The draft Australian Curriculum: Mathematics
Speaker notes to accompany the draft Australian Curriculum: Mathematics presentation
Slides
Notes
Introduction to the draft Australian Curriculum: Mathematics
Information and briefing for NSW DET schools
Events to date
The National Curriculum Board is now called the Australian
Curriculum, Assessment and Reporting Authority (ACARA).
Note how much has already been achieved in a short period.
The draft mathematics curriculum is underpinned by a series of
papers, each a development of the preceding ones.
DET teachers were encouraged to provide feedback regarding the
mathematics framing paper, written by a team led by Professor
Peter Sullivan.
In May 2009, the Interim National Curriculum Board (NCB)
published The Shape of the Australian Curriculum:
Mathematics. This paper guided the development of the Australian
mathematics curriculum in the first phase.
The Shape of the Australian Curriculum: Mathematics
(http://www.acara.edu.au/verve/_resources/Australian_Curriculum__Maths.pdf), proposed that the K-10 mathematics curriculum:
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© NSW Department of Education and Training 2010
Addresses key concept skills and processes for progression
in mathematics
Is described in three content strands: Number and algebra,
Statistics and probability and Measurement and geometry
Embeds the proficiencies of understanding, fluency,
reasoning and problem solving
Assumes teachers will make use of available digital
technology, including calculators in teaching and learning
contexts.
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What’s next?
NSW has not yet announced a plan for the implementation of the
Australian curriculum.
Any decision about such a timeline will take into account the extent
of change involved in moving from the NSW syllabuses to the
Australian curriculum
Overview
The ACARA website hyperlink is at the top of the slide. You need to
register to comment on the Australian mathematics curriculum. You
can download a pdf of the curriculum from the Home page of the
site.
CLICK You will see that mathematics is organised into Years K-10.
CLICK The curriculum is also organised into strands - content
strands and proficiency strands. You can select which strand/s you
want to look at. You can look across year levels by strand or look at
all strands in the one year level.
CLICK The general capabilities, cross-curriculum dimensions and
proficiency strands can also be selected.
CLICK You can then click on apply filters to sort your view.
CLICK This example shows a search for Kindergarten showing all
the strands with their content descriptions.
CLICK The Introduction (found in Learn in the top navigation bar) to
this curriculum is important to download and read. This outlines the
rationale/aims, organisation, glossary and the Introduction to
mathematics video.
Structure
The draft Australian curriculum contains content descriptions with
elaborations for K-10, and achievement standards organised in
years
While the content descriptions are mandatory, the elaborations are
not and have been designed to assist less experienced teachers, the
intent being that experienced teachers would only need the content
descriptions
Content strands
There are three content strands and four proficiency strands
The current content strands map to the three composite draft
content strands: Number and algebra, Measurement and geometry,
Statistics and probability
© NSW Department of Education and Training 2010
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The content strands in the draft Australian curriculum describe what
is to be taught and learnt
Process strands
In the NSW syllabus, Working Mathematically describes five
processes which do not all directly align with the four new
proficiency strands
The proficiency strands are intended to describe how content is
explored or developed and are incorporated into the content
descriptions of the three content strands.
Three content strands
“The Australian Curriculum: Mathematics is organised around the
interaction of three content strands and four proficiency strands.
The content strands are Number and algebra, Statistics and
probability, and Measurement and geometry. They describe ‘what’ is
to be taught and learnt.
The proficiency strands are Understanding, Fluency, Problem
solving, and Reasoning, and describe ‘how’ content is explored or
developed i.e. the thinking and doing of mathematics. They provide
the language to build in the developmental aspects of the learning of
mathematics and have been incorporated into the content
descriptions of the three content strands described above. This
approach has been adopted to ensure students’ proficiency in
mathematical skills is developed throughout the curriculum and
becomes increasingly sophisticated over the years of schooling.”
Draft Consultation version 1.0.1 Australian Curriculum, ACARA,
March 2010, page 2
Mathematics content descriptions
“Content descriptions specify what teachers are expected to teach.
They include knowledge, skills and understanding for mathematics
and are described for each year level. The content descriptions will
provide scope and sequence to assist teaching and learning. Within
this scope and sequence, teachers will continue to apply their
professional judgement regarding what to cover and how to best
cater for individual learning needs and interests. “ Australian
Curriculum frequently asked questions, ACARA, March 2010, p. 2
Content descriptions are mandatory.
CLICK Here is an example of a Kindergarten Content description:
2. Numeration: Understand numbers to 10, including matching
number names, numerals and quantities, and work fluently with
small numbers including subitising and partitioning
© NSW Department of Education and Training 2010
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Mathematics content elaborations
“Content elaborations are examples that illustrate each content
description. These are available for those teachers and others who
may require assistance to better understand the content
description.” Australian Curriculum frequently asked questions,
ACARA, March 2010, page 2
Content elaborations
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… illustrate and/or clarify the detail of the content
descriptions.
CLICK Here is an example of a Kindergarten Content elaboration:
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2. Numeration: making connections between the spoken
number word representing the numerical value …
Mathematics achievement standards
Achievement standards will describe the quality of learning that
students should demonstrate in relation to the content for each year
of schooling. The achievement standards will focus on students’
depth of understanding; extent of knowledge; and sophistication of
skills. Student works samples will illustrate the achievement
standards. For K-10, the achievement of the described standard will
mean that a student is well able to progress to the next level of
learning.
The mathematics achievement standard for Kindergarten:
Numeration
“By the end of Kindergarten, students are able to confidently recall
the sequence of numbers to 20, matching names and numerals and
find the total of small collections by counting. They subitise small
quantities, partition numbers to 10 and use one-to-one relations to
share and count out quantities.”
Organisation of the curriculum
The curriculum is organised according to years, not stages.
Within each content strand for each year there are several content
descriptions which are brief. This makes it difficult to determine if
they are clear without the elaboration – Can you find when fractional
indices are taught? What about negative fractional indices?
There are no outcomes.
The content elaborations provide examples of the content
descriptions – they are not as comprehensive as the NSW syllabus
content that sits beneath the outcomes.
ACARA plans to add resources to support the content descriptions,
but they are not evident in the draft curriculum.
© NSW Department of Education and Training 2010
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The achievement standards describe the levels of student
achievement typical of a given year.
Student work samples are provided to illustrate the achievement
standards. Some work samples are available now but ACARA plans
to add more in the future.
General capabilities
The Australian Curriculum, Assessment and Reporting Authority
(ACARA) has identified 10 general capabilities that will be
specifically covered in the curriculum. In mathematics, there is
specific reference to five of these in the content descriptions and
achievement standards. These include:
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Literacy
Numeracy
Information and communication technologies (ICT)
Thinking skills
Creativity
Cross-curriculum dimensions include:
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Aboriginal and Torres Strait Islander
Sustainable living
Asia and Australia’s engagement with Asia
Key similarities to NSW curriculum
The mathematics content is generally similar to that of the NSW
syllabuses, albeit appearing in different years.
Both contain process and content strands:
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The content strands are amalgamations of current syllabus
strands
There are similarities between the descriptions of the
process strands although there is only one that is the same:
Reasoning
While Literacy, Numeracy, ICT, Thinking skills and Creativity are five
of the ten General capabilities outlined in the draft Australian
Curriculum, these aspects are also identified within the current NSW
syllabuses.
Key differences with NSW curriculum
Concept sequencing
Some content placed significantly earlier or later than current
syllabus. For example:
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© NSW Department of Education and Training 2010
Decimals first appear in Year 5 in the draft Australian
curriculum, which is later than in our current syllabus
The Statistics and probability strand of the draft Australian
curriculum has moved content much earlier than is currently
the case. For example, dot plots, a topic currently taught in
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Stage 4 (Year 7-8), is introduced in Year 3 in the draft.
Similarly, median and mode are now introduced in Year 5
rather than Year 8
The achievement standard for Kindergarten is lower than
the current expectations. There also appears to be a
mismatch between the content descriptions (to 10) and the
achievement standards (to 20). According to data from last
year’s Best Start Kindergarten assessment, about 40% of
the students could identify numerals to 10, and about 8%
each to 20 and to 100, on entry to Kindergarten
There are some internal sequencing problems in the draft Australian
Curriculum. For example, in the Measurement and Geometry strand,
capacity is addressed before area. Research suggests that an
appropriate sequence for concept development is first length, then
area, then volume; working on repeated units for length to form a
row, repeated rows to form a layer for area concepts and then
repeated layers to form the volume
There is an increase in the difficulty of the fraction topic in primary
schools, particularly in Years 3 and 4, yet it is introduced later than
in our current syllabus. Therefore there is less time allocated for
teaching more concepts of increased difficulty.
There are omissions – e.g. Multiplication facts for seven not taught
with all of the other multiplication facts in Year 4. Conversion of
metric length units appears to be missing.
Achievement standards are articulated for each year whereas
Stages cover two years of learning. Are the standards in alignment
with student conceptual development for the year?
Content descriptions
Brief content descriptions – this makes it difficult to determine if they
are clear without the elaboration
No description of standard subtraction algorithms whereas in our
current syllabus, both equal addends and decomposition are
detailed as subtraction methods
The language of problem types (e.g. change and combine) referred
to in Year 1 is not familiar to NSW teachers
Calculators
Calculators appear to be introduced from as early as Kindergarten
yet order of operations is not described until Year 7.
Stronger emphasis on calculator use in the primary years will have
resource and access implications.
© NSW Department of Education and Training 2010
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General questions
These general questions may be used to evaluate the draft
Australian mathematics curriculum.
Specific questions
These specific questions may also be used to evaluate the draft
Australian mathematics curriculum.
Identifying the issues and areas where support might be needed
Some possible issues have already been identified in earlier
consultations.
Teachers may require support to deal with these aspects of the draft
curriculum.
Exceptional students
The apparent lack of flexibility in dealing with exceptional students
(those well ahead of their cohort or those well behind) is a problem
for both programming and teaching. Teachers would need support
addressing the needs of students when the curriculum is tied to a
year. What does the Year 6 teacher teach for example if the
students have not reached the previous achievement standards?
Statistics and probability
There is a real possibility that Teachers of K-6 will struggle with the
additional Statistics and probability content and will need further
assistance with the teaching of fractions
Calculators
Although calculators are referred to in the NSW Mathematics K-6
syllabus they are not described within the mandatory outcomes. The
draft Australian curriculum refers to calculators in the mandatory
content from as early as Year 2. We would need to consider the
implications of requiring all students to use calculators from Year 2.
There could be a significant resourcing issue, as our schools may
need class sets of calculators for Year 2 to 6 classes
© NSW Department of Education and Training 2010
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As well, without going into too much detail, schools will need to
consider the type of calculator to be used by students. Will it have inbuilt order of operations? This will have teaching implications. The
answer to 2+3 x 4 could be either 20 or 24, depending on which type
of calculator is used
Sharing your views
A mathematics 7-10 online forum has been established to enable
DET teachers to have their say about the Australian mathematics
curriculum.
You must register before entering this forum.
The forum also allows you to read the views of other mathematics
teachers and to engage in a professional dialogue with them.
Sharing your views: other avenues
These other avenues are available to primary teachers to share their
views about the draft Australian mathematics curriculum
© NSW Department of Education and Training 2010
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