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Junior Focus Group Developing Early Number Sense 8 March 2011 PowerPoint PPT Presentation

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

Junior Focus Group Developing Early Number Sense 8 March 2011

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Junior Focus Group

Developing Early Number Sense

8 March 2011

Number Sense

• Having a good intuition about numbers and their relationships.

• Develops gradually as a result of exploring numbers, visualising numbers, forming relationships

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

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

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

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

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

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!

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.

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

NZMaths

• Other strand information – NZC/National Standards link.

• Key Mathematical Ideas