AusVELS Mathematics: Primary

Report
AusVELS
Mathematics F–6
David Leigh-Lancaster
14 August 2013
1
Structure of the session
1.
Overview of AusVELS Mathematics
components of the VCAA website
2.
Discussion of some sample queries,
proficiencies and work samples
3.
Question …? and answer …!
2
AusVELS Mathematics: VCAA website (1)
The mandated curriculum
1. Level description
2. Content descriptions
3. Achievement standards
(Note: work samples are a supporting
resource for the achievement standards)
4. Proficiency strands ‘the proficiencies’
3
AusVELS Mathematics: VCAA website (2)
Other stuff - optional
1. AC elaborations can use be used as they are or
supplemented (e.g. with excerpts/examples
from the VELS); School may also develop their
own
2. Progression point examples are a possible
model, can be adapted and varied to suit
implementation
3. Planning template by content strand and
AusVELS level.
4
AusVELS Mathematics: VCAA website (3)
Website links – optional
1.
2.
3.
4.
5.
6.
AAMT (Top drawer)
AMSI (TIMES Modules)
ESA (Scootle)
MAV (TM4U)
MERGA (Research)
NLVM (Digital activities)
(See also: http://www.vcaa.vic.edu.au/Pages/foundation10/curriculum/resources/maths.aspx)
5
Mapping proficiency statements (0)
Level 4 Achievement Standard
Number and Algebra
Students recall multiplication facts to 10 x 10 and related division facts.
They choose appropriate strategies for calculations involving
multiplication and division, with and without the use of digital technology,
and estimate answers accurately enough for the context. Students solve
simple purchasing problems with and without the use of digital
technology. They locate familiar fractions on a number line, recognise
common equivalent fractions in familiar contexts and make connections
between fractions and decimal notations up to two decimal places.
Students identify unknown quantities in number sentences. They use the
properties of odd and even numbers and describe number patterns
resulting from multiplication. Students continue number sequences
involving multiples of single-digit numbers and unit fractions, and locate
them on a number line.
6
Mapping proficiency statements (1)
Fluency (highlight actions)
Students:
• develop skills in choosing appropriate procedures
• carry out procedures flexibly, accurately, efficiently and appropriately
• recall factual knowledge and concepts readily
• calculate answers efficiently
• recognise robust ways of answering questions
• choose appropriate methods and approximations
• recall definitions and regularly use facts
• manipulate expressions and equations and find solutions.
7
Mapping proficiency statements (2)
Problem Solving (highlight actions)
Students:
• develop the ability to make choices, interpret, formulate, model and
investigate problem situations
• communicate solutions effectively
• formulate and solve problems when they use mathematics to represent
unfamiliar or meaningful situations
• design investigations and plan their approaches
• apply their existing strategies to seek solutions
• verify that their answers are reasonable.
8
Mapping proficiency statements (3)
Understanding (highlight actions)
Students:
• build a robust knowledge of adaptable and transferable mathematical
concepts
• make connections between related concepts and progressively apply the
familiar to develop new ideas
• develop an understanding of the relationship between the ‘why’ and the
‘how’ of mathematics
• build understanding when they: connect related ideas; represent
concepts in different ways; identify commonalities and differences
between aspects of content; describe their thinking mathematically; and
interpret mathematical information.
9
Mapping proficiency statements (4)
Reasoning (highlight actions)
Students:
• develop an increasingly sophisticated capacity for logical thought and
actions, such as analysing, proving, evaluating, explaining, inferring,
justifying and generalising
• explain their thinking
• deduce and justify strategies used and conclusions reached
• adapt the known to the unknown, and transfer learning from one context
to another
• prove that something is true or false
• compare and contrast related ideas and explain their choices.
10
Developing school-based work samples (0)
Coins and combinations – developing a sample task
Students are provided with a set of Australian coins, containing some
repeated denominations, and asked to solve a variety of related problems
that could include selecting subsets to form a given value (sums and
combinations), ask related questions (smallest/largest value using exactly
4 coins) and/or problems related to payment and change in a practical
purchase situation.
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Developing school-based work samples (1)
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Developing school-based work samples (3)
Level 3 Achievement Standard (excerpt)
Number and Algebra
… students recall addition and multiplication facts for
single-digit numbers. They represent money values in
various ways and correctly count out change from
financial transactions …
13
Developing school-based work samples (4)
After the task has been conducted and student responses gathered, look
over student work and identify excerpts/sections that typically occur and
would provide a basis for judgment that the student has indicated that
they have demonstrated achievement of this aspect of the standard.
Develop relevant commentary/annotations.
For a written response, these annotations could be included by ‘comment
clouds’. For an activity which is video recorded these may be associated
verbal comments such as:
‘… we observe the student doing … which indicates that …’
‘ … the student’s explanation shows that … however …’
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Sample question and response (0)
‘Can you elaborate on this statement, found in the subject
year level overview under the achievement standards: Level
foundation "students order the first 10 elements of a set", our
main question is set of what? shapes? numbers?’
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Sample question and response (1)
Set is actually an undefined term like point. Finite sets are
easy (just list the elements), infinite sets get a lot more tricky
and interesting.
Sets are often characterised as ‘a well-defined collection’ but
this isn’t really helpful as it replaces a shorter word set with a
longer one collection – and of course we now have to worry
about what is meant by well-defined!
16
Sample question and response (2)
… one usually exhibits examples. Sets are un-ordered,
however we can order them.
So if we have a set with 10 or more elements (members)
which can be anything, numbers, letters, shapes, people,
books, whatever. Yes it is important to do this with different
kinds of sets, then students should be able to order the first
ten of them.
This means that some criterion for ‘order’ is required …
17
Sample question and response (3)
It’s a good idea to show that more than one order can be applied to a set,
for example if we have 20 students in a class we could order (the first 10
of them) in terms of:
•
•
•
•
•
arrival at class
height
age
test score
time taken to complete a cross country run
Note that ordering can include equal values. In a list these typically get
placed next to each other.
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Sample question and response (4)
We just wanted to check the terminology in the Number of Algebra
section of Aus VELS at 0.05. In the first progression point it states:
“connect number names and numerals with sets of up to 10 elements.”
We were just wondering if the term 'number names', relates to the
student being able to read the number (t-w-o), or say the number
(counting/listing numbers out loud)?
We have assessed students on both and just felt that most of our students
at this level (Prep) were unable to read number names like 'three' for
example, and that the focus was on their reading ability rather than their
proficiency at counting, matching numerals and objects etc. We are
assuming it is their ability to say the numbers not read them.
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Sample question and response (5)
Just a question I have about the Australian Curriculum for
levels F and level 1. I have noticed that there are no division
and multiplication standards for these levels as there were in
VELS.
Is this correct? This all starts at level 2.
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The End
Thank you!
21
Contacts
David Leigh-Lancaster
Curriculum Manager, Mathematics
Email: [email protected]
Telephone: 9032 1690
AusVELS Unit
Email: [email protected]
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