Student Learning

English and Mathematics Developmental Continua

P - 10Office of Learning and Teaching

OUR EDUCATIVE PURPOSE

What is powerful to

learn?

VictorianEssential Learning

Standards

What is powerful learning and

what promotes it?

Principles ofLearning

and Teaching

LEARNER

How do we know it has been learnt?

Assessment

English & Mathematics Developmental Continua P - 10

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

schoolsClosing the Loop p. 3

Office of Learning & Teaching, DE&T

Our challenge

Now The Future

Learning standards

Building on what students know and are able to do

The learner at the centre

Key MessagesThe English and Mathematics Developmental Continua P-

10will 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 - 10Improve 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

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.

Level 1

Level 3

Level 4

Level 5

Level 6

Level 2

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 forexplicit, purposeful teaching to movethe student forward in theirlearning towards the next standard

Mathematics Developmental Continuum P - 10

Illustrations:Observations & Diagnostic tasks

Indicators of Progress

Range of teaching strategies

Range of teaching strategies

Range of teaching strategies

Mathematics Developmental Overviews

Related progression

points

Standards and progression pointsfor each dimension

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

medicinethree times a day. How long will

a300ml 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.

Level 4

Level 3

Level 2

Indicator of progress

3.25

•Students choose to use multiplication and division to solve problems. •Previously, they will have used repeated addition or subtraction, even when this was inefficient.

Number:Choosing multiplication

and division for calculations

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

Activity 3: Arrays and multiplicationRectangular 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

Teaching strategy

• 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?

Level Progression Point 2.0 Standard

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).

Related progression points

Mathematics Developmental OverviewOverview of Numeration: Base Ten and Place Value

PropertiesLevel 1 2 3 4 5 6Whole Numbers two digit

(tens and ones)

three digit four digit to millions and beyond

scientific notation, calculate with

exponents Decimals

tenths hundredths thousandths and beyond

Additive properties

importance of 10 as a group

use 10 as a

group in

adding

describe place

value of digits

use 100 as a group in adding or

subtracting

rounding

Multiplicative properties

convert e.g. 100s to 10s

multiply by 10 and

multiples

convert e.g.

hundredths 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 KnowledgeWord Level Knowledge

Phonological Knowledge Letter and Letter Name Knowledge

Self Management and Direction

Writing DimensionIndicators of ProgressIdeas Communicated in Writing

Conventions of WritingWriting Strategy

Conventions of Spelling

Speaking & ListeningDimension

Indicators of ProgressOral Express / Listening Comprehension

Communicating OrallyConventions of Language

Conventions of Communication

Teaching strategiesbefore during

after

Teaching strategiesorganising phasecomposing phase

revising phaseproof reading & publishing phase

learning consolidation phase

Teaching strategiesbefore during

after

Indicators of progress in EnglishReading

• Text Level Knowledge• Word Level Knowledge• Phonological Knowledge• Self Management and Direction • Letter and Letter Name Knowledge

Writing• 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 indeveloping a reading plan.

Level 6

Level 5

Level 4

Indicator of progress

•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.

Reading Dimension:Text Level Knowledge

4.75

Teaching strategies are organised under the following:

• Before reading• During reading• After reading

Teaching Strategies

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 process1. Teacher on-balance judgement2. Align work sample to standards

and progression points3. Cross reference with indicators of

progress4. 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.

Level 6

Level 5

Level 4

Indicator of progress

5.25

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 strategyStudents

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

Level 2

Level 11.25

•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.

Writing Dimension:Ideas Communicated in Writing

Indicator of progress

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 process1. Teacher on-balance judgement2. Align work sample to standards

& progression points3. Cross reference with indicators of

progress4. Identify the area that I will focus on 5. Select the teaching strategy