...and what can we do to promote a deep understanding of the numbers from 1 to 5?

Before I start on specific references to mathematics, I need to emphasise that that educational interactions with young children should always be playful. Maths as well. Playful maths.

Maths is not just about having numerals on display. In fact, the abstract symbols of numbers, an agreed squiggle that may contain straight or curved lines, is almost pointless within itself until the understanding of amounts is established. For the understanding of number, there are two key elements that have to be worked on and developed in children. One is the skill of subitising and the other is conserving.

Subitising is the ability to recognise amounts without having to count them in ones. For children aged 2 to 4 we begin by learning to subitise up to three. Conservation of number is knowing that no matter what order or arrangement of amounts, the total remains the same if nothing has been added or taken away. Both can be taught in a ‘playful’ way. Different subitising patterns for the same amount help to develop conservation of number.

Playful maths ideas for teaching subitising and conserving

There are many playful, simple and yet effective ways of teaching these two key maths ideas that I have used over the years. One is called ‘Bunny Ears’ which develops finger gnosia (the ability to show amounts on fingers without having to count in ones and without having to look at the fingers). The children are taught to put their hands either side of their forehead, with their fingers curled over and then to lift fingers, in different ways, to show small amounts. There are ten different ways that one finger can be shown (including the thumbs) by lifting them one at a time, as there are ten fingers. The adult would say: ‘I am showing you one finger. Now I am showing you one finger again but this time with a different finger. Can you show me one finger? Can you show me one finger but use a different finger?’ Ensure children understand that they constantly have ten fingers and we are ‘showing’ it means lifting a folded finger upwards.

Then there are teaching specific patterns for children to learn ‘off-by-heart’. I like to use circles drawn on paper plates as ‘flash games’ (a bit like the teaching of phonics strategies) as well as ‘memory games’ where the plates are face down and the children take turns to turn over two of the plates. If the number represented on both plates is the same, the two plates can be kept by the player until the end of the game.

Sometimes the circles are unshaded and sometimes shaded and these particular patterns are used to prove the properties of numbers as well as to develop bonds and doubles of numbers which supports with future mental mathematics strategies. All the time, as these patterns are being used, adults are describing what they see and why the patterns are in a particular arrangement. They are referencing how the patterns are the same as each other and how they are different. The children respond to the flashed plates in a variety of ways such as showing the amount seen with their fingers, drawing an image on a whiteboard, pointing to a choice of patterns to indicate the pattern they have seen and/or saying the name of the number.

There are specific patterns for amounts up the five that I would promote as follows - 

Images of one circle that are in different places on the plate i.e. in the centre as well as at the edge, such as:

Images of two where both circles are close together as well as being further apart. Sometimes close to the centre of the plate and sometimes to the edge. Images where there are two circles where one is shaded and one is unshaded, which is discussed with the children as proving that one more than one is two:

Images of three circles where they are in a line, in a triangle, spread out and closer. Also, images of three circles with two of them are unshaded and one is shaded – this image proves that three is one more than two:

Images of four where the dots are in a line, the dots are in square, the dots are proving that four is one more than three as well as that four is double two by using shaded and unshaded circles:

Images of five where one pattern is the version we see on dice and dominoes, as well as patterns that begin to show a variety of bonds of five as well as prove that five is an odd number:

One reason that the plates work so well is that as you are flashing the plates to the children there is no definite way to show the patterns so children learn that the orientation is irrelevant. We use this understanding when looking at the top surface of dice as they drop to the surface. Even if the pattern is presented diagonally, we still read the pattern with accuracy (as long as we are very familiar with the patterns so that it is an instant reaction). We also want children to recognise the images of 2D shapes in different orientations so this is a good link with that part of understanding.

To be preparing to reach the goal at the end of Reception, at the end of Nursery you would want children to be able to comfortably subitise patterns of 1, 2 and 3 and you would also have been providing them with the opportunity to see and respond to patterns of four and five, finding the one, two and three amounts within them.

Useful resources

Subitising and conservation of number are the crucial elements of number sense way before any abstract symbols are expected to be recognised. There is a great resource that was published by the National Strategies in 2009 that I still use regularly when working with teachers to plan specific learning opportunities for the children they are teaching. The Birth to Nursery expectations are part of the phases 1 and 2 in the ‘Steps in Learning’ section from this file (which can be downloaded from this link: | STEM ) The ‘Role of the Adult’ section provides some lovely adult directed tasks that can be easily resourced, followed by creative ways of providing follow-up and taking the learning further. Check it out if you have not used it before!

Numberblocks on the BBC is a brilliant tool to use for teaching the understanding of numbers and developing early number sense. The National Centre for Excellence in Teaching Mathematics (NCETM) website contains some teaching materials that link with the content of the programmes.

As I mentioned in the article for birth to the age of two, adults commenting on what they and the children are doing is a crucial part of learning. As maths is both a language of its own, with its own specific meaning, and learning anything involves thinking about what you are learning, talking about what we are doing and thinking helps children to learn how to think. Thinking is a crucial skill for a mathematician as much of maths is ultimately done in the abstract.

As well as understanding early number sense and mathematical language, there are other key behaviours and experiences that are part of developing the mathematician: recognising and responding to patterns; spatial relationships; cause and effect; inquiry through investigation and observation. I have made reference to these elements as well in the article about maths for children from birth to two. Check it out, as many of the ideas are also applicable to children in Nursery.

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

And you'll find part three here.