1. Developing Early Number Sense
Junior Focus Group
Developing Early Number Sense
8 March 2011

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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!

9. 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.

10. 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

11. 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

12. 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.

13. Counting on
Counting on is useful to solve addition problems. But it is complex. To do 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.

14. 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.

15. 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

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