Foundation Stage

Mathematics

Aims By the end of the session participants will: 1. Appreciate the importance in creating a positive

environment for maths; 2. Explore the mathematical learning potential with

sorting, and 3. Appreciate the importance of counting in relation

to all aspects of number.

Programme 9:15 Introduction and welcome 9: 30 Session one The learning environment in maths 10:30 Coffee 11:00 Session two Counting 12:30 Lunch 1:30 Session three Sorting 3:00 Evaluation and close

The learning environment in mathematics

Gemma, aged 7, Year three

Her teacher thought that Gemma had a good understanding of the equals sign. Gemma had no problem with sums like 2 + 3 = , and even 6 + = 9. Then the teacher asked Gemma how she did 2 + = 6.

Gemma replied, “I said to myself, two, (then counting on her fingers) three, four, five, six and so the answer is four. Sometimes I do them the other way round, but it doesn’t make any difference”. She pointed to 1 + = 10. “ For this one I did ten and one, and that’s eleven.”

How does Gemma show here that she has some understanding of the concept of addition? What about her understanding of the concept represented by the equals sign? How would you analyse the misunderstanding shown at the end of the conversation?

What implications does this have for Foundation stage

maths?

What do we want for our children in terms of mathematics when they leave the

primary school after seven years?

Year 1 September 2014 Year 7 June 2021 Year 2 September 2014 Year 7 June 2020

Curious

Questioning

Clear-thinking

Collaborative

Adventurous

Open-minded

Thoughtful

Independent

Determined

Playful

Self-knowing

Open to feedback

Flexible

Imaginative

Methodical

Attentive

Observant

Integrating

Opportunistic

Empathic

Focused

Intuitive

Self-evaluative

Imitative

Assessment in Foundation Stage

From To Expansion of the levels of progression Level one

What will you

Stop Start Continue

Two big ideas

Equivalence – the same Transformation – is different

Counting We want to consider • The issues with counting? • How does equivalence affect counting? • How does the idea of transformation

affect counting?

Progression through counting

Pre counting experiences

Level One

When adding count on in ones:

• within 5

• within 10

When subtracting count back in ones:

• within 5

• within 10

Level two

When adding or subtracting count on or back in:

• ones

• tens

Pre counting experiences 1. Sorting and classifying

• separating off the objects which need to be counted

• these objects to be counted have an element of equivalence

e.g. ‘How many children are here today?’ the children know not to include the adults

2. ‘One more’ ‘Another one’

• numbers increase as you count up

3. Distinguishing between small numbers without having to count

• They know they have two feet; two eyes; one nose

Counting in Foundation Stage The five principles of counting 1. Stable order 2. Order irrelevance 3. One to one 4. Cardinal 5. Abstract

Eventually children will associate the number word with the numeral.

I was asking a child in year two what number is one more than six.

He couldn’t do it. But he could count up to 20 and beyond.

1. The idea that the next number in the counting sequence is one more than the previous number is a vital component to understanding number

2. The complementary idea that the previous number is one less is equally as important.

Before and after

The children need experiences of the ordinal aspect of number just as much as the cardinal. Using number lines, number tracks, number ladders will help this. Spend time on - one more - one less - after - before - and another one

Counting Activities

1. Between 2. I have, Who has? 3. Green Bottles 4. Human number line

What will you

Stop Start Continue

Sorting in Foundation Stage Within the number attainment target

Sorting develops mathematical ideas

• Observation • Reasoning • Language • Cardinal number • Equivalence – comparing equal sets • Difference – comparing unequal sets for more

than/less than • Conservation • Component of number • Concept of zero

Difficulties arising from limited experiences

• Unable to select their own criteria • Unable to tell you the number of

objects in a set • Difficulties sorting for anything other

than colour • Unable to talk about their decisions • Unable to make choices for

themselves

Progression through sorting

• Undirected/random sorting • One property collections • Two property collections • Three property collections • Partitioning

Different criterion/properties

Colour Shape Size Thickness Weight Length Texture Position Value Anything

Structured materials • Compare Bears

Colour

Size

Weight

• Elephants Colour

Size

• Frogs Colour

Size

• Money Colour

Shape

Size

• Logic People Colour

Size

Position

Logic Blocks/Attribute Blocks Colour

Red

Yellow

Blue

Shape Square

Circle

Triangle

Rectangle

Size Big/not big

Small/not small

Thickness Thin/not thin

Thick/not thick

How can these be sorted?

One property collection

Same colour

Same shape

Same thickness

Different size

One property collection

Same size

Same thickness

Same shape

Different colour

One property collection

Same size

Same colour

Same thickness

Different shape

Two property collection

Sort for • Shape and colour • Shape and size • Shape and thickness • Colour and size • Colour and thickness • Size and thickness

Shape and colour

Same size, same thickness, different shape and different colour

Shape and size

Same colour, same thickness, different shape and different size

Colour and size

Same thickness, same shape, different colour, different size

Create this set

Partitioning

• To partition is to divide a set into subsets • Partitioning is early component work • Children are ready to partition when they can count a collection of objects they can recognise the numerals they have conservation of number up to 5 they can resort a collection

Partitioning • Teacher needs to use carefully selected

sets • Children need to realise they are working

with the same set of objects each time

Partitioning

• Within 5, • Carefully selected sets • Identical objects • Explore zero • Recording

Components of three

Components of four

Components of five

Components of six

Activities 1. The missing game 2. Match my piece 3. Happy families 4. Find the right place 5. Copycat 6. Feely bag 7. The Gatekeeper 8. Difference of one

What will you

Stop Start Continue