Thanks to Caroline Clissold for this guest blog post that focuses on the youngest children at school, exploring ways to use a mastery approach to support them on their learning journey and to prepare them for the demands of the Years 1 programme of study. Caroline is a primary mathematics consultant and author of Rising Stars Mathematics.
Gelman and Gallistel are well known for their research into young children’s development of their understanding of number. They researched the stages in counting that everyone goes through when they are young and subsequently published their findings in 1978. This research may well be old but it stands the tests of time and EYFS teachers can often relate these stages in counting to the children they teach. Ideally, all children will leave Reception having mastered counting. Below is a brief summary of their research into the stages of counting and what mastering this vital skill entails:
The one-to-one principle: Children can count a certain number of objects by touching them and matching the count with the touch, but they can’t necessarily tell you how many they have.
The stable order principle: Knowing that numbers come in a sequence. Children can only count a set of objects according to the number that they can count up to. For example, if they can count in order to five, they will not be able to count six objects.
The cardinal principal: Knowing that the last number counted indicates the number in a set. Children will point to or touch objects using one-to-one correspondence and when they get to the last object, they can tell you that the number counted is how many objects they have.
The abstraction principle: Understanding that any types of objects can be collected together and counted. Children will often be given the same objects to count initially, for example, counters, cubes or plastic animals. We need to give them the experience of collecting totally different items and counting them so that they can see that counting works for everything.
The order irrelevance principle: Understanding that the number of objects does not change when they are placed in different positions, so they do not need to count again. Eight objects is always eight wherever they are placed because nothing has been added or taken away from the set.
Read more about the research of Gelman and Gallitel.
It is worth creating small intervention groups with children at the same stage in counting so that they can practise for short five minute daily sessions in order to master the stage that they are at. I know of nursery and reception teachers that do this and are finding it really successful.
Once children can count they need to be able to explore numbers, initially to ten. For example, children need to know about the number five, what it is greater than and less than, how five can be made (1 and 4, 2 and 3, 3 and 2, 4 and 1), whether it is odd or even and recognise the numeral. They need to show five in lots of different ways, for example, using counters, a tower of cubes and straws.
They also need to be able to subitise, (knowing how many there are without counting). Dice and dominoes are really helpful resources for practising this skill for numbers to six.
It is often helpful to concentrate on shape, comparative measures, position and direction with the whole class until everyone has mastered counting. When they have mastered this concept, whole-class work on number based topics will be more successful.
When teaching shape it is best to start with 3D shape because this is a child’s first experience of shape. Children will, for example play with balls, dice and building blocks from an early age. It therefore makes sense to teach shape from the experiences that they have from home. We can then teach 2D shape from the faces of the 3D shape we are exploring. It is a good idea to focus on one shape at a time. For example, begin with a sphere:
- What can the children tell you about it?
- Where would they see one in real life? You could have a collection of spherical objects for the children to explore.
- What can spheres do? Let’s try rolling one – who can roll it the furthest? Do the same for kicking and catching.
- You could give each child a sphere and ask them to put them in different positions so reinforcing positional language.
- Cut one in half. What 2D shape can they see? Now is the time to explore circles. I know teachers that explore one shape a week, introducing the appropriate vocabulary as it comes up. Once they have explored a sphere, cone, cylinder, cube, cuboid and pyramid, they then look at all of them and sort according to different criteria. Doing this will help the children to master their shape curriculum.
Are you interested in discussing these points and more about comparative measures including coins? If so, we are running a free webinar on this topic on 24th May.
Find out more and register to attend.
Interested in maths resources for the Early Years? Rising Stars Mathematics in the Early Years, a new resource that includes creative, free-flow activities that encourage open-exploration of maths concepts. The free-flow activities help to develop children’s understanding through play-based learning and support them towards the Year 1 programme of study.