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.
Content strands
CLICK – currently the mathematics curriculum has five content
strands – number, patterns and algebra, data, measurement, space
and geometry
CLICK - the draft Australian curriculum has three content strands –
number and algebra, measurement and geometry, statistics and
probability
© NSW Department of Education and Training 2010
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Process strands
CLICK – currently the mathematics curriculum has five process
strands – questioning, applying strategies, communicating,
reasoning and reflecting
CLICK - the draft Australian curriculum has four proficiency strands
– understanding, fluency, problem solving, reasoning
Understanding
Students build robust knowledge of adaptable and transferable
mathematical concepts, make connections between related
concepts and develop the confidence to use the familiar to develop
new ideas, and the ‘why’ as well as the ‘how’ of mathematics.
Fluency
Students develop skills in choosing appropriate procedures, carrying
out procedures flexibly, accurately, efficiently and appropriately, and
recalling factual knowledge and concepts readily.
Problem solving
Students develop the ability to make choices, interpret, formulate,
model and investigate problem situations, and communicate
solutions effectively.
Reasoning
Students develop increasingly sophisticated capacity for logical
thought and actions, such as analysing, proving, evaluating,
explaining, inferring, justifying, and generalising.
Draft Consultation version 1.0.1 Australian Curriculum, ACARA, March
2010, page 3
Draft Australian Mathematics Curriculum
“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 ie 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
© NSW Department of Education and Training 2010
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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 Year 9 Content description:
2. Index laws
Work fluently with index laws, in both numeric and algebraic
expressions and use scientific notation, significant figures and
approximations in practical situations,… (Year 9 Index laws)
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
CLICK Here is an example of a Year 9 Content elaboration:
2. Index laws
“understanding that the use of index notation is an efficient way of
representing numbers ...”
Mathematics achievement standards
Achievement standards will describe the quality of learning 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 Year 9
Index laws
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© NSW Department of Education and Training 2010
By the end of Year 9, students … have a sound
understanding of linear functions and index laws, and are
developing fluency with quadratic and simple non-linear
functions.
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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.
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
Content strands
Number and algebra, measurement and geometry content similar
although there are some concept sequencing and terminology
differences
Proficiency strands
Working mathematically outcomes incorporate reasoning,
understanding and problem solving
© NSW Department of Education and Training 2010
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Key differences with NSW curriculum
Statistics and probability
“In terms of difference, the draft K–10 Australian Curriculum for
mathematics contains a greater emphasis on statistics and
probability in recognition of the need for students to be able to
interpret data in the 21st century.” Australian Curriculum Information
Sheet Mathematics, ACARA, March 2010
The Statistics and Probability strand shows a dramatic increase in
the level of challenge from an early age (e.g. median is in Year 5).
Calculators
Calculators appear to be introduced from as early as Kindergarten
yet order of operations is not described until Year 7.
CAS calculators are identified in the ICT general capability for
mathematics. Currently, scientific calculators are used.
Concept sequencing and terminology differences
How is fluency with the standard algorithms for addition, subtraction,
multiplication and division developed in the Australian Curriculum?
The term ‘additive processes’ appears to refer to both addition and
subtraction, similarly ‘multiplicative processes’ refers to both
multiplication and division. This is not clear from the glossary.
Curriculum organised in Years not Stages
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 not outcomes
Are the content descriptions clear and explicit? Do you need to read
the elaborations to know what to teach? Outcomes in the NSW
syllabus are supported by the key ideas, students learn to and
students learn about.
Year 10 and Year 10A not Stage 5.1,5.2 and 5.3
The draft Australian Curriculum shows content descriptions for Year
10 and Year 10A. Curriculum differentiation in the NSW syllabus
currently may start in Year 8.
This is a draft curriculum that is open for consultation and feedback.
Our focus with this consultation is to work towards making this
curriculum the best it can be for our students now and in the future.
Therefore it is important that we look forward and consider what we
want as well as looking back and mapping it against our current
syllabus.
© 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
Computer algebra system (CAS) calculators are identified in the ICT
general capability for mathematics.
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 mathematics teachers to share
their views about the draft Australian mathematics curriculum.
© NSW Department of Education and Training 2010
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