1 Mathematics education in the early yearsSue Gifford University of Roehampton

2 What are the issues? The curriculum content pedagogyassessment: baseline & EYFS profile dislocation between EYFS & primary The workforce Need for: professional development centralised guidance diverse settings, eg playgroups, childminders

3 What research tells us What predicts maths success?in the early years: parents’ education and home learning a balance of adult and child-led activities early number sense at primary school: mathematical reasoning a growth mindset

4 Parents • More information directly to parents on how to develop their children’s maths skills. • Early years settings to work with parents to support children’s development. • A national ‘positive about maths’ drive to draw in parents as well as early years staff.

5 Child-led activities

6 Images from the Froebel block play projectGura, P. (1992) Exploring learning: young children and blockplay London: Paul Chapman Publishing

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8 Adult initiated: Faster than Usain Bolt Mastery: generalisingClass teacher: Georgina Harris Marlborough Primary School, Falmouth. Researcher: Dr Helen Williams

9 Pre-school number knowledge helps later achievement. (TIMSS)Pre- schools that helped children to understand early number concepts led to better outcomes in mathematics at (EPPSE)

10 APPG: Number Sense should be a Prime Area in the EYFSThe government should increase the focus of maths and numeracy in the early years curriculum, by including number sense as a prime area of development – alongside: communication and language physical development personal, social and emotional development.

11 The Numbers Goal Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing. (DfE, 2012) New simplified and reduced Numbers Goal. Taking items from the previous higher level and making them what is now expected (prev: count up and num facts) Government aims: to raise achievement by providing a good foundation for mathematics and literacy Counting on& back added by Tickell- less than half Aussie children counted on at 5, even when taught by specially trained teachers 21% NZ 6 yr olds counted on and back Sharing OK for counting, children recognise doubles by symmetry, but no evidence they understanding doubling and halving numbers

12 Children need to meet the Early Learning Goals to achieve a Good Level of DevelopmentIf reception children do not achieve this, it can affect their teachers’ pay and careers.

13 Dislocation between reception year and Y1There is confusion about expectations among teachers and heads leading to inconsistency in practice and approach… potentially isolating reception teachers from their other colleagues…critical impact on pupils. ‘Early Learning Goal 11: Numbers’ focuses on a counting based approach to calculation. This is in contrast to research suggesting knowledge of composition of number is the critical factor in successful calculation and future attainment in maths, and that counting is a strategy relied on disproportionally by low attainers. It also conflicts with the most effective teaching of maths in key stage 1 where pupils are taught subtraction by complementary addition (being able to partition numbers), leading teachers to have to teach pupils to avoid previously learnt approaches. Teaching Schools Council: Effective primary teaching practice 2016 p44

14 Number sense a feeling for numbersCounting -sequence & synchronisity Cardinality - the eightness of 8 Comparison - relative size Composition- numbers hidden inside numbers

15 Developing counting and cardinality takes a long timenumber sequence forwards and back - crossing boundaries 29/30 one number one object – rhythm & synchronisity keeping track – being systematic cardinal principle - last number is ‘how many’ Krystel

16 Key assessment: Counting out a number from a larger groupCan you get me 9? Young-Loveridge (1991) The cardinal principle - last number you say is the number of the group Counting out from a larger group Demonstrate with jar of nuggets

17 Finger numbers

18 Subitising Subitising: being able to see how many there are without counting

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20 How do you know how many there are?What numbers do you see?

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22 How do you develop subitising?Do it huge – and outdoors!

23 Understanding number symbolsHow do we know that children see numerals as number concepts?

24 When do children see everyday numerals with cardinal meanings?(referring to a number of things)

25 When do children see everyday numerals with cardinal meanings?(referring to a number of things)

26 Numerals referring to numbers of objects are rare!

27 The tricky teens

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30 Placing numbers on an empty number line is a reliable predictor of difficulties. Relative value of numbers- people tend to stretch and bunch numbers on a line for a range they do not yet understand ie this is a common indicator of a lack of understanding, not necessarily a disability, but this is an extreme example!

31 track games (Laski & Siegler 2014) A rich mental model for a mental number line?Sinclair & Coles (2015) ‘children attending to and becoming engaged by symbol-symbol relations, sequencing and ordering, i.e., the more relational and ordinal aspects of number. ..we see evidence of the mathematical thinking and playfulness that working more symbolically with number can occasion. Batchelor et al: some children focus on the counting system Sarama and Clements (2009:93) conclude that connections between the numerical magnitudes and all the visual-spatial, kinaesthetic, auditory and temporal cues in Siegler’s games (ie all magnitudes increase together: numerals, distance moved, number of moves, number of counting words etc.) may provide a rich mental model for a mental number line. Davydov ref Schmittau, & Morris (2004) ANS – approximate mental number line

32 Track games Ramani et al 2012

33 Number sense Estimation How many’s in the jar?

34 How do young children learn number sense?routines – snacktime, tidying up games –tracks, skittles, hidden numbers number rhymes & books – fingers & symbols problem solving eg sharing playfulness- eg making mistakes ‘sustained shared thinking’ with adults NRICH REPEY Siraj Blatchford et al (2012)

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36 Predictors of later achievementcounting out a number from a group subitising numeral meanings relative number size predicting adding one / taking one number combinations finger gnosis! pattern awareness spontaneous focusing on numerosity

37 Awareness of mathematical pattern and structureMulligan & Michelmore (2009) Children drawing from memory Sarama &Clements 2009 : Children need to make sense of mathematical structures. Suggest they need to say what they see and make such structures for themselves.

38 Developing awareness of mathematical pattern and structurePapic, M., Mulligan, J. & Mitchelmore, M.(2011) Journal for Research in Mathematics Education 42(3) ) Assessing the development of preschoolers’ mathematical patterning

39 Teaching pattern awarenesscopy draw /when hidden continue create own /make with other materials repair explain

40 Patterns Erikson early mathematics website

41 Mastery? mathematical reasoning

42 Developing mastery The Characteristics of Effective Mathematical LearningReception teachers must report on these- how do they do this for maths?

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45 Sharing biscuits Davenall, J. (2015)

46 Making sense: diagramatisingSharing biscuits Davenall ref Making sense: diagramatising

47 Fox and chickens storiesDavenall, J. (2015)

48 Moving between representationsChildren’s own representations help them make sense and give clues to their understanding of notation. Playing with what they know Davenall (2015)

49 Early algebraization the route to Mastery ?pattern and functions equivalence and equations generalisation Cooper & Warren (2011) cited by Dooley et al 2015

50 Mastery: generalisingFaster than Usain Bolt Mastery: generalising Class teacher: Georgina Harris Marlborough Primary School, Falmouth. Researcher: Dr Helen Williams

51 Generalising: The smaller the unit the more you need …

52 Workforce education All early years practitioners, both new entrants and the existing workforce, should be trained in children’s mathematical development. • The government should extend its Maths Hubs programme to include pre-schools. • The government must provide more guidance for practitioners on the use of effective approaches and resources.

53 Workforce diversity: child minders, pre-schools, children’s centres, nurseries, reception classesEarly Childhood Mathematics Group representatives: ACME Action for Children ATM/MA primary committee DfE Early Education National Numeracy NAMA NCETM NCB NDNA NRICH OfSTED PACEY PSLA TACTYC Universities of Oxford, Leicester, Roehampton Eastwood Children’s Centre, Primary schools: Netley, St John’s Angel Town, Ravenswood, Ridgeway

54 Workforce qualificationsLevel 3 EY practitioners: GCSE required If GCSE is normative, where do the bottom 30% work? Are functional skills appropriate for EY practitioners? Does ITE sufficiently cover early maths learning? Where do practitioners learn about early maths?

55 ACME recommendations review Numbers goal for EYFSgreater focus on mathematical thinking develop clear guidance: progression map of big ideas online support with exemplification develop and disseminate pedagogy prioritise professional development for EY staff: survey needs familiarise with learning trajectories engage with parents, carers and families

56 Foundation Years Mathematical Resources websiteTop Ten lists eg: websites professional books picture books number books number rhymes ideas for babies and toddlers

57 NCETM: Big Ideas for EY?

58 The way forward? Primary assessment consultation: implications for accountability. This will cover key issues, including the best starting point to measure the progress that children make in primary school, and the role and operation of teacher assessment. Whilst we take time to consult on assessment arrangements, the Early Years Foundation Stage Profile will remain in place for the 2017 to 2018 academic year. BEIS Green paper: improved pre-school education to reduce the divergence of achievement which opens up before school (p21) https://beisgovuk.citizenspace.com/strategy/industrial-strategy/supporting_documents/buildingourindustrialstrategygreenpaper.pdf? And?

59 References All Party Parliamentary Group Maths and numeracy in the early years Davenall, J. (2015) Developing Number Through Tidying Up Emerson, J., and P. Babtie The dyscalculia assessment: Emerson House Mathematics London: Continuum. Effective Pre-School, Primary and Secondary Education project (EPPSE) 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. Gifford, S. (2005) Teaching mathematics to 3 – 5s: developing learning in the Foundation Stage Maidenhead: Open University Press Gifford, S. (2014) ‘A good foundation for number learning for five year olds: an evaluation of the English Early Learning ‘Numbers’ Goal in the light of research’. Research in Mathematics Education 16 (3) Griffiths, R., Back,J. & Gifford, S. (2016) Making numbers: using manipulatives to teach arithmetic. Oxford: Oxford University Press Laski,E.V. & Siegler, R.S.(2014) Learning from number board games: you learn what you encode Developmental Psychology 50 (3) Office for Standards in Education. (2013). Mathematics in school inspection January 2013 information pack for training https://www.whatdotheyknow.com/request/additional_guidance_for_inspecto Office for Standards in Education. (2015) Teaching and play in the early years: a balancing act? https://www.gov.uk/government/publications/teaching-and-play-in-the-early-years-a-balancing-act Rittle-Johnson,B., Fyfe,E.R., Hofer, K.G., Farran, D.C. (2016) Early math trajectories: low income children’s trajectory mathematics knowledge from ages 4 to 11, Child Development DOI: /cdev Siraj-Blatchford, I., Sylva, K., Muttock, S., Gilden, R. and Bell, D. (2002) Researching Effective Pedagogy in the Early Years, (REPEY) Research Report 356. London: Department of Education and Skills. Teaching Schools Council (2016) Effective primary teaching practice Trundley, R. (2008). The value of two. Mathematics Teaching, 211, 17–21 Young-Loveridge, J. (1991). The development of children’s number concepts from ages five to nine. Hamilton: University of Waikato.