Student Learning English and Mathematics Developmental Continua P - 10

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Student LearningEnglish and Mathematics
Developmental ContinuaP - 10

• Office of Learning and Teaching

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OUR EDUCATIVE PURPOSE
LEARNER
What is powerful learning and what promotes it?
What is powerful to learn?
English Mathematics Developmental Continua
P - 10
Principles of Learning and Teaching
Victorian Essential Learning Standards
How do we know it has been learnt?
Assessment
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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, DET

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Our challenge
Learning standards
Now
The Future
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Building on what students know and are able to do
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The learner at the centre
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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.

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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

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In the English and Mathematics Developmental
Continua you will find

• standards and progression points for each
  dimension
• indicators of progress
• teaching strategies

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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 6
Level 5
Level 4
Level 3
Level 2
Level 1
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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

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Teaching Strategies

• Teaching strategies are designed for
• explicit, purposeful teaching to move
• the student forward in their
• learning towards the next standard

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Standards and progression points for each
dimension
Related progression points
Mathematics Developmental Overviews
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• Begin with the students 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.

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• Example
• Problem
• John has to take 20ml of medicine
• three times a day. How long will a
• 300ml bottle last?

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• 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.
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Indicator of progress
Level 4
Number Choosing multiplication and division for
calculations
3.25
Level 3

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

Level 2
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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
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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.

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• 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 students understanding?
• What would you do if they showed evidence of
  learning and moved in their learning?
• What would you do if they hadnt moved in their
  learning?

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Related progression points
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).
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Mathematics Developmental Overview
Overview of Numeration Base Ten and Place Value
Properties
Level 1 1 2 2 2 2 3 3 3 3 3 4 4 4 5 5 5 6
Whole Numbers two digit(tens and ones) two digit(tens and ones) three digit four digit three digit four digit three digit four digit three digit four digit three digit four digit three digit four digit to millions and beyond to millions and beyond to millions and beyond to millions and beyond to millions and beyond to millions and beyond to millions and beyond scientific notation, calculate with exponents scientific notation, calculate with exponents scientific notation, calculate with exponents
Decimals tenths tenths hundredths hundredths hundredths hundredths hundredths thousandths and beyond thousandths and beyond thousandths and beyond scientific notation, calculate with exponents scientific notation, calculate with exponents scientific notation, calculate with exponents
Additive properties importance of 10 as a group use 10 as a group in adding use 10 as a group in adding describe place value of digits describe place value of digits use 100 as a group in adding or subtracting use 100 as a group in adding or subtracting use 100 as a group in adding or subtracting use 100 as a group in adding or subtracting rounding rounding rounding rounding rounding rounding rounding rounding rounding
Multiplicative properties convert e.g. 100s to 10s convert e.g. 100s to 10s convert e.g. 100s to 10s multiply by 10 and multiples multiply by 10 and multiples multiply by 10 and multiples convert e.g. hundredths to tenths convert e.g. hundredths to tenths convert e.g. hundredths to tenths convert e.g. hundredths to tenths divide and multiply by powers of 10 convert e.g. 100s to tenths, and vice versa convert e.g. 100s to tenths, and vice versa appreciate exponential growth of numbers as powers of 10 increase appreciate exponential growth of numbers as powers of 10 increase
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Indicators of progress in English
Reading
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
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• 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.

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Indicator of progress
Level 6
Reading Dimension Text Level Knowledge

• 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.

Level 5
4.75
Level 4
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Teaching Strategies

• Teaching strategies are organised under the
  following
• Before reading
• During reading
• After reading

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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

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To reiterate the process

• Teacher on-balance judgement
• Align work sample to standards and progression
  points
• Cross reference with indicators of progress
• 4. Identify the area to focus on
• 5. Select the most appropriate teaching strategy
  

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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?

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• 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?

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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)
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Think, Pair, Share

• Positives .
• Negatives .
• Questions

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• 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_at_edumail.vic.gov.au

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Further examples ..
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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?
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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.
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Indicator of progress
Level 6
Number Adding and taking off a percentage
5.25

• 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.

Level 5
Level 4
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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?
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• 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 students understanding?
• What would you do if they showed evidence of
  learning and moved in their learning?
• What would you do if they hadnt moved in their
  learning?

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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)

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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.

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Indicator of progress
Level 3
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.

Level 2
1.25
Level 1
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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

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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?

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To reiterate the process

• Teacher on-balance judgement
• Align work sample to standards progression
  points
• Cross reference with indicators of progress
• 4. Identify the area that I will focus on
• 5. Select the teaching strategy