have the opportunity to become positively involved in their children’s mathematics
education, the stronger their support can be as motivators and positive role models (Ford, Follmer & Litz
1998). It was noted that parents need to understand that instructional practices are different from their own
experiences of mathematics; that mathematics is more than arithmetic; and that mathematics can be exciting
and enjoyable. They noted that as children are the main focus of parent–teacher partnerships, practices that
encourage parent–teacher relationships have a positive effect on children’s sense of wellbeing. The effects of
quality teaching are maximised when supported by effective school–home partnership practices focused on
student learning. School–home partnerships that have shown the most positive impacts on student outcomes
have student learning as their focus (Alton-Lee 2003).
All learners are entitled to become numerate.
It is unreasonable to expect classroom teachers to address the needs of learners who have fallen many years behind
the expectations for their class (Sullivan 2011). The focus of intervention for students at risk is on enabling every
student to develop the in-depth conceptual knowledge needed to become a proficient and sustained learner and user
of mathematics. (National Numeracy review, 2008).
The key sources of data for diagnosis in numeracy learning outcomes are :NAPLAN, PAT-Maths and the Early
Numeracy Interview (ENI)
Early Numeracy Interview
The Australian National Numeracy Review (2008) recommended that the necessary resources be directed to
support teachers, to use diagnostic tools including interviews to understand and monitor their individual
students’ developing strategies and particular learning needs. In addition to this, Sullivan (2011) argued that
assessment should be school-based and directed toward improvement rather than system monitoring.
Sullivan (2011) stated, “the more a teacher knows about the strengths of a student, the better the teacher can
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It is unreasonable to expect classroom teachers to address the needs
of learners who have fallen many years behind the expectations for their class (Sullivan 2011). The focus of
intervention for students at risk is on enabling every student to develop the in-depth conceptual knowledge needed to
become a proficient and sustained learner and user of mathematics. (National Numeracy review, 2008).
All teachers demonstrate competence in teaching for numeracy
Professional Learning for numeracy teaching in Tasmanian Catholic Schools will focus on the following
dimensions:
Pedagogical Content Knowledge (PCK)
Ball, Thames, and Phelps (2008) reported on their efforts to elaborate Shulman’s (1986) notion of pedagogical
content knowledge (PCK), which was an amalgamation of content knowledge and pedagogic knowledge
needed for the work of effective teaching. Ball et al. (2008) through the study of teaching practice concluded
that the knowledge required for teaching mathematics was substantial and distinctive. Teachers need to be
aware of the range of pre partial and misconceptions of the mathematical concept they are teaching in order to
scaffold learning just beyond student’s current level of knowledge.
Knowledge of Content and Students (KCS)
This is the combined knowledge of knowing about student’s mathematical thinking and knowing about
mathematics. Teachers need to know and understand the development of the mathematical concept that is
relevant to the students learning. Knowledge of common mathematical pre, partial and misconceptions related
to the mathematical concept is central to KCS. Teachers can foresee what students are likely to think and have
the skill to modify mathematical tasks or questions often “on the fly” to scaffold learning. This demands
knowledge at the intersection of content and students (Ball et al., 2008). Teachers cannot effectively cater for
the diverse range of students in their classes without this knowledge.
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Knowledge of content and teaching (KCT)
This is the combined knowledge of effective teaching pedagogies and mathematics. This includes choice of
representational models, sequence of tasks, choice of questions to ask students in order to probe
learning. For example, knowing that multiple models of representation support the development of whole
number place.
The following strategies are available to schools and colleges to support this guiding principle:
Numeracy coaching (Co-coaching)
Knowledgeable coaches can have a profound effect on teacher effectiveness and student learning.
Successful coaching requires unique talents and sensitivities by the coach and a willingness and openness
by the teacher being coached. (Routman, 2012)
A successful numeracy coach must possess all three of the following crucial qualities:
• Respectful and trusting relationships with colleagues;
• Ability to work well with adult learners; and
• Deep knowledge of mathematics/numeracy and learning
A fundamental missing piece in many coaching experiences is demonstrating effective teaching to teachers in
their classrooms. The coach needs to include the teacher in planning decisions, the on- the-spot teaching and
assessing moves, the specific questioning to check for understanding, the evidence of learning, and how to use
that evidence to shift instruction (Routman, 2012).
Modelled lessons
The aim of the model is to promote a process whereby principals and teachers experience gradual and
incremental professional growth through the collaborative inquiry into practice.
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The Numeracy Strategy has as it’s foundation, the Learning and Teaching Platform for Tasmanian
Catholic Schools and Colleges.
Just as a political party is supposed to base its decisions and actions on a party platform, so too educators carry
on their work, make decisions, and plan instruction based on their education platform.
(Sergiovanni & Starrat, 2001, p.70)
CURRICULUM
LEARNER
All learners are capable of being numerate.
Learners present with diverse
understandings, experiences and
dispositions, which determine their
readiness to apply their mathematical
thinking in diverse contexts.
Numerate learners demonstrate tenacity in
solving problems and applying mathematical
understanding in different contexts.
In applying understanding they use the
language of mathematics to question,
challenge, inquire and communicate
A curriculum for numeracy inspires,
motivates, supports and challenges the
learner. This curriculum promotes the
proficiencies of reasoning, fluency, problem
solving and understanding that enable the
application of mathematical knowledge and
skills in all curriculum areas.
A learning environment that promotes
numeracy, supports, activates and
challenges all learners to apply and
communicate their mathematical thinking.
The physical environment has motivating
and agile learning spaces, current and
appropriate technologies and is sufficiently
resourced.
A quality dynamic learning environment has
flexible groupings and opportunities for
shared, guided, independent and
collaborative learning. It caters for all
learners.
Pedagogy for numeracy is intentional and
contextual. It caters for diversity and
motivates, challenges and extends all
learners.
Multiple and diverse opportunities, promote
positive dispositions for learning and
activate learners’ mathematical
proficiencies.
Rich, authentic assessment underpins and
informs practice.
PEDAGOGY
LEARNING ENVIRONMENT
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References
Alton-Lee, A (2003) Quality teaching for diverse students in schooling: best evidence synthesis, Ministry of
Education, NZ
Ball, D.L & Forzani, M (2009) The work of teaching and the challenge for teacher education Journal of
Teacher Education, 60(5) 497-511
Ball, D.L, Thames, M.H,, and Phelps, G (2008) Content Knowledge for teaching: What makes it special.
Journal of Teacher Education, 59(5) 389-407
Council of Australian Governments Human Capital Working Group (2008) National numeracy review
report. Canberra ACT COAG
Sullivan, P. (2011) Teaching Mathematics: using research informed strategies Australian Council for
Educational Research Victoria ACER
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