In mathematics, by the end of Reception, children are expected to.....
To create a strong number sense in children from an early age, we focus on subitising for calculation. Subitising is a skill that is within us from birth, and means 'to see instantly'. We are able to immediately 'see' up to about 5 objects, and more if they are arranged in a familiar pattern. This is known as perceptual subitising. Look at the dots below. What do you see in each section?
As an adult you were likely able to instantly subitise the spots in each section (perceptual subitising). For some, your brain probably did a quick calculation without you even realising, such as seeing a 3 and a 2, therefore you knew it was 5. Or seeing two 3s, therefore you knew it was 6). This is knows as conceptual subitising. Conceptual subitising is one of our aims for the children, as it is an early form of calculation. Without realising they are practising the early skills of addition, subtraction and even multiplication and division just by being able to see numbers within numbers.
As we teach the children to 'see' what amounts look like, we introduce the numeral to match. For example, it's firstly important that they learn that this is 'five' and the numeral '5' is the character we use to represent it.
Counting is the least effective tool for calculation. When a child creates a habit of counting in order to calculate, they often retain that habit for life. This hinders their ability to calculate quickly and effectively and can often be seen in older children, who, when calculating larger numbers still count on their fingers, or make marks on paper. When children have a solid grasp of numbers within numbers, number bonds and the base 10 system, they have a much better chance of succeeding in maths than those that rely on the one tool of counting.
In order to strengthen the children's understanding of number bonds to 10 and the base 10 system, we spend a lot of time looking on amounts on 10 frames. We talk about what we see and how we know how many there are without the need to count.
When we look at numbers over 10, the children find it really easy to transfer this knowledge onto two 10 frames.
"I know there are 16 because there is 1 full ten and 6 of the next ten."
So do we not teach children to count?
Of course, it is vital that children learn to count! We need to be able to count things out, for example, "please give me 9 counters". We need to count things that we cannot see all in one go, such as cars driving past or children in a long line. We need to be able to count things we hear, for example, we practise this by counting the number of bangs on a drum. We need to count actions, such as "can you jump 5 times or clap 10 times?". The children love to count and we count regularly by singing songs and rhymes and even counting to 100, which the children love and is so important for their understanding of the pattern and repetition of number.
Counting 'things', however is a tricky skill to master. Firstly, children need to know the order of the numbers. They need good 1-1 correspondence, whereby they have to be able to say the number names at the same time as move their fingers to touch the objects. Too fast or too slow results in the wrong total. They also need to understand that the last number they say is the total of ALL of all of the objects, not just the last one they pointed to. This is the cardinal principle and is quite a tricky concept for young children to grasp. They also need to understand that whatever order they count objects in, the total amount is always the same. You can see here why counting for calculation is so unreliable.
When we subitise from the start, the children see the total amount and understand that this is the name for ALL of the objects. We then look at what amounts are within that number. "I see 4. In it I see 2 and 2. I see 2 and 1 and 1. I see 3 and 1." The children become amazing at seeing numbers within numbers and this gives them a really good foundation for good number sense.
We use White Rose Maths which supports teaching and learning in this way.
Below is a video by Karen Wilding from EY Maths. This video was made during lockdown to support parents to teach maths but it explains the meaning and importance of subitising for young children.
Karen has other videos about early years maths on her YouTube page should you wish to learn more.
Thank you for your time.