Student Learning English and Mathematics Developmental Continua P - 10
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Transcript of Student Learning English and Mathematics Developmental Continua P - 10
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:[email protected]
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