Early Learning Goals: Subitising Numbers
As we grapple with a multitude of changes and challenges this year, many of them most unwelcome, now is the perfect time to celebrate some good news; the arrival of a long overdue omission from the Early Learning Goals.
Number Early Learning Goals
Children at the expected level of development will:
- have a deep understanding of number to 10, including the composition of each number
- subitise (recognise quantities without counting) up to 5
- automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.
Have you spotted it? In fact, you may be staring at it and wondering what it actually entails: ‘Subitise (recognise quantities without counting) up to 5’. Teachers across the world see subitising as a key foundational step in mathematical understanding and the term ‘subitise’ is very much part of their mathematical lexicon, but that isn’t the case in England.
So what does the term ‘subitise’ (or subitize) mean and what does the act of subitising look like in practise? Imagine the scene:
Adult: “Yes! Ducks! How many ducks?”
A familiar scenario, yes, but let’s stop and consider for a moment how the child knew there were three ducks. Did she count? No, she didn’t have time, and as young children typically count aloud, we would have heard her counting. She instinctively knew there were three because she could see three. Sarama and Clements (2009) explain subitizing as “a quick attention toward numerosity when viewing a small set of objects”.
This relies on a high degree of spatial reasoning which is something the vast majority of children develop at a much younger age than we give them credit for. Subitising begins very early on. Babies notice the attribute of size, recognising when one group is larger or smaller than another. Then, year on year, children develop the ability to recognise increasingly larger collections, often before they can label the size of the collection with the correct number name. By the time they reach the age of five, most children can subitise to the same number, quickly recognising a group of five items, without the need to count. However, it is all too easy for us adults to dissuade children from relying on this valuable skill, replacing it instead by counting.
Let’s return to the duck pond for a moment. Having told her carer that she has seen three ducks, the conversation continues:
Adult: “Can you count to check?”
Child: “One, two, three.”
The child has now been given the message that subitising cannot be relied upon as a tool for answering the question: ‘how many?’; what’s more, counting has been reinforced as a more reliable strategy. Imagine this child a few years later, now in KS2; when faced with the task of working out how many, there she is, counting on her fingers.
Around the age of five, children can typically subitise five objects (Perceptual Subitising), seeing them as one complete collection. As the collection increases in size, we begin to move towards Conceptual Subitising – seeing the collection as being made up of groups or parts that add together to form the whole. So, in a collection of six items, we may see three and three; or three, two and one; or two, two and two maybe. This is the foundation of part whole understanding. What’s fascinating is that we have a tendency to see different group within the whole collection, or different arrangements. Jo Boaler a professor at Stamford University in the United States invests significant time and attention in what she calls ‘dot card number talks’. Working way beyond kindergarten, she explores dot patterns with high school pupils, asking them not just ‘how many?’ but also, ‘how do you see them?’. This is an essential step for learners who may only see one way, their own method, of partitioning a collection, rather than the multitude of approaches they see as a class collective.
In KS1, we introduce children to place value partitioning, or standard partitioning. In KS2 we need learners to think more flexibly about partitioning if they are to become efficient calculators. However, many junior mathematicians (and adults) become wedded to standard partitioning. Take 26 + 37 for example. What is your first inclination when it comes to adding these two numbers together? For many the default approach is to partition into tens and ones: 20 + 30 = 50, 6 + 7 = 13, 50 + 13 = 63. But look again; is there a way of partitioning the numbers that results in fewer component calculations? How about partitioning the 26 into 23 and 3, using our number bonds we know that rounds the 37 up to 40 so now we only need to add 23 to 40.
Whilst mental calculation is less prominent in many classrooms since the removal of the mental arithmetic text, mental mathematics is what we use most in ‘real life’ on a day to day basis. However, it requires flexibility in the strategies we use and an eye for the most efficient approach that reduces cognitive load while we calculate. Often, place value (standard) partitioning increases this cognitive load, making it harder for children to perform mental calculations. This is not good preparation for the future!
So, when you are discussing the new ELGs in your school, don’t brush over the term ‘subitising’ as a mere step to be ticked off; see it as the absolute bedrock upon which all other mathematical understanding will be based.
If you would like to find out more, The Education People have a half-day Zoom course on Monday 29 March (2pm to 5pm) Understanding the New EYFS Framework for Maths: What’s all this about ‘subitising’?. This is suitable for EYFS practitioners but also Maths Subject Leaders, and any teacher recognising some of the struggles mentioned above in their own classroom.