AusVELS
Mathematics F–10
David Leigh-Lancaster
29 August 2013
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Structure of the session
1.
Elaborations
2.
Curriculum sequence
3.
Q and A
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Elaborations (1)
1. Not mandatory
2. Accessed from AusVELS website via View E
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Elaborations (2)
Level 4 Content Descriptions
Number and Algebra
Number and place value
Recall multiplication facts up to 10 × 10 and related
division facts (ACMNA075)
Elaboration
using known multiplication facts to calculate related
division facts
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Elaborations (3) – can supplement
From the VELS Level 3
http://pandora.nla.gov.au/pan/129125/201212060015/vels.vcaa.vic.edu.au/maths/index.html
•They devise and use written methods for division by a single-digit divisor
(based on inverse relations in multiplication tables).
•recognise that the sharing of a collection into equal-sized parts (division)
frequently leaves a remainder.
•investigate sequences of decimal numbers generated using multiplication
or division by 10.
•Students test the truth of mathematical statements and generalisations,
for example computations - the patterns of remainders from division
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Elaborations (4) – can supplement
From DEECD Mathematics Continuum
•
•
http://www.education.vic.gov.au/school/teachers/teachingresources/dis
cipline/maths/continuum/Pages/earlydiv225.aspx
http://www.education.vic.gov.au/school/teachers/teachingresources/dis
cipline/maths/continuum/Pages/factfamilies275.aspx
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Elaborations (5) – can supplement
From the National Statements of Learning (2008)
http://www.mceetya.edu.au/verve/_resources/SOL_Maths_Cop
yright_update2008.pdf
These are the current curriculum basis for NAPLAN Numeracy testing
• interpret number sentences and describe them using their own words (eg
describe number sentences like c ÷ 2 = 12 by saying ‘what number do I
halve to get 12?’ …).
• use arrays and other grouping strategies to represent and solve
multiplication situations, involving single digit numbers, and show how
these also relate to division
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Elaborations (5) ctd
• model and solve both sharing and grouping division situations and
problems involving single digit divisors using concrete materials
• create problems based around a selected operation and identify similar
problems based on the same operation
• explore situations where inverse operations can be applied and describe
how inverse relationships apply to other situations and problems (eg use
a 4 by 3 array to work out related multiplication and division facts …)
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NAPLAN Year 3 sample question
http://www.nap.edu.au/naplan/the-tests/thetests.html
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NAPLAN Year 5 sample question (1)
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NAPLAN Year 5 sample question(2)
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NAPLAN Year 5 sample question (3)
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Other resources: AMSI – Times modules
http://www.amsi.org.au/teacher_modules/multiplication_and_divisio
n.html
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ESA - Scootle resources (1)
VCAA link: Aligned Australian Curriculum Resources
(Mathematics) can be accessed directly through
Scootle
(www.scootle.edu.au/ec/curriculum?learningarea=%22
Mathematics%22&menu=3).
Scootle is an online repository, managed by Education
Services Australia (ESA). Currently it has over 10,000
digital resources, with a range of these resources being
progressively aligned to the relevant learning area of
the Australian Curriculum.
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Other resources: ESA - Scootle (2)
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Other resources: ESA - Scootle (3)
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Other resources: ESA – NLVM (1)
http://nlvm.usu.edu/en/nav/vlibrary.html
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Other resources: ESA – NLVM (2)
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Elaborations (7)
Level 7 Content Descriptions
Number and Algebra
Linear and non-linear relationships
Given coordinates, plot points on the Cartesian plane,
and find coordinates for a given point (ACMNA178)
Elaborations
plotting points from a table of integer values and
recognising simple patterns, such as points that lie on a
straight line
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Elaborations (8)
Investigate, interpret and analyse graphs from
authentic data (ACMNA180)
Elaborations
using travel graphs to investigate and compare the
distance travelled to and from school
interpreting features of travel graphs such as the slope
of lines and the meaning of horizontal lines
using graphs of evaporation rates to explore water
storage
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Elaborations (9) - Activity
• Carry out a similar process of developing
supplementary elaborations as in the division
example
• Look at the curriculum sequence of concepts, skills
and processes from level 6 through to 10/10A as
indicated in the content descriptions and
achievement standards for linear and non - linear
relations.
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Elaborations (10) – Activity (ctd)
Develop key concepts such as:
Function, domain, range, co-domain, increasing,
decreasing constant(steady), minima and maxima (local
and global), rate of change (when is it getting cold most
quickly?), solving equations (when was the
temperature 12 degrees?), periodicity, in non-rule
based real life contexts, such as variation in daily
temperature over a 24 hour period.
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Elaborations (10) – Activity (ctd)
http://www.weatherzone.com.au/station.jsp?lt=site&lc
=86071&list=ob
(Note: Source of weather charts and graphs.)
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Curriculum sequence (1)
To develop curriculum sequence teachers employ:
• Pedagogical knowledge (general knowledge of
teaching and learning)
• Content knowledge (mathematical knowledge)
• Pedagogical content knowledge (knowledge of how
to effectively teach/how students learn
mathematics)
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Curriculum sequence (2)
• The close alignment between VELS and the AC/AusVELS indicates that a
suitable (previous) curriculum sequence for the VELS could be used as a
substantive basis for developing a similarly suitable curriculum sequence
for the AC/AusVELS
• The extra levels in the AusVELS (two to a VELS level, apart from
Foundation) provide further detail as to what content/topics can be
covered in a given year
• The revised Victorian achievement standards (and related progression
point examples) in conjunction with the content descriptions also provide
further detail to assist in curriculum sequence work (for example these
explicitly include reference to aspects of working mathematically such as
estimations and the use of technology)
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Curriculum sequence (3)
When teachers plan, develop, implement, evaluate and
review/refine curriculum sequences, this work is
informed by:
• Research in neuroscience , cognitive psychology, social
theory, mathematics education
• Structure and history of mathematics and mathematical
practice
• Formal curriculum and documentation
• Their own experiences and the experiences of colleagues
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Curriculum sequence (4)
To do this they draw on their own curriculum
understanding as this interacts with that of their
colleagues. There are a range of resources which
provide frameworks/models, for example:
•
Structured Activities for Primary Mathematics (how to
enjoy real mathematics) Volumes 1 and 2 (1989).
Skemp. Routledge.
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Curriculum sequence (5)
• The Mathematical Brain (1999). Butterworth. Macmillan.
• Elementary and Middle School Mathematics – Teaching
Developmentally (2010, 7th Edition). Van der Walle et al.
Pearson.
• Teaching Mathematics – Foundations to Middle Years (2011).
Siemon et al. Oxford.
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Curriculum sequence (6)
The aim is to achieve effective alignment (congruence)
between:
•
•
•
•
Curriculum
Pedagogy
Assessment
Reporting
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Curriculum sequence (7)
VCAA sample program:
•
•
•
•
•
•
Currently under development
For P – 6 and 7 – 10/10A
Digital resource to be available from AusVELS website
Intended to be available for use in 2014
Overview of sequence of topics across 4 terms
Detail of topics by weeks
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Curriculum sequence (7)
VCAA sample program (ctd)
Detail of topic will include:
•
•
•
•
Content and related activities, use of technology
Mapping to AusVELS content descriptors and achievement
standards
Proficiency strand emphases
Linked resources from ESA, AMSI and other relevant sources
eg ABS
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Questions …? and answers …! (1)
Does the VCAA have a definition for Progression Points and elaborations?
Just to gain a better understanding of the two. Similarities and differences?
Across all curriculum.
Elaborations were developed by ACARA and provide some examples of pedagogical
context. Progression point examples were developed by the VCAA and relate to
assessment. The achievement standard applies at the end of a learning period
(typically ‘by the end of the year’) . Progression point examples provide a model for a
substantive intermediate stage of achievement (progress), they can be
adjusted/refined to reflect a school’s actual curriculum sequence.
So elaborations are more about the teaching of content rather than
assessment?
Yes .
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Questions …? and answers …! (2)
Are there more samples of work we can use as a scope and sequence
between the levels?
No.
Work samples were developed by ACARA in conjunction with the states and
territories to illustrate achievement at and around the level. These have a
certain robustness, and are agreed Australia-wide. The more one tries to put
in between the less robust are the distinctions. As the progression point examples
can be adapted for school curriculum sequence, local samples work well.
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Questions …? and answers …! (3)
How much of the standard needs to be achieved to move on to the next level?
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Questions …? and answers …! (4)
Are there any other opportunities of professional development in AusVELS
maths?
There will be a range of professional learning opportunities, through the
sectors (DEECD, CEO, ISV), VCAA, the Mathematical Association of Victoria (MAV),
regions and networks and other third party providers. The nature scope
and purpose of these will naturally vary depending on the role of the provider
and areas for attention that have been identified. Suggestions on these are
appreciated.
Are there any other great resources to assist our EAL students deal with
Numeracy?
Digital manipulatives such as those from Scootle, NVLM and other sources
are helpful.
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Questions …? and answers …! (5)
Is there a suggested‘ ‘scope and sequence ' for topics in the Australian
Curriculum?
There is an ACARA scope and sequence document that can be accessed from
the VCAA website
(http://www.vcaa.vic.edu.au/Documents/auscurric/Maths_scope_and_sequence_AusVELS.pdf)
this can be used in conjunction with the VCAA planning templates
(http://www.vcaa.vic.edu.au/Pages/foundation10/curriculum/resources/templates/maths.aspx).
The DEECD continuum also contains scope and sequence material. The VCAA is in the
process of developing a sample program for F – 6 and for 7 – 10. There are also
various resources of this kind from the MAV and other third parties such as publishers.
Where does assessment using the Early Years Numeracy online test sit with
assessing AusVELS Maths?
DEECD is in the process of aligning various resources with the AusVELS.
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Questions …? and answers …! (5)
Is there a plan to update the On Demand testing?
See:
http://www.vcaa.vic.edu.au/Documents/ondemand/transition_vels2ausvels_ontests.pdf
Why has estimation been removed from F and level 1 in Measurement?
Estimation was a key theme in the Working mathematically strand of the VELS applied
across the other strands including Measurement ‘… they make rough estimates and
check their work with respect to computations and constructions in Number, Space,
and Measurement, chance and data. ’
In the AC/AusVELS this is encompassed more generally within the proficiencies
‘…verify that their answers are reasonable.’ It could be incorporated as a schoolbased elaboration for the related content description.
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Questions …? and answers …! (6)
Why is it that a year 1 student is working towards a level 1, shouldn't they be
working to a level 2 instead? Start with foundation students on level 0 instead
of working towards level 0?
The achievement standards apply at the end of a period, so, for example, content that
students learn to be able to demonstrate achievement at Level 4 Is typically taught in
Year 4.By using the levels F, 1, 2 … 9, 10 one can interpolate and extrapolate
progression point examples at 0.5, F, F.5, 1, 1.5, 2 … 9.5, 10, 10.5.
How does Michael Ymer's plan fit into AusVELS? Is it a good planning model
for a whole school approach? We find the Ymer AUSVels planners most
useful.
This is a third party resource that some may find useful. Related information can be
obtained from the internet.
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Questions …? and answers …! (7)
What is the difference in the portfolios between Level 1 above satisfactory
and below satisfactory in Level 2?
Educational measurement seeks to provides a robust confidence for agreed
and recognisable locations (eg a level) on a scale. This confidence is greatest
at or around each location on the scale. Samples above satisfactory and below
satisfactory with respect to a level has been obtained in the same context as samples
at the level, and are close to the level but indicate additional elements of achievement
or do not fully indicate that level of achievement yet. However they are not an
interpolating location in their own right. They are centred around the relevant level.
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Questions …? and answers …! (8)
Rather than having samples at, above, and below, wouldn't it be more useful
to have similar tasks that demonstrate achievements at various levels - F, 1, 2
and so on to create through lines?
Developing valid and robust work samples that are agreed around the country has
been an involved process, a lot of material is required to obtain reasonable samples,
and these must be based on actual implementation of the curriculum. The initial need
(which was completed over 2011/12, a period of trialling for participating schools) was
to develop a selection of samples across levels and content strands.
Any further developmental work would need to be suitably resourced and in the first
instance would likely address requests for broader coverage of aspects of the
achievement standards. Tasks such as those suggested are also valuable and could be
incorporated in any further work.
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The End
Thank you!
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Contacts
David Leigh-Lancaster
Curriculum Manager, Mathematics
Email: leigh-lancaster.david.d@edumail.vic.gov.au
Telephone: 9032 1690
AusVELS Unit
Email: vcaa.ausvels@edumail.vic.gov.au
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