How do they understand numbers and how do they learn to count? What early rich experiences can we give them that develops the skills of the mathematician?

Being a mathematician involves noticing and wondering about what has been noticed, producing thoughts such as ‘I wonder if this is something in maths that is always true? Or if this is not a general mathematical rule?’ Mathematicians go through this process of reasoning by comparing and contrasting information, testing their ideas in order to come to a place where they can justify their findings and provide a mathematical proof. But how does this process begin and what do those starting points look like in babies and toddlers?

There are some key behaviours and experiences that are part of the developing mathematician: recognising and responding to patterns; spatial relationships; cause and effect; inquiry through investigation and observation; developing mathematical language; developing number sense.

Recognising and responding to patterns

Babies are now given books and images to look at that use black and white only. These high contrast patterns are easier for babies to see. Having items around that include different patterns for young children to interact with and adults describing the patterns to the children, such as fabric that has patterns (as mentioned in the statutory framework for the early years foundation stage: gingham, polka dots and stripes) is a precursor to future maths, as interacting with patterns helps children to predict what comes next.

When setting up areas of provision, and planning experiences for your babies and toddlers, ensure that they promote the understanding of both straight lines and curved lines - so include items with stripes, grids and rectangles as well as circles and swirls.

We also want children to learn that the patterns can go in different directions, sometimes beginning in the centre and moving outwards, such as spirals, and sometimes going across such as with stripes. Include zig zags and dots. Use patterns that are seen in the natural world, such as the veins on leaves and the fur of a tiger, as well as patterns that are created by people.

The patterns that you choose need to be repeating patterns as well as symmetrical patterns. As well as having items around that are decorated with patterns, give children the experience of moving individual items into patterns, such as when playing alongside toddlers, place different coloured cubes into a repeating pattern of red, blue, red, blue, etc. commenting on what you are doing and the effect that this is creating. At this stage it is unlikely that a child from 0 to 2 will engage fully in your demonstration but you are beginning the process of these types of behaviour by modelling it to them.

Moving in repeated patterns, such as clapping and waving, also helps with the sense of being able to predict what is coming next. As children begin to walk, they are creating one of their first repeating patterns of moving with alternate feet. Repeating patterns are the first stage in understanding multiples and sequences which then progresses to being able to find the nth term in a sequence. Who would have thought that being able to walk would eventually lead to an element of algebra!

Spatial relationships

Babies are already getting a sense of where they fit in the spaces around them and how they are being moved around by adults. As they begin to move independently, they become fascinated by when they can fit into spaces and when they can’t. Who would have thought that squeezing themselves into small spaces and climbing was a stage of mathematical development, but I am observing my eighteen month old grandson doing both of these things and smugly thinking how good he is at maths! Putting items in and out of each other and stacking things are also part of the spatial relationships in mathematical development. Recognising and responding to when something fits into a space or not, and when something will balance on something else are starting points for young children also being able to plan and pursue mathematical investigations. Again, commentary by an adult is crucial in beginning the process of refining thoughts of the ‘when, how and why’ of maths.

Cause and effect and developing inquiry through observation and investigation:

Simply shaking a rattle and knowing that the action of moving it causes a sound, as well as a response from someone else, develops in young children the knowledge that an action leads to an outcome (Kamii and Devries 1993). Dropping something from their highchair and looking at the food on the floor, sometimes accompanied with the cry of: ‘Oh no!’ and pointing at it (again I am quoting my grandson) also demonstrates this growing understanding of cause and effect.

In mathematics, when calculating, amounts are manipulated and changed. This understanding is underpinned by a variety of experiences where young children are exposed to and interact with actions that cause something to happen. Ensure that your setting includes: equipment that can be pushed, pulled and rolled; musical instruments that can be shaken and hit; blocks that can be piled and knocked down.

Young children are curious. They observe and investigate objects and events in their everyday life, touching and playing with them using all their senses. They discover which textures are pleasing and can become apparently attached to the feel of a particular toy or muslin cloth that they have snuggled when feeding.

Talking to very young children about what you have noticed and what you think about it begins the process of thinking like a mathematician. Commenting on how shaking the rattle harder makes it louder and gentler makes it quieter, for example.

Mathematical language and Number Sense:

Modelling vocabulary is crucial. Why does my son speak to his very young son in full sentences? Why have they done this since the moment he was born, and even before? That new-born baby could not understand the words and yet we speak and speak to him until he begins to try some words of his own – we do not give up after the first time because he has not instantly spoken back.

Counting up to three and from three to one before something is about to happen helps children to begin to learn the names of the first three numbers. ‘One, two, three, go’ and backwards: ‘Three, two, one, blast off!’ Also, ‘ready, steady, go’ supports this idea.

Counting the sequence of the numbers when going upstairs and counting each stair as you go as well as counting items as you are laying them out in rows, in a tower, in a circle, (different directions) all help to establish the idea that objects can be counted, as well as teaching the sequence of the names of the numbers when counting in steps of one. Often toddlers will like the sound of some of the number names and will join in with this. My grandson’s favourite number names are two and five and he always joins in with them when someone counts for him.

Babies and toddlers can detect whether amounts of items are only one or two things but also when amounts are more or less than each other despite not having the words to label these amounts yet. (Samara and Clements 2009). Encouraging them to react to changes in amounts, and playing peekaboo, are part of learning that things can come and go. My grandson loves to be able to see how many of his snacks he has left as he is eating them and he understands that when they have all gone that there are none left. Talking about and experiencing items of different sizes and weights, commenting on what you see and feel, helps babies and toddlers to understand scale and is part of understanding numbers.

And then there is subitising. A new and welcome addition to the expectation of achieving the Early Learning Goals at the end of Reception. This is a crucial skill that humans have naturally, especially for small amounts. It is where we see an amount and know how much is there without counting. We use the skill of subitising when reading the patterns of dice. Most of us, from a very young age, can recognise amounts of, or images that contain one, two or three things. Have collections of equipment that are in pairs, such as socks and mention the number of eyes, ears, hands on each of us. Also comment on shelving equipment that has three shelves, read stories that include three characters (there are so many: three bears, three pigs, three wishes, etc.). We are endeavouring to show that we do not always need to count everything in ones and that some amounts can simply be recognised.

Getting your ‘maths goggles on’ when planning your areas of provision and adult interactions can really elevate the status of maths for you and the children that you are developing. Hopefully this article has helped you to do that.

You can find part two of Sharon's Maths series here.

And you'll find part three here.