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Junior Focus Group Developing Early Number Sense 8 March 2011

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Junior Focus Group Developing Early Number Sense 8 March 2011. Number Sense. Having a good intuition about numbers and their relationships. Develops gradually as a result of exploring numbers, visualising numbers, forming relationships Grows more complex as children learn more.

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slide1
Junior Focus Group

Developing Early Number Sense

8 March 2011

number sense
Number Sense
  • Having a good intuition about numbers and their relationships.
  • Develops gradually as a result of exploring numbers, visualising numbers, forming relationships
  • Grows more complex as children learn more.
key mathematical ideas
Key Mathematical Ideas

Early number sense

  • Counting tells how many are in a set. Ordinality leads to Cardinality
  • Numbers are related to each other through a variety of number relationships more than, less than, connection to ten
  • Number concepts are intimately tied to the world around us. Application to real settings marks the beginning of making mathematical sense of the world.

Van de Walle , Karp & Williams

Elementary & Middle School Mathematics: Teaching Developmentally

Allyn & Bacon 2010

early number sense develops when
Early number sense develops when

Children

  • make connections
  • Are able to instantly recognise patterns
  • See relationships related to more, less, after, before,
  • Are able to anchor numbers to five and ten
tens frames
Tens Frames
  • Crazy Mixed up Numbers – Read the activity page 46
  • A diagnostic task – give your children a blank piece of paper and ask them to draw a tens frame and show a number on it
  • In groups – discuss useful activities for tens frames for children at your level
subitizing
Subitizing
  • The ability to recognise and name small quantities without counting – links directly to cardinality
  • Use dot cards, dot plates, tens frames, slavonic abacus to provide opportunities every day for children to practise
dot plates
Dot Plates
  • Hold up a dot plate for 2-3 seconds, ask “How many? How did you see it?
  • Discuss other uses for dot plates – share and record.
  • More, less, same
counting principles
Counting Principles

Gelman and Gallistel (1978) argue there are five

basic counting principles:

  • One-to-one correspondence – each item is labeled with one number name
  • Stable order – ordinality – objects to be counted are ordered in the same sequence
  • Cardinality – the last number name tells you how many
  • Abstraction – objects of any kind can be counted
  • Order irrelevance – objects can be counted in any order provided that ordinality and one-to-one adhered to

Counting is a multifaceted skill – needs to be given time

and attention!

the counting sequence
The counting sequence
  • Learning the counting sequence is essential and will precede what counting one to one achieves.
  • It is a rote process that is needed to lighten mental load.
  • Knowing the word sequence pattern comes before understanding why the pattern occurs.
counting one to one
Counting one to one
  • A critical piece of understanding is that ordinality – position in a sequence – is intimately linked to cardinality – the number in a set.
  • In order to make the crucial linkage children need to be able to:
    • Say the number words in the right order starting at one
    • Point at objects one-by-one
    • Co-ordinate saying the correct words with identifying the objects one-by-one
  • Need to spend time on this, do not expect it will happen quickly
counting from ten to twenty
Counting from ten to twenty
  • In English the number words from ten to twenty have no regular pattern from a child’s point of view.
  • Learning to count from ten to twenty there is a heavier load:
    • Eleven bears no relationship to ten and one
    • Twelve is not linked to ten and two
    • Thirteen is not decoded by knowing “thir” means three and “teen” means ten
    • Fourteen is not decoded by it means four and ten, which logically should be ten and four
  • Learning to count from one to nineteen is a rote process
counting to a hundred
Counting to a hundred
  • The next number after nineteen is twenty
  • It’s difficult for children to understand that “twen” means two and “ty” means tens.
  • Then the numbers follow the rote by ones count – to twenty-nine…
  • Understanding the meaning of thirty, not twenty-ten, is a place value issue.
  • Therefore counting to one hundred needs to be rote first and place value understanding must be given time to develop.
counting on
Counting on
  • Counting on is useful to solve addition problems. But it is complex. To do 19 + 4 children need to:
    • Start the count at 20, not 19
    • Say the next four numbers after nineteen and then stop
    • Understand the last number they say is the answer.
    • Have a reliable way to check four numbers have been said
  • Place Value is the critical understanding here.
what do we need to do with counting
What do we need to do with counting?
  • Talk with children about the counting process.
  • Help them to make links with one more and one less.
  • Connect number words with objects
  • Make sets and count, reorganise the same set, do we need to count.
  • Watch how children operate – it tells us a lot about what they know.
a thought to leave you with
A thought to leave you with

…listen to children’s mathematical explanations rather than listen for particular responses.

Fiona Walls

in Handling Number

p.27s

Teaching Primary School Mathematics and Statistics

Evidence-based Practice

Averill & Harvey (Eds)

NZCER 2010

nzmaths
NZMaths
  • Other strand information – NZC/National Standards link.
  • Key Mathematical Ideas
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