Student Learning
English and Mathematics
Developmental Continua
P - 10
Office of Learning and Teaching
OUR EDUCATIVE PURPOSE
LEARNER
What is powerful
to
learn?
Victorian
Essential Learning
Standards
English & Mathematics
Developmental
Continua P - 10
How do we know
it has been learnt?
Assessment
What is powerful
learning and
what promotes it?
Principles of
Learning
and Teaching
Beliefs about Student Learning
• All students can learn
• Schools and particularly teachers make a difference
• If students are assisted to work hard and make an
effort they improve
• An assessment culture in schools and the classroom
is critical
• Failure is not an option for students, teachers or
schools
Closing the Loop p. 3
Office of Learning & Teaching, DE&T
Our challenge
Learning
standards
Now
The Future
Building on what students know and
are able to do
The learner at the centre
Key Messages
The English and Mathematics Developmental Continua P-10
will assist teachers to:
• deepen their understanding of the English and
Mathematics domains
• monitor individual student progress towards achievement
of the Victorian Essential Learning Standards in English
and Mathematics
• enhance teaching skills to enable purposeful teaching
• identify the range of student learning levels within their
classes
• develop a shared language to describe and discuss
student progress.
Purpose of the English and Mathematics
Developmental Continua P - 10
Improve student learning …
• The Continua identify evidence based indicators
of progress consistent with the standards and
progression points
• The Continua provide a range of powerful
teaching strategies that support purposeful
teaching for students with similar learning needs
In the English and Mathematics
Developmental Continua you will find:
• standards and progression points for
each dimension
• indicators of progress
• teaching strategies
Level 6
Level 5
Level 4
Level 3
Level 2
Level 1
Each dimension in the English
and Mathematics domains are
based on an underlying
continuum of learning.
Standards define what students
should know and be able to do
at different levels.
Progression points indicate what
typical progress towards the
standard may look like.
Indicators of progress
• Indicators of Progress are points on the
learning continuum that highlight critical
understandings required by students in order
to progress through the standards
• They support teachers’ understanding of
student growth along the learning continuum
They do not capture all aspects of learning
within a dimension
Teaching Strategies
Teaching strategies are designed for
explicit, purposeful teaching to move
the student forward in their
learning towards the next standard
Mathematics Developmental Continuum P - 10
Standards and progression points
Related
progression
points
for each dimension
Indicators of Progress
Illustrations:
Observations & Diagnostic tasks
Range of teaching
strategies
Range of teaching
strategies
Range of teaching
strategies
Mathematics Developmental Overviews
Begin with the student’s
knowledge, skills and behaviours
The challenge for all teachers is to
accurately identify where a student is
located on the learning continuum and
to design learning experiences which
enable all students to make progress.
Example
• Problem:
John has to take 20ml of medicine
three times a day. How long will a
300ml bottle last?
Student work sample
This student knows
that multiplication is
involved.
She uses repeated
addition to correctly
show that there are 15
doses in 300ml of
medicine.
It appears from this
sample of work, she
may not know division
is useful here.
Indicator of progress
Level 4
3.25
Number:
Choosing multiplication
and division for
calculations
Level 3
Level 2
•Students choose to use
multiplication and division to
solve problems.
•Previously, they will have used
repeated addition or subtraction,
even when this was inefficient.
Teaching strategy
Activity 2: Strengthening recognition of
operations
• Recognising situations where division applies.
• At this level, most situations for division will be either partition or
quotition. Partition division problems (sharing problems) split a
quantity into a given number of parts. Quotition division problems
allocate a given quota to an unknown number of recipients.
• Examples of the types of questions to ask students:
I spent $1.95 on 3
apples. How much
each?
3 groups of ? =
195c
3 x ? = 195
partition situation
I spent $1.95 on
some 65c apples.
How many did I
buy?
? groups of 65c =
195 c
? x 65 = 195
quotition situation
Teaching strategy
Activity 3: Arrays and multiplication
Rectangular arrays are a fundamental tool in teaching about multiplication, but some
students in the middle years do not have a thorough understanding of the link.
•
•
Place 13 counters in a row on a table, and a second row underneath it. Ask students
how they could work out the number of counters in total.
Discuss responses, especially highlighting 2 rows of 13 (2 x 13) and 13 columns of 2.
Link these expressions to 2 groups of 13 and 13 groups of 2 and to 2 x 13 and 13 x 2.
Ensure that students see the array from both of these points of view.
2 groups of 13
•
13 groups of 2
•
Add more rows asking similar questions. Then ask students to use calculators to
find the number of counters in arrays with more rows (e.g. 8) both by repeated
addition and by multiplication.
•
• What are the strengths of this teaching strategy?
• Are there limitations?
• How will this teaching strategy support the student in
moving from an understanding of multiplication as
equal addition to a process of multiplication?
• After this teaching strategy has been used how would
you assess the student’s understanding?
• What would you do if they showed evidence of learning
and moved in their learning?
• What would you do if they hadn’t moved in their
learning?
Related progression points
Level
2.0 Standard
Progression Point
They describe and calculate simple multiplication as repeated addition , such as 3 × 5 = 5
+ 5 + 5; and division as sharing, such as 8 shared between 4.
2.5
They solve multiplication problems using strategies such as commutativity ( a × b = b × a
and a × b × c = c × b × a ), skip counting and building up from known facts.
3.25
They choose multiplication or division rather than repeated addition or subtraction, such
as finding how many 20ml doses in a 300ml bottle of medicine by division.
Students find equivalent fractions, multiples and fractions of fractions, such as twice one
sixth or half of one third, (Can't always do this as repeated addition)
and perform simple addition and subtraction with fractions using fraction models,
including linear models.
3.5
They use the language of multiplication to describe enlargement and reduction, such as 3
times as tall or one fifth the size. ( Can't always do this as repeated addition)
4.75
Students use equal multiplication by 10 to divide by decimals, such as 0.24 ÷ 0.04 = 24 ÷ 4
= 6.
They use a range of strategies for estimating multiplication and division calculations with
decimals, fractions and integers.
(Can't always do this as repeated addition subtraction).
Mathematics Developmental Overview
Overview of Numeration: Base Ten and Place Value Properties
Level
Whole
Numbers
1
2
two digit
(tens and
ones)
3
three digit
4
four digit
5
to millions and beyond
scientific notation,
calculate with
exponents
Decimals
Additive
properties
Multiplicative
properties
import
ance of
10 as a
group
use 10
as a
group
in
adding
tenths
hundredths
describe
place
value of
digits
use 100 as
a group in
adding or
subtracting
convert e.g.
100s to 10s
multiply by
10 and
multiples
6
thousandths and
beyond
rounding
convert
e.g.
hundredth
s to tenths
divide
and
multiply
by
powers
of 10
convert
e.g.
100s to
tenths,
and
vice
versa
appreciate
exponential
growth of
numbers as
powers of 10
increase
English Developmental Continuum P - 10
Standards and progression points
Reading Dimension
Indicators of Progress
Text Level Knowledge
Word Level Knowledge
Phonological Knowledge
Letter and Letter Name Knowledge
Self Management and Direction
Writing Dimension
Indicators of Progress
Ideas Communicated in Writing
Conventions of Writing
Writing Strategy
Conventions of Spelling
Teaching strategies
Teaching strategies
before
during
after
organising phase
composing phase
revising phase
proof reading & publishing phase
learning consolidation phase
Speaking & Listening
Dimension
Indicators of Progress
Oral Express / Listening Comprehension
Communicating Orally
Conventions of Language
Conventions of Communication
Teaching strategies
before
during
after
Indicators of progress in English
Reading
Writing
• Text Level Knowledge
• Word Level Knowledge
• Phonological Knowledge
• Self Management and
Direction
• Letter and Letter Name
Knowledge
• Ideas Communicated in
Writing
• Conventions of Writing
• Writing Strategy
• Conventions of Spelling
Example
A teacher has identified that a student is
currently working at reading level 4.75,
however needs to further build skills in
developing a reading plan.
Indicator of progress
Level 6
Reading Dimension:
Text Level Knowledge
Level 5
4.75
Level 4
•Students describe
their reading plan for
these types of texts
noting most of the
actions mentioned in
level 4, and modify their
reading plan to include
the use of the
strategies below.
Teaching Strategies
Teaching strategies are organised under the following:
• Before reading
• During reading
• After reading
Teaching strategy
4.75 Before Reading
Developing a reading plan
Students say the strategies or
actions they will use to:
• read each piece of text
• compare each piece of text
• develop an integrated
understanding across the
pieces of texts
For example the student says:
•
•
•
•
•
I will first read the pieces of
text
I will highlight key phrases
I will summarise key information
across paragraphs
I will make links between the
pieces of texts I have read and
I will compare information that
is presented
To reiterate the process
1. Teacher on-balance judgement
2. Align work sample to standards
and progression points
3. Cross reference with indicators of
progress
4. Identify the area to focus on
5. Select the most appropriate teaching
strategy
Planning
The Continua are a powerful resource for planning
purposeful teaching:
• Know the students’ existing knowledge, skills and behaviours
• Identify the most powerful teaching strategy
• Implement:
– When it will be used with the student/s?
– When will the student/s will be involved in learning with the
teacher?
– What will I do first with the student/s?
– What will I do next?
– What will the students do to apply their understanding?
– What will the students do independently to consolidate and
demonstrate their understanding?
– How will I organise my classroom?
Consider …
What were the main messages?
How can I encourage and support teachers
to use the English and/or Mathematics
Developmental Continua P – 10
to improve student learning?
Instruction is powerful only when it is sufficiently
precise and focused to build directly on what
students already know and to take them to the next
level. While a teacher does and must do many
things, the most critical is designing and organising
instruction so that it is focused.
Without focus instruction is inefficient and students
spend too much time on completing activities that
are too easy and do not involve new learning or too
little time on tasks that are too difficult and involve
too much new learning or relearning.
‘Breakthroughs’ Fullan, Hill & Crevola (2006)
Think, Pair, Share
• Positives ……….
• Negatives ……….
• Questions ………
Further indicators of progress and teaching
strategies will be added over time to
enhance and strengthen these resources
Speaking & Listening will be online by the end
of October
To provide feedback contact:
studentlearning@edumail.vic.gov.au
Further examples …..
Problem:
My football team had 2000 members
last year. There has been a 15 %
increase in membership this year. How
many members are there now?
Student work sample
This student has correctly found 15% of 2000, and added it
on to find the total required to solve this problem in two steps.
It appears from this sample of work, he may not know how to
solve this problem in one step i.e. multiplying by 1.15.
Indicator of progress
Level 6
5.25
Level 5
Level 4
Number:
Adding and taking off a
percentage
• Success at this level depends on
students being able to add or
subtract a percentage in one step
by multiplication.
• Previously, students will do this
in two steps by calculating the
mark-up or discount separately,
and then adding or subtracting
from the price.
Teaching strategy
Students
should match
each entry in
the right hand
column with an
entry in the left
hand column.
For example, is
multiplying by
0.95 the same
as subtracting
5%?
• What are the strengths of this teaching strategy?
• Are there limitations?
• How will this teaching strategy support the student in
moving from an understanding of multiplication as
equal addition to a process of multiplication?
• After this teaching strategy has been used how would
you assess the student’s understanding?
• What would you do if they showed evidence of learning
and moved in their learning?
• What would you do if they hadn’t moved in their
learning?
Student work sample
This work shows
evidence of:
• Writing from
personal
experience
• Two sequenced
ideas
• Appropriate nouns
and verbs
• Simple sentences
• Some capital
letters and full
stops
• Some high
frequency words
and one syllable
words spelt
correctly
• Phonological
awareness (letter
sounds to attempt
unfamiliar words)
Indicators of Progress
1.25 Writing dimension
Ideas Communicated in Writing
•
Students continue to write about familiar events and personal experiences or
feelings but use a greater range of ideas in a coordinated way, for example,
they support topic with data, and reasons or opinions with simple detail or
comments. They extend their use of topic-relevant and high-frequency
vocabulary. They combine their personal writing with supportive drawings.
•
Their texts begin to identify a main idea and subordinate or particular ideas.
They may write multiple sentences on a particular topic. Their texts have a
beginning, a body and an end. Their texts begin by defining or describing the
topic. They begin to sequence ideas, data, reasons and opinions.
•
While much of their writing is to convey their own ideas and thoughts, they
begin to attempt to write directly for a particular audience. They write for
different purposes: to tell a story, to entertain, to inform, to reflect, to
describe or to observe.
Level 3
Indicator of progress
Writing Dimension:
Ideas Communicated in Writing
Level 2
1.25
Level 1
•Students continue to write about
familiar events and personal
experiences or feelings but use a
greater range of ideas in a
coordinated way, for example, they
support topic with data, and
reasons or opinions with simple
detail or comments. They extend
their use of topic-relevant and highfrequency vocabulary. They
combine their personal writing with
supportive drawings.
Teaching Strategies
Teaching strategies ‘Ideas communicated in writing’
are organised under the following:
• Organising phase
• Composing phase
• Revising phase
• Proof reading and publishing phase
• Learning consolidation phase
Teaching strategy
1.25 Organising Phase
Establishing a purpose for writing
• Students say that they are writing to tell other people about their
favourite minibeast. What they will do is describe what their
favourite minibeast is like, for example. My favourite minibeast is a
slater. I am going to tell you all about slaters.
• To begin, the students in small groups can decide the questions their
writing might answer. What are some who / what / how / why/ when
/ where questions?
To reiterate the process
1. Teacher on-balance judgement
2. Align work sample to standards
& progression points
3. Cross reference with indicators of
progress
4. Identify the area that I will focus on
5. Select the teaching strategy