There are stages in development for maths, as with every aspect of development, and the current framework for the Early Years Foundation Stage lists and exemplifies these stages very well.

Maths in your areas of provision 

When referring to the framework we need to be thinking of the elements of mathematical learning that can be promoted though our areas of provision, which are continuously provided, supporting children in developing day-by-day, bit by bit, through regular ‘drip-feed’ experiences.

Each area of provision links naturally with different measurement elements of mathematics. The table shows a few examples of these links:

Using Daily Routines

Daily routines can also be used to practise maths concepts regularly. Here are a few examples:

·         promote positional language - when tidying up with the children, describe and show where items are positioned compared with other items i.e. ‘The scissors are stored in the pot behind the sticky tape.’

·         comment on and talk about the fractions of items being used where these items are ‘continuous’ i.e. ‘You have eaten one half of your banana. You have one half of it left to eat’ and ‘Fold your piece of paper into two halves to make a card.’ And ‘You have drunk all of your milk; there is none left.’

·         Embed the use of regular references to statistical representations, for example simple block diagrams and pictograms (where each image represents one) to record preferences such as lunch choice, how we came to school, etc.

·         use ten frames as a base for recording the number of children attending each day where each child places a photo of their face into a part of a ten frame (you will probably need three ten frames for your whole class!). ‘Are we all here or are some children away?’ and ‘How many are away?’ and ‘How many are here?’

·         look at sorting your collections of items in your areas of provision into properties mathematically, such as train tracks being sorted into their parts on the shelf into straight track, curved track and paint brushes being sorted into thick and thin brushes, etc.

The maths area is where the children play teachers and play and invent number games. Provide whiteboards, pens, card, paper, mark making equipment, dice, spinners, dominoes, etc.

Thinking and behaving like a mathematician 

Learning to think and behave like a mathematician needs to be constantly modelled by adults in order for the children to copy these behaviours. Mathematicians will tell you that they are a ‘seeker of patterns’ and that they often begin their mathematical enjoyment by noticing and wondering. Examples of how you can promote this in your setting include regularly saying out-loud to children, ‘I have noticed that…’ (it is raining; the door is still open; you have finished your milk); ‘I think that…’ (it will be sunny again soon; we should close the door; you should put your carton in the bin); ‘I wonder …’ (when it will stop raining/why it is raining; the door keeps coming open/what will happen if we leave the door open; if you are always the first one to finish your milk/how much milk you have in your tummy now). After often hearing these sentence stems the children will begin to use them independently.

Another skill required for a mathematician is to be able to compare and contrast (notice and describe how things are the same and how they are different). Model and then ask the children to tell you what is the same and what is different about two items. The two items need to be simple and not too detailed and of the same type i.e. two conkers, two cups, two different shoes, etc. Once the children are confident with two items you could move to three items to compare and contrast. Finally, being able to discuss four similar items. Children will naturally find it easier to tell you how the objects are different but persevere with modelling and asking about the same qualities/properties as this underpins sorting and classifying. The numbers 2, 4, 6 and 8 don’t look the same but they are numbers that can be put into groups of two with nothing left over so that makes them even numbers; that is how they are the same.

Being able to test ideas and conjectures is a crucial element of reasoning. Be sure to include out-loud wondering that leads to testing ideas and deciding if something is always going to be true or not. I wonder what will happen if… Ask children this question as they are playing in different areas of continuous provision i.e. ‘I wonder what will happen if I keep filling this container?’; ‘I wonder what will happen if I put this ball on top of this tower?’ Encourage children to choose what they are going to use in the areas of CP and what they are going to make. Ask them to talk to you about the choices they have made and whether they were good choices or bad choices. If a tower falls over after a child puts a heavy block on the top, for example, ask these questions:

1)       ‘What are you trying to do?’ (child attempts to show/tell you)

2)      ‘What keeps happening?’  Or ‘What happened?’ (the child attempts to show/tell you)

3)      Ask questions to generate ideas on ways to solve the problem such as: ‘Why do you think it is happening?’; ‘What could we do?’; ‘How could we solve it?’

4)      The child needs to be encouraged to decide what to do (If the child has a solution then let them try it even if you know it won’t be the right solution - much better if they realise their own mistake than be told it – that is when true learning happens: learning from their own noticed mistake. However, be aware that, for some children, you may need to step in if the child is not realising that it is still not working to avoid frustration.)

5)      ‘Did that work?’ and ‘Why do you think it worked?’

6)      ‘What can we learn from this experience?’

Specific teaching of concepts

There are certain elements of the framework that have to be explicitly taught by the adults and planned as adult directed time.

Understanding numbers and knowing how to count are crucial to mathematical development but even when working with shapes we are establishing key ideas to support with calculations. Knowing that putting two or more shapes together makes a new shape, for example, is developing the concept of part-part-whole for numbers.

Once subitising up to three has been established we teach subitising various arrangements of items up to four then work on five. Learning to subitise a variety of images for the number four and the number five contributes to the children’s understanding of the conservation of number (knowing that no matter how the amount is arranged the total remains the same).

The game ‘Bunny Ears’, that I mentioned in the article about children aged 2 to 4, is described by the adult in a more sophisticated way when working with 4 to 5 year olds. As the hands are either side of the head the adult would be talking about each hand showing a part and then, when the hands are brought together, talking about that amount being the ‘whole’. So, for example, the hands are showing four fingers up on one hand and two fingers up with the other hand and the adult commentary would be something like this: two is a part; four is part; the whole is six (as the hands are moved so that they touch). Further comments could include: both parts are not equal to each other. Then six fingers could be shown in a way that shows two equal parts such as three fingers on each hand: ‘Six fingers can be put into two equal parts of three.’

The expectation for the end of Reception is that children can subitise a variety of arrangements of amounts up to five. They also need to have a deep understanding of numbers up to ten. Experiences to promote this includes being able to count forwards and backwards as well as the conservation of each of the numbers up to and including ten. Also, ‘bunny ears’ that develops finger gnosia and subitising and discussing a variety of arrangements for each number (see more detail from the article aimed at teaching children aged 2 to 4) both add to that deeper understanding. This also means that children begin to learn some of the numbers facts off by heart including doubles of numbers up to five and some of the number bonds of ten. They also should know number relationships in terms one less and one more as numbers and one fewer object and one more object when using items. They are beginning to learn to classify numbers, specifically odd and even numbers. Numberblocks (BBC TV programme) has a great episode called ‘Odd and Evens’ with helps to understand this.

As you can see, maths learning can be promoted in the areas of your continuous provision and daily routines as well as the times when we are specifically teaching the children knowledge and skills. Remember to make it fun though!

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

And you'll find part two here.