The case for shape and

space

Sue Gifford

University of Roehampton

Pattern awarenessThere is emerging evidence to suggest that preschool children’s patterning ability – that is, the ability to recognise predictable patterns in stimuli – also supports numerical awareness.

(EIF, 2018:140)

Spatial awarenessThere exists a distinct cognitive factor that could be called ‘spatial ability’ .. forming and manipulating visual-spatial mental images

Mix & Cheng (2012)

Improving spatial experiences prior to school entry is likely to increase children’s readiness for school.Optimizing spatial performance may be an underutilized route to improving mathematics achievement. (Verdine et al, 2017: 93,102)

Ball skills predict maths: ‘Interceptive timing’ Giles et al. (2018)

Awareness of mathematical pattern and structure

Teaching pattern awareness improves children’s number understanding

Some children focused on one element of the pattern

Dots

Number

Shape

Dotty triangles

Most common response:dotty triangle- ish

One child’s thinking

Different kinds of patterns

Repeating patterns: ABC, ABC,..

Regular arrangements eg dot patterns

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

Reflecting patterns: ABB C BBA

Repeating patterns predict maths

a range of resources Lucy Parish The Grange

fruit and forest 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 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

Pattern structures

Progression:

AB, and beyond

ABC, ABCD, AABB, ABB, ABBC …

Do children identify the unit of repeat?

What is your pattern?

What is your pattern unit?

Pattern novices Can they..

• continue third unit?

• edit by changing objects or colours?

• identify errors: extras, swops, missing items?

• fix errors?

What is my pattern?

Chesterton reception

What is the pattern?

Chesterton reception

Creating pattern rules

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

How do we develop young children’s pattern awareness?

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

.. 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.

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

Moving from linear to continuous patterns

• circular patterns

• border patterns:

- turning corners

- fixed number of spaces

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

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.

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: 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.’

Reception Christ Church Primary Surbiton

Karen Moses

‘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.’

Action patterns in the nursery

Recording action patterns

What is the action pattern?

Which of these fold to make a pyramid?

5 year olds’spatialreasoning predicts number line knowledge Gunderson et al (2012)

http://news.uchicago.edu/story/learning-about-spatial-relationships-boosts-understanding-numbers

A year-long intervention developed 4- 7year-olds’ spatial

thinking skills and improved number comparison

Hawes et al (2017)

Spatial language: hearing, describing,

directing

Rich spatial language has a general positive effect on spatial cognition, promoting children’s attention to spatial information and their ability to solve spatial problems Pruden et al (2011)

Shape, size and features of objects:circle, big, tall, curvy, edge

Spatial language:Position: in, on, underProximity: beside, betweenDirection: In front of, behind

Which picture goes best….?

Spatial thinking

• treasure hunts

• route finding

• robots

• picture books

• small world

models & maps

Where is it?

Which way?

Erikson Early Math Collaborative: Rosie’s Walk

Puzzles & perspectives: mental rotation Puzzle play predicts spatial skills

Levine et al (2012)

https://earlymath.erikson.edu/transforming-three-dimensional-shapes-with-child-36/

Patternblocks:how shapes fit together

Erikson Early Mathematics Collaborative: Composing shapes with child 12 https://earlymath.erikson.edu/composing-shapes-with-child-12-math-challenge-puzzles/

Picture books for spatial reasoning

Snapshots: What do you see?

Building a cube structure in your mind://www.kqed.org/mindshift/47269/why-spatial-reasoning-is-crucial-for-early-math-education

Block building correlates with high school maths

Wolfgang et al (2001)

https://earlymath.erikson.edu/the-math-in-blocks-preschool-educational-game/

Copying lego models

What might children find difficult?

Blockplay – development

2-3: stacking, assembling pieces

3-4: composite shapes eg arches; trial and error

4-5: plans composite shapes, towers of arches

5-6: complex with repeated units; stairs

6-8: units of units; ceilings From Clements & Sarama (2009)

• younger children building alongside older

• progressive challenges: a wall with an arch,

a box 4 blocks square

• making 3D models from 2D pictures

Key aspects

Shapes and properties:

combining and decomposing,

describing- shape puzzles

and construction

Location:

following and giving instructions,

remembering and finding,

creating routes-

treasure hunts, small world, outings

Visualising and representing:

predicting and solving problems,

making models, drawings and maps

Proposed Number ELG

Children at the expected level of development will:

• Have a deep understanding of number to 10, including the composition of each number;

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

• Automatically recall (without reference to rhymes, counting or other aides) number bondsup to 5 (including subtraction facts) and somenumber bonds to 10, including double facts.

Proposed Numerical Patterns ELG

Children at the expected level of development will:

• Count confidently beyond 20, recognising the pattern of the counting system;

• Compare sets of objects up to 10 in different contexts, considering size and difference;

• Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.

What is missing?

• Cardinal counting eg Give me 5• Understanding number symbols• Problem solving• Shape, space and measures• Patterning• Communicating mathematically

Consultation deadline 31st Janwww.education.gov.uk/consultations

ReferencesClements . D.H. & Sarama, J. (2009). Learning and teaching early math: the learning trajectories approach. Abingdon: Routledge

Davenall, J. (2015) Developing Number Through Tidying Up http://nrich.maths.org/11528

Early intervention Foundation (2018) Key competencies in early cognitive development: Things, people, numbers and words. Public Health England https://www.eif.org.uk/report/key-competencies-in-early-cognitive-development-things-people-numbers-and-words

Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293–304.

Giles, O.T., Shire, K.A., Hill, J.B., Mushtaq, F., Waterman, A., Holt, R.J., Culmer, P.R., Williams, J.H.G., Wilkie, R.M., & Mon-Williams, M. (2018) Hitting the target: mathematical attainment in children is related to interceptive-timing ability. Psychological Science.29(8) 1334–1345. (Link to Telegraph report: https://www.telegraph.co.uk/news/2018

Griffiths, R., Back, J. & Gifford, S. (2016) Making numbers: using manipulatives to teach arithmetic. Oxford University Press

Gunderson, E.A., Ramirez, G., Beilock, S.L. & Levine, S.C. (2012) the relation between spatial skill and early number knowledge: the role of the linear number line Developmental Psychology 8(5) 1229-1241

Gura, P. ( 1992) Exploring blockplay: The Froebel blockplay project. London: Paul Chapman.

Hawes, Z., Moss, J., Caswell, B., & Poliszczuk, D. (2015). Effects of mental rotation training on children’s spatial and mathematics performance: A randomized controlled study. Trends in Neuroscience & Education, 4, 60–68. doi:10.1016/ j.tine.2015.05.001

Laski,E.V. & Siegler, R.S.(2014) Learning from number board games: you learn what you encode Developmental Psychology 50 (3) 853-864

Levine, S.C., Ratliff, K.R., Huttenlocher, J. & Cannon, J. (2012) Early puzzle play: A predictor of preschoolers; spatial transformation skill Developmental Psychology, 48(2) 530-542,

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

Pruden, S.M., Levine, S.C. & Huttenlocher, J. (2011). Children’s spatial thinking: Does talk about the spatial world matter? Developmental Science, 14(6),1417-1430. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3372906/

Verdine, B.N., Golinkoff,R.M., Hirsh-Pasek, K, & Newcombe, N.S. (2017) “Links Between Spatial andMathematical Skills Across the Preschool Years” Monographs of the Society for Research in Child Development http://onlinelibrary.wiley.com/doi/10.1111/mono.v82.1/issuetoc

WeblinksDREME TE: Anna Counts

http://prek-math-te.stanford.edu/counting/anna-countsAubree: http://prek-math-te.stanford.edu/counting/additional-counting-videos

Erikson Early Mathematics collaborativehttps://earlymath.erikson.edu/?s=spatial+relationshipsPattern block puzzle:https://earlymath.erikson.edu/composing-shapes-with-child-12-math-challenge-puzzles/Rotating shapes:https://earlymath.erikson.edu/transforming-three-dimensional-shapes-with-child-36/Walk with Rosie: https://earlymath.erikson.edu/walk-with-rosie-math-game-education-and-classroom-ideas/Blockplay game:https://earlymath.erikson.edu/the-math-in-blocks-preschool-educational-game/

Learning Trajectories www.learningtrajectories.org

Mind shift: Visualising - Building a cube structure in your mind://www.kqed.org/mindshift/47269/why-spatial-reasoning-is-crucial-for-early-math-education

Nrich: Tidying up https://nrich.maths.org/13371

Number Talks http://ntimages.weebly.com/photos.html

Oxford Owl: Making Numbers https://www.oxfordowl.co.uk/for-school/pd-books/making-numbers

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

Youtube: sharing problem: https://www.youtube.com/watch?v=1zguAec3AaE