Counting Principles

1. Counting Principles Gelman and Gallistel (1978) argue there are five basic 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 time and attention!

2. 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.

3. 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

4. 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

5. 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.

6. 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.

7. 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.

8. 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

9. Activities to assist with counting • Number tiles • Counting practise – hundreds board • Rote activities • Skip counting – not always 10, 20, 30

10. Tiles 1 2 3 4 5 6 7 8 9 Roll a dice – (1-6) – 5 is rolled Count out number of counters, cover a tile as you count Last number you say tells you how many

11. Tiles 1 2 3 4 5 6 7 8 9 You have five marbles. Your friend gives you three more. How many marbles do you have now?

12. Tiles 1 2 3 4 5 6 7 8 9 You have nine marbles. You loose three to your friend. How many marbles do you have now?

13. 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

14. 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?