Making Effective Use of the Renewed Framework for

MathematicsDay 3

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

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

‘’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

Phases of planning a unit in mathematics

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?

How did the different approach to planning

impact on the learning in your classroom?

How did the teaching and learning strategies differ at

different phases of the learning cycle?

Successful teaching…Successful learning

Two commonly accepted ways of understanding teaching and learning are:

transmission teaching/acquisition learning

participation teaching/constructive learning

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

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?

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

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?

Monitor-Evaluate-Action plan

What do children like to do in the playground?

Year R

The Data Handling Cycle

Task:

“Practice improves estimation skills”

True or false?What’s the evidence?

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

Phases of planning a unit in mathematics

‘Eight out of ten cats prefer Whiskas’

How do they

know?!

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

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

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

Supporting Underperforming Pupils

How were the needs of all learners actively

addressed in the lesson?

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?

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

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

Do your underperforming children have similar characteristics to the children who

struggle or do they have different characteristics?

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

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

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

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

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.

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

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.

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)

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?

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?

Year 4 Pair - Share

Share - share with the other pair why you think you are correct

Snowballing

Pair Pair

Group/class

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

Talk prompts

It can’t be that because

I thinkWhy do you think that?

Talk Cards

How might you use these with pairs or groups?

Have them on view as prompts?

Choose one each?

Select one prompt

Talk prompts

What is the largest odd number you can make?

What is the smallest odd number you can create?

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

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?

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

Leading improvement and next steps

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

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

5 key themes

Encouraging flexibility

Structuring learning

Raising expectations

More effective use of assessment

Broaden and strengthen pedagogy

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?

Reviewing priorities 2

How will success be measured?

What are the criteria for success? What actions are to be taken?

The school improveme

nt cycle

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

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)

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?

Supporting colleagues

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

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)

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.

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?

-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.

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

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?

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.

PNS Subject leader materials-mathematics

There are three suggested CPD themes for mathematics:

Calculation Using and applying mathematics Under-performing pupils

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

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?