Are You Teaching 'Composition of Number' Wrongly? (and how would you know?)

It doesn't matter which Maths scheme you use (or whether you have a scheme in place or not), what matters is what YOU as the educator know (your subject knowledge) and understand (your pedagogy) about the Maths you're teaching and the ways it's most effectively taught.

Think of a scheme as like a recipe book, whereas investing in your knowledge and skills is like going on a cooking course.

Simply buying the latest recipe books will not make you a better cook.

Teaching Maths effectively is just the same.

EYMaths isn't another 'recipe book' instead we aim to offer you the very BEST cookery course you could wish for.

So let's start uncovering what 'you didn't know you didn't know' about teaching 'Composition of Number'.

Understanding the 'Composition of a Number' is what leads to our ability to add, subtract, multiply and divide. It's vital we as educators know this is the destination or we may, mistakenly miss that we're providing a vital step here in their mathematical progression (and not a standalone set of activities to meet an objective or step in a scheme).

All learning in Maths begins with noticing.

Maths is a science and our children are highly scientific (from birth!).It's what keeps us all safe and alive.

When it comes to 'Number Sense', noticing begins with judging whether amounts are equal.

'Do I have more food here or here?'

The brains of even our youngest children learn to recognise patterns of 'number' (up to 3 items) very early on.

They know a group of 3 things isn't the same as a group of 2 things.

They haven't at this early stage, however, learned the words to label them as 'three' and two' yet nor match them to the digits but they have number sense.

(Don't forget that humans used 'number sense' for thousands of years before a number system was invented).

So the first step in understanding 'Composition of Number' (meaning how a number is 'made up' 'what's in it?' you could see it as) is to recognise the role of 'perceptual subitising'.

Perceptual Subitising: This is the ability to see and recognise an amount as a whole (and distinguish it from other amounts)

Myth Buster: When objects are randomly arranged, the limit of perceptual subitising for adults as well as children is typically 3 (and not '5' as stated by many schemes)

Myth Buster: When amounts greater than 3 are arranged in a known pattern (e.g. on a five or ten frame) then it's possible to perceptually subitise much larger numbers (Many schemes state that 5 is the maximum and describe this, incorrectly, as being possible in a random arrangement - see myth above).

Our children demonstrate their early 'Number Sense' skills in many ways:

• They consistently select the greater amount of a food they prefer when offered the same food in greater and lesser quantities
• They pull a face when they realise 'it's not fair'
• They go to get 'more' to even up an amount
• They show the same number of fingers to communicate what they see or how many they would like
• They adjust the number of fingers to match a total

And all of this without ever saying a number name nor recognising a digit.

This is 'Number Sense' and if you're not seeing it (as your 'destination' is for them to correctly say a number name or match a quantity with a digit) then you're unintentionally squashing their progress, assessing them inaccurately and missing hundreds of opportunities to build upon the skills they're showing you all day every day.

Our role at this stage (whatever their age) is to begin modelling what we notice around us. This should be language rich and encourage them to be curious about EVERYTHING. (We're not just aiming for Maths skills here!).

Notice in particular, items with a 'low cognitive load'.

This means things that have the same (or similar in the case of natural objects) shape, size and colour.

Keeping the 'cognitive load' low means the brain can focus on the number pattern (or concept image) being created by the objects. Ultimately we want children to be able to perceptually subitise using more 'interesting' items but in the early stages this will distract the brain into wondering about the object rather than the 'how manyness'. Makes sense doesn't it?

When we see a group of 2 blueberries in snack time or 3 conkers whilst exploring natural objects, we can use our finger to circle around them as a whole group and say what we see 'I can see 2 blueberries here and 1 blueberry here'.

(Don't worry about ideas, I have LOTS more games I can share with you to develop this!)

You might notice at this stage that, if the children are sharing out the fruit for snack time, the child takes one more so that there are 2 in each set. This will often happen without the use of number names but may involve 'we need more' or '1 more'. Notice when number sense is being communicated without spoken language. It's happening all the time all around you.

Noticing and beginning to model labelling groups of 1, 2 and 3 with number names within meaningful situations is your first step towards teaching 'composition of number'.

Next, you need to understand how 'conceptual subitising' fits in with this....keep an eye out for Part 2

Taking Action: Want to learn more about 'Perceptual Subitising' and why it's so different to counting?

Click HERE to watch a free video on our EYMaths YouTube channel

I can't WAIT to share more EYMaths #wowbombs with you,

P.S. There's so much more to share so make sure you're also a member of our free 'EYMaths 3-5 With Karen Wilding' Facebook group (you need to answer all 3 questions to be admitted).