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 • a balance of adult and child-led activities • early number sense at primary school: • mathematical reasoning • a growth mindset • an autumn birthday
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)
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 overall school achievement and their success in entering the workforce. (Early Intervention Foundation 2018)
Spatial reasoning predicts maths 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 Erikson Early Math Collaborative https://www.tes.com/news/clumsy-children-need- extra-help-three-rs
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)
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
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
Number sense Counting sequence & synchronisity Cardinality the eightness of 8 Comparison relative size Composition numbers made up of other numbers
Counting: It takes 4 years to learn to count to 20 So children need a lot of counting opportunities!
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’
Counting What helps Anna count? http://prek-math-te.stanford.edu/patterns- algebra/patterns-counting-words
Number patterns
Counting and cardinality
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
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
Cardinality: ‘ how manyness ’ the number of things represented by the number 5
All at once finger numbers
Subitising
How do you develop subitising? Do it huge – and outdoors!
Hiding game: subitising https://www.learningtrajectories.org/activity/fantastic-five-tricky-two
Understanding number symbols How do we know that children read numerals as number concepts?
When do children see everyday numerals with cardinal meanings? (referring to a number of things)
Numerals referring to numbers of objects are rare!
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?
Numerals and cardinal values
The tricky teens 15 50 51
Comparison: relative size • comparing two numbers • estimating ‘ about how many? ’ • predicting adding /taking 1
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)
Key to number sense ‘ Five is a number which is medium small’ Children need to link: • counting • cardinality - the size of numbers
Comparison Griffiths, Back & Gifford (2016) Making numbers
The voting station Nrich 4 more people to vote: what might happen?
track games (Laski & Siegler 2014) A rich mental model for a mental number line?
track games- counting on A rich mental model for a mental number line? (Laski & Siegler 2014)
Track games
A handful: how many have you got? • Estimate • Count and label • Order
The Estimation Station https://nrich.maths.org/content/id/13339/Estimation%20Station.pdf
Estimating herbs You can pick 2 out of every 100 I picked 4 because I thought there were about 200!
Linking counting and number size: The three-plus-one-ness of four (Trundley 2008 NRICH)
Janine Davenall
Erikson early math : making a staircase pattern from a story
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
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
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
Number games collecting games target games track games
How might you record scores of outdoor target games?
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.
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?
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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