Mathematics Mastery in Reception - Pimlico Primary · •To understand the key principles of the Mathematics Mastery approach ... Two cubes and one more ... Challenge and differentiation

Mathematics Mastery in Reception

Aims of the day

• To know our mission and why Mathematics Mastery exists

• To understand the key principles of the Mathematics Mastery approach

• To know how to effectively implement Mathematics Mastery in Reception

Session One

• Why we are here

• Growth Mindset

• Mathematics Mastery Key Principles:

– language & communication

Our vision

For every child to enjoy and succeed in

mathematics, regardless of background.

Our mission

To transform mathematics education

in the UK.We work in partnership to

empower and equipschools to deliver world-class

mathematics teaching.

Core belief

Mathematics Mastery schools want to ensure that their aspirations for every child’s mathematics success become reality

• Success in mathematics for every child ispossible

• Mathematical ability is not innate, and is increased through effort

Growth Mindset

‘All pupils can achieve in mathematics’

Innate ability(fixed mindset)

Effort-based ability(growth mindset)

Inborn intelligence is

the main determinant

of success

Consistent effort and effective strategies are

the main determinantsof success.

Negative perceptions of mathematics

• If children hear ‘I can’t do maths’ from parents, teachers, friends they begin to believe it isn’t important

• People become less embarrassed about maths skills as it is acceptable to be ‘rubbish at maths’

• Self-fulfilling prophecy• There is no maths gene• Develop perseverance and resilience

and good ‘habits of mind’From www.nationalnumeracy.org.uk

http://www.nationalnumeracy.org.uk/

How can we overcome this in the classroom?

• Teaching pupils that talent and giftedness are dynamic attributes that can be developed.

• Through the portrayal of challenges, effort, and mistakes as highly valued.

• Through process praise and feedback.

From Dweck, C, Mindsets and Math/Science achievement, Stanford University, 2008

Conceptual

understanding

Language and communication

Mathematical

thinking

Mathematical problem solving

Conceptual understanding

Mathematical thinking

The Key Principles

Drury (2014)

Why is problem solving ‘at the heart’?

“Teaching is for learning; learning is for understanding; understanding is for reasoning and applying and, ultimately problem solving.”

Ministry of Education, Singapore (2012), p.21

A representational-reasoning model of understanding

Barmby et al. 1999

A representational-reasoning model of understanding

Deeper understanding

100

place value

ˈhʌndrəd

hundred

Connectionist pedagogies“…highly effective teachers seemed to pay attention to:

• Connections between different aspects of mathematics

• Connections between different representations of mathematics

• Connections with children’s methods

Askew et al 1997

Connectionist paradigm“Mathematics is an interconnected subject, in which pupils need to be able to move fluently between representations of mathematical ideas….

… pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems.”

The national curriculum in England, DfE (2013)

Language & Communication

Language and communication Pupils deepen their understanding by explaining, creating problems, justifying and proving using mathematical language. This acts as a scaffold for their thinking and deepening their understanding further.

Mathematical

problem

solving

Conceptual

understanding


Mathematical

thinking




Mathematical reasoning

“Mathematical reasoning, even more so than children’s knowledge of arithmetic, isimportant for children’s later achievement in mathematics.”

Nunes et al. (2009) p.1

Mastering Mathematical Language

Mathematics Mastery lesson guides plan opportunities for pupils to develop mathematical language through:

• Sharing the key vocabulary at the beginning of every lesson and insisting on its use throughout

• Expecting children to respond using a full sentence

• Modelling clear sentence structures using mathematical language.

• Purposeful Talk Task activities

Opportunities for pupils to reason and explain (in sentences) the maths they are learning about.

Key vocabulary

“plus”

Share the key vocabulary (star words) in every lesson and consistently use throughout

‘Full’ sentence expectations

HOWZAT?!!

Can you say that in a full sentence, please?

To make ten, I need to partition __ into __ and __.The number bond I am using is…

Developing sentence structures

Two cubes and one more

is what?

Three.Talking about early number


is …

Two cubes and one more is three cubes.


is three.

Two cubes and one more is three cubes.

Varying sentence structuresTwo

One greater than two is three.

One less two is one.

Two is one less than three and one greater than one.

Three is one greater than two.

The number that is one less than three

and one greater than one is two.

One greater than two is three.

Talk TasksEvery lesson has a purposeful task where the focus is on talking and using mathematical language.

Developing verbal reasoning in Reception

Naming Describing Re-telling Justifying

The focus is on the whole

object

The focus is on one part of

the object

The focus is on the whole

context

The focus is on

relationships between

objects and contexts

Blank, Rose & Berlin (1978)

Shape

I used a circle because it is curved. A wheel is curved like a cylinder so that it can roll.

I have used three circles for the wheels in the picture.

The circle has a curved side.

This is a circle.

Justifying

Re-telling

Describing

Naming

Is equal to / makes / equals?

7 + 4 = 11

35 + 9 = 35 + 10 – 1

14 + 27 = 26 + ___

14 27

How can you solve this?

“there is an association between the quality and frequency of mathematical language used by carers, parents and teachers as they interact with young children, and children’s development in important aspects of mathematics.”

Dunphy et al (2014)

The Big PicturesChildren’s songs and rhymes

• practise counting skills

• recall information

• develop a richer vocabulary

• look for patterns and extend sequences

• solve problems

Jenny Goddard

NCETM 2009Primary and Early Years magazine Issue 6

Big Pictures• Opportunities to

relate maths to ‘real’ life applications

• Opportunities for pupils to make connections

• Opportunities to promote and develop pupil reasoning

Plenary

• Mathematics Mastery key principles

–Conceptual understanding

–Mathematical thinking

Session Two

New Learning

Mathematical

problem solving


Mathematical

thinking




Conceptual understandingPupils deepen their understanding by representing concepts using objects and pictures and, more abstractly, with words and symbols. They make connections between different representations and consider what different representations stress and ignore.

14Abstract representations

• Symbolic stage

• Numbers, letters and symbols

• Most formal stage of mathematical understanding

• Efficient way of representing the maths

Four more than ten

XIV

fourteen

10 + 4

Concrete representations

Pictorial representations

8 10 14

+2 +4

• Images of actual concrete manipulatives

• Tallies, dots, circles• Drawing• Jottings• Bar models• Number lines (mixture of

pictorial and abstract)

14

11 3

Multiple representations

Concrete

The DOING

Abstract

The SYMBOLIC

Pictorial

The SEEING

Demonstrating depth

1

/'wʌn/

one

‘Pupils who use concrete materials develop a more precise and more

comprehensive mental representation, they often show

more motivation and on task behaviours, understand

mathematical ideas and better apply these to life situations.’

(Anstrom, 2006)

Develop Learning

Mathematical

problem solving


Mathematical

thinking




Mathematical thinking Pupils deepen their understanding by giving an example, by sorting or comparing, or by looking for patterns and rules in the representations they are exploring problems with.

Mathematical Thinking

We believe that pupils should:

• Explore, wonder, question and conjecture

• Compare, classify, sort

• Experiment, play with possibilities, modify an aspect and see what happens

• Make theories and predictions and act purposefully to see what happens, generalise.

“Mathematics can be terrific fun; knowing that you can enjoy it is psychologically and intellectually empowering.” (Watson, 2006)

Arithmagons

1 2 3

4 5 6

7 8 9

Choose a different number for eachWrite the sum inMake at least three examples

Complete these:

7 8

9

4 8

6

11 7

12

Compare these:

7 8

9

4 8

6

11 7

12

3 3

4 5 1 53

8 4

Can you complete this one?

2 3

4

Why doesn’t it work?

2 3

4

Convince yourself. Convince your partner.

Explore odd and even

• What happens if all the numbers in are even?

• What happens if all the numbers in are odd?

• Can all the numbers in be odd?

• Can you have exactly two of as even numbers?

Generalise & explain

Conjectures:It is impossible to have all odd numbers in

It is impossible to have exactly two even numbers in

True? False? Why?

• Unpick the task that you just did.

• What mathematical thinking was promoted and how?

• How will you encourage mathematical thinking in your classroom/school?

Independent Task

Big Pictures

How could you use the Big Picture to encourage pupils to develop mathematical thinking?

What questions and prompts might you give?

Plenary

Growthmindset

“Teaching is for learning; learning is for understanding; understanding is for reasoning and applying and, ultimately problem solving.”Ministry of Education, Singapore (2012), p.21

Mathematica

l problem

solving

Mathematic

al thinking


Conceptual

understanding




• Programme of Study and curriculum structure

• Lesson structure

Session Three

• Cumulative curriculum

• Opportunities to practise and consolidate in future units

• Structure of the curriculum must be followed

• Each year group has approximately 30 weeks of planned lessons

Mathematics Mastery Curriculum

Yearly Planner

Unit resources

Mathematics Mastery curriculum and the EYFS

Embedding learning What children can do consistently, independently and in a range of situations.

Enabling environment An early years provision planned to enable each pupil to demonstrate their learning and development fully.An environment that truly enables successful learning for all.

Challenge and differentiation Challenge through rich problems which require pupils to initiate ideas and activitiesOpportunities to practise and consolidate before moving on.

Three models for implementation

The Child-initiated model

(CI)

The Focus group model

(FG)

The Six-part model(SP)

Child-initiated model

Do Now

Child-initiated

play

New Learning

Develop Learning

Talk Taskor

Let’s Explore

Child-initiated

play

Child-initiated

play

Child-initiated

playChild-

initiated play

a

s

a

MODEL Talk Task

Address misconceptions

Focus group model

Do Now

Child-initiated

play

New Learning

Develop Learning

Talk Taskor

Let’s Explore

Child-initiated

play

Child-initiated

playChild-

initiated play

Focus group Independent

Task Plenary

MODEL Talk Task


Lesson Structure – Six parts

Do Now

PlenaryIndependent Task

MODEL Talk Task

New Learning


Develop Learning

Talk Taskor

Let’s Explore

MODEL TaskAddress

misconceptions

Six-part lesson


Do Now:• Independent work for pupils

to complete with ease, without too much instruction from the teacher.

• Consolidates previous learning.

Fluency First:• Teacher led• May consolidate or introduce

New Learning• An opportunity to rehearse,

reinforce and consolidate mental calculation skills

or

Do Now


New Learning

Develop Learning

Talk Taskor

Let’s Explore


New Learning:• Everyone says the most important key vocabulary.• Ideally, the teacher and children model using

concrete manipulatives.• Everyone uses words and symbols accurately.• Everyone is ready to answer questions in full

sentences.• Connections are made.• The Talk Task is modelled.• Misconceptions are anticipated and incorporated.

Do Now


New Learning

Develop Learning

Talk Taskor

Let’s Explore

Transitions

• Quick recall

• No time wasted

• Keep key fundamentals on the boil

• Smooth and speedy transition between the different parts of the lesson

• An opportunity to refocus learning behaviours


Talk Task:• Opportunity to use

mathematical language with given sentence structures

Let’s Explore:• Opportunity for pupils to

apply the skills they have learnt, discussing and reasoning mathematically. E.g. In pairs, pupils discuss which number is the odd one out using the key vocabulary.

or

Do Now


New Learning

Develop Learning

Talk Taskor

Let’s Explore


Develop Learning:• References are made to previously learnt

models, representations, skills and concepts.

• Everyone is ready to answer questions in full sentences.

• Connections are made. • Everyone uses words and symbols

accurately.• Misconceptions are anticipated and

incorporated.

Do Now


New Learning

Develop Learning

Talk Taskor

Let’s Explore


Independent Task:• Everyone is engaged in completing the

task, 100% of the time.• Everyone has access to appropriate

concrete manipulatives.• Everyone is engaged in learning about the

same mathematical concept or skill, with an appropriate amount of scaffolding.

• There is an emphasis on understanding and developing fluency, rather than rushing to ‘finish’ the work.

Do Now


New Learning

Develop Learning

Talk Taskor

Let’s Explore


Plenary:Celebrating effort and successThe plenary should always include a celebration of success and reaffirmation that success comes from effort.

Do Now


New Learning

Develop Learning

Talk Taskor

Let’s Explore

Considerations for each model

• Refer to the planning materials

• Plan the continuous provision to provide opportunities for pupils to apply learning in play

• Have maths toolkitsin different areas

• Consider the role of the adult to ensure purposefulinteraction


• Select a task or devise your own task.

• Ensure the keylearning from the week is incorporated

• Vary the days and the focus groups


• Be flexible with the timings for each segment

• Follow the children’s learning with the keylearning for the lesson in mind

• Be confident to usethe resources that you have available

Child-initiated model Focus Group model 6-part lesson model

• Differentiation

• Maths Meetings

• Assessment

• Toolkit

Session Four

• Without looking, choose either easy, medium or hard and solve the problem on the other side.

• Reflect – How did you feel when the task was set? How did you feel during the task and after?

• How might pupils in your class have responded to a task presented like this?

Do Now

Which fraction task will you pick??

EASY MEDIUM HARD

• What is differentiation?

• What does it currently look like in your classroom?

• Is there anything you would like to change about the way you differentiate?

Discussion

• Addressing learner variance in the classroom (Thomlinson et al, 2003)

• The level of the content is commonly used to guide planned differentiation.

Main task:

“Addition and subtraction of 2-digit numbers”

Support task:

“Adding and subtracting

numbers to 10”

Extension task:

“Solve practical number problems

adding or subtracting 2-digit numbers.

Differentiation

Adapting and differentiating

Next Steps for Depth

Questioning

Differentiation through scaffolds and constraints

Scaffolding

ConstraintsConstraints

Next Steps for Depth

• End of half term assessments

• End of year assessments (Y1, Y3, Y4, Y5)

• Key Constructs

Assessment

The key purpose is to develop fluency and confidence with the skills and understanding for the year group.

The emphasis should be on a small selection of routines that are used every day so that they are:

• building over time to develop fluency, mastery and number sense

• based on oral work and conversation• fun and enjoyable, linking maths to real life• providing variety in the practice of skills• use to pre-teach concepts

Maths Meetings

Toolkit

What to expect from us:

• Dedicated Development Lead

• Aim to support the implementation of MM

• Two half-day visits across the school year

– Pre-visit questionnaire– all teachers teaching MM asked to respond

– Visits may involve action planning with MMSL and teacher(s); co-planning; lesson observation; learning walk

• Collaborative workshops provide the opportunity to meet other MM teachers in local schools

Hart & Risley (1995) Meaningful differences in the everyday experience of young American children. Baltimore, MD: Paul H Brookes

Askew, M., Brown, M., Rhodes, V. Johnson, D., William, D. (1997) Effective Teachers of Numeracy: Final Report.

Kings College: London

Barmby, P., Harries, T., & Higgins, S. (1999) Teaching for Understanding / Understanding for Teaching in Issues in

Teaching Numeracy in Primary Schools (2nd Edition) edited by Thompson, I. (2010)

Blank M, Rose SA, Berlin LJ (1978) The language for learning: the pre-school years. New York; Grune and

Stratton Inc

Nunes, T., Bryant, P., Sylva, K. & Barros, R., (2009) Development of Maths Capabilities and Confidence in Primary

School. DCSF

Drury, H. (2014) Mastering Mathematics. Oxford University Press

Haylock, D. (2010) Mathematics Explained for Primary teachers (4th Edition). Sage.

Ministry of Education, Singapore (2012) Mathematics Syllabus Secondary One to Four

References

Documents

Mathematics Mastery in Reception - Pimlico Primary · •To understand the key principles of the Mathematics Mastery approach ... Two cubes and one more ... Challenge and differentiation