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Making Effective Use of the Renewed Framework for
MathematicsDay 3
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Aims
Supporting colleagues in developing a shared view of what is successful learning in mathematics
Supporting colleagues in developing an approach to planning that will enable all children to learn successfully
Supporting colleagues in enabling underperforming children to become successful learners
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Programme
SESSIONS• ‘Quality first’ learning
opportunities
• Supporting underperforming pupils
• Leading improvement and next steps
10.30-10.45 Coffee
12.15-1.00 Lunch
2.30-2.45 Tea
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‘’Quality first’ learning opportunities
Wave 3Additional
highly personalised interventions
Wave 2Additional interventions
to enable children to work at age related expectations or above
Wave 1Inclusive quality first teaching for all
3.11
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Phases of planning a unit in mathematics
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Planning a teaching and learning cycle
Is there a context which will facilitate learning and develop the connections between the objectives?
What prior learning will need to be activated? What is the new teaching? How will the children practise and consolidate this
new learning? How will the learning be applied, extended and
secured by all? How will the learning be reviewed by the children
and the teacher?
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How did the different approach to planning
impact on the learning in your classroom?
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How did the teaching and learning strategies differ at
different phases of the learning cycle?
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Successful teaching…Successful learning
Two commonly accepted ways of understanding teaching and learning are:
transmission teaching/acquisition learning
participation teaching/constructive learning
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Transmission teaching, acquisition learning
Some facts are arbitrary: the units we use to measure length are
centimetres, metres and kilometresSome facts are useful to learn by rote: 3 x 7 = 21, 100 cm = 1mSome skills need clear demonstrations: how to use a protractor
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Jar A contains 25 marbles
Jar B contains 75 marbles
Each jar’s contents is poured into a third jar
How many marbles are in the jar?
Jar A contains 1 litre of water at 25oC
Jar B contains 1 litre of water at 75oC
Each jar’s contents is poured into a third jar
What is the temperature of the water in the jar?
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Participation teaching, constructive learning
New knowledge needs to connect with established knowledge:
I can choose the appropriate unit to measureKnown facts can be used to derive unknown facts: 3 x 7 = 21, 6 x 0.7 = 4.2, doubling and halving
can be used to derive multiplication facts – derive 6 x 7 = 42 from 3 x 7 = 21
Knowledge can be applied in a variety of contexts: Fractions can be used to solve problems involving
shape, involving numbers and can be used to order numbers
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Quality first teaching and learning
What does it look like? What are the key elements? How does it fulfil the needs of all
children? How do we know? How can the Renewed Framework
support this?
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Monitor-Evaluate-Action plan
What do children like to do in the playground?
Year R
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The Data Handling Cycle
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Task:
“Practice improves estimation skills”
True or false?What’s the evidence?
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Practice improves
estimation skills
Specify the ProblemBrainstorm
What? How? Who?
Specify the ProblemBrainstorm
What? How? Who?
Collect Data Who? How? When? Why?
Where will the data come from?
What skills will you use – Why?
Collect Data Who? How? When? Why?
Where will the data come from?
What skills will you use – Why?
Process and Represent the Data
What? How? Why?
Process and Represent the Data
What? How? Why?
Interpret and discuss data
Summary of all your results
Interpret and discuss data
Summary of all your results
EvaluationWas your hypothesis right?
Improvements - & how?Does it raise another
problem?
EvaluationWas your hypothesis right?
Improvements - & how?Does it raise another
problem?
Plan
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Phases of planning a unit in mathematics
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‘Eight out of ten cats prefer Whiskas’
How do they
know?!
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Personalising learning and teaching through:
matching high quality teaching to the different and developing abilities of pupils
regular monitoring of progress, and rapid response at the point at which pupils begin to fall behind
dialogue between teachers and pupils, encouraging them to explore their ideas through talk … and to reflect on what they have learnt
2020 Vision - Report of the Teaching and Learning in 2020 Review Group
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Personalising learning and teaching through:
collaborative relationships which encourage and enable all pupils to participate
judicious use of whole class teaching, as well as paired and group work
using more open ended tasks with pupils
2020 Vision - Report of the Teaching and Learning in 2020 Review Group
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Personalised learning is …
…learner-centred and knowledge-centred …
learners are active and curious create their own hypotheses and ask their
own questions coach one another set goals for themselves experiment with ideas for taking risks,
knowing that mistakes and being ’stuck’ are part of learning
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Supporting Underperforming Pupils
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How were the needs of all learners actively
addressed in the lesson?
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Successful learning… successful teaching?
Discussion groups: What are the characteristics of children
who are successful at mathematics? What are the characteristics of children
who struggle to learn mathematics?
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Children who are successful at learning in mathematics
We need to plan learning that may: add breadth (for example enrichment
through a broader range of content, tasks and resources).
increase depth (for example extension through complexity).
accelerate the pace of learning by tracking forward to future objectives within or across key stage
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Children who struggle to learn mathematics
We need to plan learning that will: be aligned to age appropriate objectives use a range of learning and teaching
styles accommodate children’s individual needs
and differences include challenge and high expectations
for all
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Do your underperforming children have similar characteristics to the children who
struggle or do they have different characteristics?
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Supporting children with difficulties
How can we understand and begin to identify where children are having difficulties? One starting point is to categorise types of misunderstanding to help identify possible ways of addressing them:
Language Conceptual Procedural
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Language
Our system is irregular until 60!
Eleven “ “ onety-one Twelve “ “ onety-two… Sixteen “ “ onety-six… Twenty “ “ twoty Thirty “ “ threety Fourty sounds OK but is incorrectly
spelt Fifty should be fivety
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The variety of mathematical language
7,8 and 157 add 8 is
15
15 take away 8 is 7
8 added to 7 gives a total of 15
8 is 7 less than 15
15 is 8 more than 7
8 more than 7 is 15
The difference between 7 & 15 is 8
15 take away 8 leaves 7
8 plus 7 is 15
15 minus 7 is 8
15 is 7 added to 8
8 less than 15 is 7
7 and 8 make 15
15 subtract 8 is
When I count on 8 from 7 I get 15
If you take 8 from 15, 7 is left
I count back 7 from 15 to get to 8
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ConceptualWhy might children: not identify the following shapes
as rectangles
calculate 24% of 525 by finding one twenty-fourth of 525
put these decimal numbers in this order: 73.5, 73.32, 73.64
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Procedural
A shepherd has 14 sheep and 9 goats altogether. How old is the shepherd?
If Henry the 8th had 6 wives, how many wives did Henry the 4th have?
To multiply by 10 you add a 0.
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Supporting underperforming children
mathematical difficulties are highly susceptible to intervention
intervention should be as early as possible, partly because mathematical difficulties can affect performance in other areas of the curriculum, and partly to prevent the development of negative attitudes to and anxiety about mathematics
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Supporting underperforming children
interventions should focus on the particular components of mathematics with which the child has difficulty rather than follow a set ‘programme’
interventions using peer support, ICT or TA support work best when they are managed by a skilled teacher who orchestrates and retains overall responsibility for the child’s learning
Dowker, A, (2004) What works for children with mathematical difficulties. London: DfES Research Report 554.
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An enquiring classroom creates a culture of learning when both adults and children’s questions are valued and genuine dialogue is promoted
From Excellence and enjoyment: learning and teachingin the primary years (DfES 0518-2004G)
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Year 4 Block A unit 1
Objective Partition, round and order four-digit whole numbers;
use positive and negative numbers in context and position them on a number line; state inequalities using the symbols < and > (e.g. –3 > –5,–1 < +1)
Assessment for learning
What is the biggest whole number that you can make with these four digits: 3, 0, 6, 5? What is the smallest whole number that you can make with the digits?
Look at this number sentence: + = 1249. What could the missing numbers be?
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Year 4 Pair - Share
PairsDecide :– what is the biggest whole number you can make with the digits?–what is the smallest whole number you can make with the digits?
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Year 4 Pair - Share
Share - share with the other pair why you think you are correct
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Snowballing
Pair Pair
Group/class
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Ground rules for dialogue
Making eye contact with the speaker Everyone taking a turn One person speaking at a time Speaking in a clear voice Using vocabulary Being clear about what you mean Responding to the other speaker Making a longer contribution than just one
or two words Using facial expressions and gestures
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Talk prompts
It can’t be that because
I thinkWhy do you think that?
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Talk Cards
How might you use these with pairs or groups?
Have them on view as prompts?
Choose one each?
Select one prompt
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Talk prompts
What is the largest odd number you can make?
What is the smallest odd number you can create?
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Roles in the group
Leader – organises the group, encourages all to participate
Scribe – notes main points of discussion
Reporter- works with the scribe to organise their ideas, summing up etc
Mentor – helps group members carry out the task, explaining and organising
Observer – makes notes on how the group works and shares it with group
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Task
Can your group create instructions to work out the largest even number from your four digits
Can you write it so that it works for any four digits
Can another group follow your guidance?
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Personalising learning and teaching through:
collaborative relationships which encourage and enable all pupils to participate
judicious use of whole class teaching, as well as paired and group work
using more open ended tasks with pupils
2020 Vision - Report of the Teaching and Learning in 2020 Review Group
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Leading improvement and next steps
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Aims
To review priorities in the light of this course
To explore approaches to monitoring and evaluation
To consider how colleagues can be supported in developing learning and teaching in mathematics
To develop an action plan for next steps in school
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The renewal marks an important step and brings new impetus and new structures that are a significant development in teaching and learning in literacy and mathematics… Changes in the structure and content of objectives, along with core guidance are significant, and schools and settings are encouraged to understand the changes and to move towards implementation..
The renewal of the framework
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5 key themes
Encouraging flexibility
Structuring learning
Raising expectations
More effective use of assessment
Broaden and strengthen pedagogy
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Reviewing priorities 1
Where do improvements need to be made?
What is it that needs improving? Sharpening the focus – what? which pupils?
What outcomes are expected?
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Reviewing priorities 2
How will success be measured?
What are the criteria for success? What actions are to be taken?
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The school improveme
nt cycle
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PDM 4 Reviewing ProgressImportance of: monitoring implementation of actions and
evaluating the impact these have had on children’s learning, particularly those in the focus group
using evidence to inform learning and teaching to make informed judgements about standards and to develop future priorities and actions
making links to school self-evaluation and the completion of the SEF
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Monitoring and evaluation
Monitoring – about keeping track & making sure what is planned happens
Evaluation – about making a judgement, assessing the extent to which the intended outcomes have been met (using success criteria to make the judgement)
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Consider, in relation to your school priorities:
What monitoring and evaluation activities will help you to get a clear picture of the impact on teaching and learning in your school?
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Supporting colleagues
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Effective CPD: is likely to have a direct relationship with what
teachers are doing in their own schools and classrooms
uses external expertise linked to school-based activity
involves observation and feedback – especially teachers observing and learning from each other and expert colleagues
includes peer support – colleagues supporting one another rather than leadership by supervisors
provides scope for participants to identify the focus of their development
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Effective CPD: enables all staff to be reflective and focus on
their contribution to children’s learning and attainment
provides opportunities to work with other colleagues and share practice
includes opportunities to receive regular and structured feedback
applies processes for sustaining CPD, over time, to embed learning in classroom practice
includes opportunities for independent self-study*From Excellence and enjoyment: learning and teaching
in the primary years (DfES 0518-2004G)
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Using coaching to sustain change 1
Co-coaches are professional learners committed to reciprocal learning and providing non-judgemental support to each other based on evidence from their own practice.
Co-coaching involves activities which promote and enhance reflective practice.
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Using coaching to sustain change 2
Look at the co-coaching skills. Can you give examples of how you
demonstrated these when you worked together in school?
How did this help your thinking and learning?
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-A learning conversationFor each learning conversation there will be
a presenter and a note taker. Members of the group take turns to carry out these roles. Each conversation lasts a total of 6 minutes.
The note taker needs to keep summary notes and ensure that the group keeps to the timings. At the end of the conversation the notes are given to the presenter as a record for them to refer to later.
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Learning through co-coaching – a learning conversation
1. The presenter outlines how they worked with their co-coach, giving examples of the co-coaching skills they used and why they were successful.
2 minutes2. The other group members respond by asking
questions/seeking further information. They also offer any suggestions to the presenter, who may also ask questions.
3 minutes
3. The note taker reads a summary of the notes.1 minute
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Using coaching to sustain change 3
What insights did you gain from how you worked with your colleague with the gap task, for supporting colleagues in school?
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PNS School–based CPD materials
The 5 key messages run throughout. They could contribute to your on-going
school professional development over the next 2 years.
They provide opportunities for staff to engage in their own action research.
They could support you with identified focus groups.
You will need to SELECT, TAILOR and ADAPT the materials.
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PNS Subject leader materials-mathematics
There are three suggested CPD themes for mathematics:
Calculation Using and applying mathematics Under-performing pupils
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Professional Development Meetings
PDM 1 – Introduction to the Renewed Framework
PDM 2 – Pace and progression PDM 3 – Strengthening pedagogy PDM 4 – Review and evaluation of
impact on children’s progress
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Reviewing priorities
Where do improvements need to be made? What is it that needs improving? What outcomes are expected? How will success be measured? What are the criteria for success?
What actions are to be taken? Timescale?
What support will you need from the Senior Leadership Team?