Early number pv workshop

Early Number Concepts

Learning outcomesAt the end of this tutorial and self study you should have:

•developed your knowledge of the stages of development towards acquiring mathematical concepts, particularly number•raised your awareness of the mathematics going on in an early years setting•helped you devise and encourage relevant mathematical experiences leading to mathematical ideas for young children•Examined some resources and considered their use in the early years

Margaret Donaldson Children’s Minds 1978 (Fontana)

‘An adults knowledge of the general nature of the subjects taught to children when they first enter school is apt to be so well established that it blocks the realisation of precisely what the children need to be helped to see.’

Early Years Mathematics

Counting 1 - 19

• I have explored numbers, understanding that they represent quantities and I can use them to count, create sequences and describe order

MNU 0-02a

Counting What does it mean?

View video – ‘Twice five plus the wings of a bird’

Early Years Mathematics

Counting and NumbersFrom the video we can see that a child must

• know the sequence of number names. • Be able to match one-to-one words with objects being counted

(one-to-one correspondence).• Be able to identify a set to be counted (or a subset)• Understand that the last number name in a count gives the

numerical size of the set of objects (ie. the cardinality) of the set.

• have conservation of number.• understand the abstract concept of number ie. sets of 4

whatever have the common property of 1, 2, 3, 4.• can start counting a set in a different place and realise the

number is the same (advanced conservation).

Refer to the concept maps for ‘Number’ and ‘Counting’

Early Years Mathematics

Counting and NumbersAssessment of learners

• Activity – Read and discuss ‘Talk 1’

• Activity – Read and discuss ‘Talk 2’

Early Years Mathematics

Children should explore number situations, count, begin to calculate, talk about how they worked things out and record or represent their mathematics in their own ways

“Learning involves moving progressively from concrete examples to the use of symbolic representations.”

Building the curriculum 2 – Active learning, A guide to developing professional practice, Scottish Government (2010)

Early Years MathematicsChildren’s Mark Making

Consider:'Children’s Mathematical Graphics: Understanding the Key Concept’

Carruthers and Worthington (2009)

Task: Consider the sample recordings in relation to the key concepts of number and counting.• knows the sequence of number names. • can match one-to-one words with objects being counted

(one-to-one correspondence).• can identify a set to be counted (or a subset)• understands that the last number name in a count gives the

numerical size of the set of objects (ie. the cardinality) of the set.

• has conservation of number.• understands the abstract concept of number ie. sets of 4

whatever have the common property of 1, 2, 3, 4.• can start counting a set in a different place and realise the

number is the same (advanced conservation).

What assessments can be made?

Early Years MathematicsChildren’s Mark Making

Introducing place value

I have investigated how whole numbers are constructed, can understand the importance of zero within the system and can use my knowledge to explain the link between a digit, its place and its value.

Responsibility of allMNU 1-02a

Introducing place valueUse unstructured materials to show the number 34

Use semi-structured materials to show 34

Now make 34 using structured materials

How is 34 displayed on an abacus?

Discuss the difference between each of the materials in terms of helping children develop understanding of place value.

Online manipulatives - Chip AbacusClick here for an interactive abacus

Using Structured MaterialActivity

Use structured material to show these numbers

256 1089

Using Structured Materia

Children should be given practice in investigating different ways of partitioning numbers using blocks:-

234 - 2 hundreds 3 tens 4 units23 tens 4 units2 hundreds 43 units234 units

Activity - Investigate six different ways to make 248

A comparisonActivity

Discuss the difference between the two types of cards.

3 00604

3

46

What do you think is meant by the ‘quantity value’?

Place Value Mark-up

Play this game.

What knowledge and understanding does this activity reinforce?