Junior Focus Group Developing Early Number Sense 8 March 2011

1. 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 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.

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