Developing mathematical pedagogy in the early years: Number sense - - PowerPoint PPT Presentation

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Developing mathematical pedagogy in the early years: Number sense - - PowerPoint PPT Presentation

Aug 30, 2022 241 likes •855 views

Developing mathematical pedagogy in the early years: Number sense Session 1: Games Sue Gifford S.Gifford@roehampton.ac.uk What predicts maths success? What research tells us in the early years: p arents education and home learning

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Developing mathematical pedagogy in the early years: Number sense Session 1: Games

Sue Gifford S.Gifford@roehampton.ac.uk

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What predicts maths success?

What research tells us 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
  • an autumn birthday
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What research tells us: How to produce children with maths difficulties

Anxiety blocks working memory space

  • acceleration rather than understanding
  • anxious teachers and parents create anxiety

Fixed mindsets

  • ‘no good at maths’
  • ability grouping (Bradbury, NEU, 2017)
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Pre-school number knowledge

Children’s understanding of number during preschool is consistently associated with their mathematical achievement in primary and secondary school. Mathematical achievement in turn is consistently found to be the strongest predictor of children’s

  • verall school achievement and their success in

entering the workforce. (Early Intervention Foundation 2018)

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Spatial reasoning predicts maths

Erikson Early Math Collaborative Ball skills predict maths - Interceptive timing The neural circuitry used to build up a child’s understanding of their external environment, the way they orientate themselves spatially.. is also used to process numbers and more abstract thinking. Mon-Williams (2018) University of Leeds, Psychological Science https://www.tes.com/news/clumsy-children-need- extra-help-three-rs

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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)

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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.

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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

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Number sense: a feeling for numbers ‘Five is a number which is medium small’

Counting Cardinality Comparison Composition

NCETM: Main areas of early years maths

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Number sense

Counting sequence & synchronisity Cardinality the eightness of 8 Comparison relative size Composition numbers made up of

  • ther numbers
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Counting: It takes 4 years to learn to count to 20

So children need a lot of counting opportunities!

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Developing counting with cardinality takes a long time

  • number sequence
  • forwards and back
  • numbers to 20- takes 4 years
  • crossing boundaries 29/30
  • one number one object - rhythm & synchronisity
  • keeping track
  • being systematic
  • cardinal principle - last number is ‘how many’
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Counting

What helps Anna count?

http://prek-math-te.stanford.edu/patterns- algebra/patterns-counting-words

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Number patterns

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Counting and cardinality

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Key assessment: Counting out a number from a larger group

Can you get me 9?

Young-Loveridge (1991)

The cardinal principle - last number you say is the number of the group

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When do we use counting to find

‘How many’?

  • getting a number of things

‘Give me nine’

  • counting to check
  • counting to share and compare
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Cardinality: ‘how manyness’

the number of things represented by the number

5

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All at once finger numbers

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Subitising

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How do you develop subitising?

Do it huge – and

  • utdoors!
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Hiding game: subitising

https://www.learningtrajectories.org/activity/fantastic-five-tricky-two

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Understanding number symbols

How do we know that children read numerals as number concepts?

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

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Numerals referring to numbers of

  • bjects are rare!
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The cardinal meaning of numerals:

When do children see number symbols linked to numbers of things in school?

  • tidy up labels
  • recipes (with pictures)
  • number books and rhymes
  • numeral dice for games
  • scoring goals etc
  • others?
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Numerals and cardinal values

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The tricky teens

15 50 51

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Comparison: relative size

  • comparing two numbers
  • estimating ‘about how many?’
  • predicting adding /taking 1
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Comparing numbers Which is bigger 5 or 8?

‘Which is bigger, 5 or 4?’ 5/6 yrs:

High SES - 96% Low SES -18%

Gersten et al (2005)

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Key to number sense ‘Five is a number which is medium small’

Children need to link:

  • counting
  • cardinality - the size of numbers
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Comparison

Griffiths, Back & Gifford (2016) Making numbers

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The voting station Nrich

4 more people to vote: what might happen?

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track games (Laski & Siegler 2014)

A rich mental model for a mental number line?

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track games- counting on

A rich mental model for a mental number line?

(Laski & Siegler 2014)

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Track games

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A handful: how many have you got?

  • Estimate
  • Count and label
  • Order
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The Estimation Station

https://nrich.maths.org/content/id/13339/Estimation%20Station.pdf

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Estimating herbs

You can pick 2 out of every 100 I picked 4 because I thought there were about 200!

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Linking counting and number size: The three-plus-one-ness of four

(Trundley 2008 NRICH)

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Janine Davenall

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Erikson early math:

making a staircase pattern from a story

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Predictors of achievement

  • counting out a number from a group
  • subitising
  • numeral meanings
  • relative number size
  • predicting adding one / taking one
  • number combinations
  • finger gnosis!
  • pattern awareness
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Predictors of later achievement

  • counting out a number from a group
  • subitising
  • numeral meanings
  • relative number size
  • predicting adding one / taking one
  • number combinations
  • spontaneous focusing on numerosity

(SFON)

  • finger gnosis!
  • pattern awareness
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How do young children learn number sense?

  • routines –snack time, tidying up
  • games – collecting, tracks, targets
  • number rhymes and picture books
  • playfulness- eg making mistakes
  • problem solving eg sharing
  • ‘sustained shared thinking’(REPEY)

See NRICH for examples

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Number games

collecting games target games track games

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How might you record scores of

  • utdoor

target games?

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Ten Nice things

  • Each player has ten nice things.
  • Take it in turns to throw the dice.
  • Give that many things to the person on

your right.

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Ten Nice Things

Play with a dot dice, then a numeral dice. What might you observe and assess? Questioning and comments? How might you adapt and develop?

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For next time..

Try out and develop some games: – Collecting, Target, Track, Estimating ? – indoors and outdoors – scoring and recording Bring or send notes and photos! Check your school policy on photos first.

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References

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. 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) 219-233 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) 853-864 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: 10.1111/cdev.12662 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. www.327matters.org/Docs/RR356.pdf Trundley, R. (2008). The value of two. Mathematics Teaching, 211, 17–21 http://nrich.maths.org/11527 Young-Loveridge, J. (1991). The development of children’s number concepts from ages five to nine. Hamilton: University of Waikato.