Counting PrinciplesGelman and Gallistel (1978) argue there are fivebasic counting principles:• One-to-one correspondence – each item is labelled

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 timeand attention!

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• 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• 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• 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 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?• 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.

Subitizing

• The ability to recognise and label small quantities without counting – links directly to cardinality

• Use dot cards, tens frames, slavonic abacus to provide opportunities every day for children to practise

Activities to assist with counting

• Number tiles• Counting practise – hundreds board• Rote activities• Skip counting – not always 10, 20, 30

Tiles

Roll a dice – (1-6) – 5 is rolledCount out number of counters, cover a tile as you count Last number you say tells you how many

Tiles

You have five marbles. Your friend gives you three more. How many marbles do you have now?

Tiles

You have nine marbles. You loose three to your friend. How many marbles do you have now?

Counting – we need to discuss…

• Cardinality – the last number tells how many• Ordinality – why are the numbers in the order

they are?• One more, two more, one less, two less

• Talk about the patterns when skip counting• Fluency

Reflection time – in groups discuss

• What has the discussion so far made you think about in regard to counting?

• What impact does counting have on children who are having difficulty?

• What will you start to do differently with children who are having difficulty?