Developing pattern awareness in the early

years

Sue Gifford

From last time:Develop a story to promote problem

solving

The doorbell rang Pat Hutchins

The great pet sale Mike Inkpen

Pirates’ gold NRICH

Mouse Counts Ellen Stoll Walsh

9 ducks nine Sarah Hayes

5 friends counting OxfordOwl web animation

Caterpillar sandwiches, foxes and chicks.. Make up your own?

How did you get on?

Pattern around us

How do you know

it is a pattern?

What is pattern?Any predictable regularity, usually involving numerical, spatial or logical relationships.. In early childhood ..Repeating patterns, spatial patterns, and growing patternsThe way the pattern is organised is its structure

Mulligan & Mitchelmore (2009: 34)

The power of mathematics lies in relations and transformations which give rise to patterns and generalisations. Abstracting patterns is the basis of structural knowledge, the goal of mathematics learning

(Warren 2005 cited by M&M)

Children and patterns

Froebel blockplay project (Gura, 1992)

Eastwood Forest school

Shape space and measures: ELG

Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems.

They recognise, create and describe patterns.

They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

National curriculum Y1 Number & place value: notes and guidance (non–statutory) They recognise and create repeating patterns with objects and with shapes. .. counting in twos, fives and tens from different multiples to develop their recognition of patterns in the number system (for example, odd and even numbers)

Y2Number & place value: notes and guidance (non–statutory)

As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations.

Geometry: Statutory requirements ..order and arrange combinations of mathematical objects in patterns and sequences

notes and guidance (non–statutory)

..work with patterns of shapes, including those in different orientations.

Pilot Framework ELG Number:

Children at the expected level of development will:

• Have an understanding of number to 10, linking names of numbers, numerals, their value, and their position in the counting order;

• Subitise (recognise quantities without counting) up to 5;

• Automatically recall number bonds for numbers 0-5 and for 10, including corresponding partitioning facts.

Pilot Framework: ELG Numerical Patterns

Children at the expected level of development will:

• Automatically recall double facts up to 5+5;

• Compare sets of objects up to 10 in different

contexts, considering size and difference;

• Explore patterns of numbers within numbers

up to 10, including evens and odds

Numerical patterns?

Different kinds of patterns in the early years curriculum

• Regular arrangements eg dot patterns

• Repeating patterns: ABC, ABC,..

• Growing patterns: staircases; 2,4,6,8

• Reflecting patterns:

Recognising patterns

Why is pattern important?

• Pattern awareness predicts later mathematics achievementRittle-Johnson et al (2016)

• Students who recognise the structure of mathematical processes and representations acquire deep conceptual understanding.

• High achievers are good at visualising, involving recognition of pattern and structure.

• Low achievers produce poorly organised pictorial and iconic representations. High achievers use abstract notations with well–developed structures

Mulligan & Mitchelmore (2009: 33)

Awareness of Mathematical Pattern and Structure

Mulligan et al

PASA Pattern and Structure AssessmentMulligan, J., Mitchelmore, M., Stephanou, A. (2015)

Pattern Project participants

• Chesterton Primary: John Stanghon (Libby Meyer, Isobel Henderson)

• Christ Church Primary: Karen Moses, Katie, Ruth James• Eastwood Nursery School: Mary Edgar, Sarah

Samuel,(Karen Pearson)• Ravenstone Primary: Jack Davidson, Simon Lewis• Riversdale Primary: Helen Barnard, Tracey Tattersall

With support from:Catherine Gibson, Wandsworth LA

Dotty triangle

Look at this pattern -can you copy it here?

If successful with 6 dots, point to the space below the last line of dots the child has drawn :What do you think comes next? Draw it here.

(Then ask the child to write their name.)

Most common response:dotty triangle- ish

Dots

Number

Shape

Focused on one element of the pattern

Dots and the number

Dots and the shape

Dots drawn in rows

Two elements

Three dots on eachside of the triangle

6 dots in rows

Dots arranged in rows in atriangular shape

Three elements

Extending the pattern:

What do you think comes next?

Four elements

Dots, number, shape and spacing/rows

One child’s thinking

10 Dotty triangle

Numberblocks:Stepsquad 15

Ravenstone nursery

Huge and Outdoors

Ravenstone nursery

Regular arrangements: Subitisingnumber talks

https://joelea.github.io/subitiser/

Teaching Channel: Quick

Images

www.teachingchannel.org/videos/visualizing-number-combinations

Creating Patterns for 10

(animation) https://www.oxfordowl.co.uk/for-school/pd-books/making-numbersGriffiths, Back & Gifford (2016) Making numbers

Repeating patterns: describing and extending

Which of these are harder and why?

Repeating patterns

–Trains–Necklaces–Towers–Stickers –Stamps–Found objects

Action patterns

Activity progression

• continue

• copy

• edit- change in one way

• errors- identify and fix

• generalise to other contexts, modes

• symbolise: ABB, own symbols

Further challenges:• draw from memory

• identify screened part

Pattern structures

Progression:

AB, and beyond

ABC, ABCD, ABB, ABBC …

Do children identify the unit of repeat?

What is your pattern?

What is your pattern unit?

Pattern novices: do they..

• continue third unit?

• edit by changing objects or colours?

• identify errors: extras, swops, missing items?

• fix errors?

Pattern experts: generalising

Sean made an ABBC pattern with bears.

Simon introduced the terminology of ‘ABBC pattern’.

Sean: So it could be dog, cat, cat, sheep?

Ravenstone reception

Pattern experts:

symbolising

Other contexts: shoes, people..

How do we develop young children’s pattern awareness in the nursery and

reception?

Whole class and independent learning:Now I’ve got into a mindset of just introduce and show and just put it out there and see what happens.

..Allowing them to explore and get things wrong.. observe what they are doing, not just intervene, listen to their language

‘Co-worker working’

.. And they do enjoy challenging each other,.. because they can see if somebody else has created a pattern, or if there’s a mistake or if there’s something wrong, they can see that together.

..And its not just maths, its language and its PSED skills, because of the social skills that they have to have.

Contexts for patterns: Forest school

Chesterton reception

Eastwood Nursery

Creating pattern rules

.. she’s been challenging her teacher with patterns. And its a way of communicating with

her.

Eastwood Nursery Chesterton reception

What is my pattern?

Chesterton reception

What is Veronica’s pattern?

Chesterton reception

Moving from linear to continuous patterns

• Linear patterns

• circular patterns

• border patterns:

- turning corners

- fixed number of spaces

Activity

• Using the materials at your table make a circular repeating pattern around a plate

• What might a child learn?

• What questions might you ask?

• Make a border pattern for 12 or 14

White, white, white, 3 whites…Yellow, blue and start over and over.

First attempt at bringing the repeated pattern around the shape. R needed a lot of support to work out how to continue her pattern in a different direction

D worked with his friends to continue the pattern. They didn’t keep all of the colours close to the shape however, preferring to ‘make the pattern fit’.Once completed, D commented:‘It’s not fair because we haven’t made the pattern fit properly – look, we’ve left lots of spaces.’ He then set about fixing the problem which meant that his pattern would not ‘work’. D: We need to try a different pattern, ABC doesn’t work. We can try AB first because that’s 2 and it might work better.’

B starts to change the AB pattern round the square into an AABB pattern because:‘I want to see if an AABB pattern will fit around the square, AB did so 2 works but I don’t know about 4 yet.’ He checks as he goes and lifts the shape at the end. ‘It does work – look! AABB goes on and on all the way round.’

The girls were investigating all the different formations of patterns they could think of. ‘We won’t do AB because that’s too easy. We can try 3 first.’ The girls found the magnetic letters and decided to use these to see if they could make the pattern work.‘It’s an ABC pattern, we tried it and we writed down that it works – we even did ticks and smiley faces!’ The girls then realised that they had left spaces at the corners and added another unit of repeat to make the pattern complete.

Whole class carpet session. Prior to the children’s arrival, the pattern was laid out for the children to discuss and identify.

D identified an AABB pattern and removed the unit of repeat from the pattern to show the children.

D was challenged to find another unit of repeat and with support from the teacher found that AABB can also be ABBA

Misconceptions still occur – A separated ABA and the other children helped him to see that it wouldn’t work.‘Look, there’s 2 purple ones beside each other so they are the same – you’ve just got 1.’ The child came and demonstrated.

The picture was presented as a pattern to the children and they were asked to identify the unit of repeat.

All said AABBC - identified shoe, shoe (AA), glove, glove (BB), duck (C).

After discussion – they agreed it could be ABC as it was 1 pair of shoes (A), 1 pair of gloves (B) and 1 duck (C).

T brought up ABCDE suggestion – each shoe is different (AB), the hands are different (CD) and then the duck (E). The children would not accept this as an answer.

Children are encouraged to think for themselves.A didn’t want to use the shapes but also didn’t want do a ‘boring’ straight pattern. She found the pencils and chose 3 colours, then laid them out before her.‘It’s an ABCC pattern – see. The red one is just 1 so it’s on its own, so is the yellow one – that’s the B, but the orange is 2 so they have to be beside each other not in a line. Then it’s A, B, then CC and then it happens again and again!

The children worked together to create a pattern using AABC and then separated the units of repeat out so everyone could see.

‘There’s 3 units of repeat and there’s 3 of us, we can put our names on 1 each!’

Will an ABB pattern work?

What about ABA? ABBC?Vote!Why? Why not?

AABBC pattern, 12 spaces:“So its 5 and 5 and 2 more, so it’s not enough and I need 3 more to make it”.

AABB works: ‘Because it’s four, three times’.

Number learningunitising and counting units

How many ‘blue-red-greens’ are there?

Action patterns in the nursery

Eastwood Nursery

Mary Baratta-Lorton: Maths Their Way(1976) London: Addison-Wesley

Activity: follow these!Make up your own and record

Pattern Expert: Recording repeating action patterns

What is the action pattern?

Make up your own action patternand record it.

See if your friend can read your pattern

Musical instrument pattern

Sound patterns?

Other pattern possibilities

• Visual timetable, calendars

• Songs and rhymes

• Reflective patterns

• Mirrors

• Pattern blocks

• Construction

• Growing patterns

• Stories?

Action songs

The shopping basket

John Burningham

Making a staircase pattern from a storyErikson early math: http://earlymath.erikson.edu/

Patterns Erikson early mathematics website

http://earlymath.erikson.edu/big-ideas/patterns-are-sequences-repeating-or-growing-governed-by-a-rule-they-exist-both-in-the-world-and-in-mathematics-pre-elementary-1st-grade-math-activities/

Child31

Key points in teaching pattern

Copying and comparing patterns: noticing

What is the same and what is different?

Identifying repeated relationships

Unit of repeat: underpins measuring (repeated units) and multiplication (counting groups)

Abstracting and generalising: same structure, different context

Early algebraic thinking

• noticing mathematical features

• identifying the relationship between elements

• observing regularities

Blanton et al. (2015) cited by Kieran, Pang, Schifter & Ng (2016)

For next time

• Please send examples of pattern activities and children’s responses.

• (and anything else!)

• Make sure you have permissions for pictures.

• All published contributions will be gratefully acknowledged with your name and school.

Thank you!

The Characteristics of Effective Learning

• How to provide mathematical opportunities for these?

• Develop some problem solving opportunities with shape, space and measures and report on these next time.

ReferencesGifford, S. (2017) Developing pattern awareness with young childhttps://nrich.maths.org/13362

Mulligan, J. & Mitchelmore,M. (2009) Awareness of Pattern and Structure in Early Mathematical Development Mathematics Education Research Journal 21(2) 33-49

Papic, M., Mulligan, J., & Mitchelmore, M. (2011) Assessing the development of pre-schoolers’mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237-268.

Rittle-Johnson, B., Fyfe, E.R., Hofer, K.G., & Farran, D.C. (2017). Early Math Trajectories: Low-Income Children’s Mathematics Knowledge From Ages 4 to 11, Child Development, 88(5), 1727-1742.

Websites

https://joelea.github.io/subitiser

https://www.oxfordowl.co.uk/for-school/pd-books/making-numbers

https://www.ncetm.org.uk/resources/52504

www.teachingchannel.org/videos/visualizing-number-combinations

Erikson early math collaborative: Patternhttps://earlymath.erikson.edu/foundational-concepts/pattern/

Nrich activity: What is your pattern?https://nrich.maths.org/content/id/13250/Pattern%20Making.pdf