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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

- 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.

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

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

- 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

- 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

- 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

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!

- 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.

- 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

- 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

- 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 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.

- 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.

…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

- Other strand information – NZC/National Standards link.
- Key Mathematical Ideas