### Early Years Counting - techniques to help kids really understand numbers

I just googled 'learn to count'. The first page is full of online games, videos, activity worksheets and even apps to download. These are all engaging, fun ways for children to practise counting, but they do not teach children what it really means to count. There is much more to counting than is initially obvious. This post explains what is really involved in learning to count and provides ideas of tasks that can be used to really develop a child's understanding of counting.

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There's a lot more to counting than you might think

I found a fantastic blog by komodo that suggests that children are born with the instinct to count and that toddlers as young as 12 months are able to recognise how many objects are in a set (up to 3). We therefore do not need to 'teach' our children to count; we must nurture their natural ability and help them to link their sense of 'how many there are' to the names and symbols that we use.

Learning to count should not be about learning a sequence of number names. Children need to develop their sense of quantity, and then be able to use the correct names to accurately describe that quantity. Learning to count by simply reciting the number sequence does little more than require you to remember a pattern of words - it is vitally important that children can hear the word "three" (for example) and get a sense of the quantity that it represents.

Being able to associate each of the numbers from 1 to 10 with a sense of the size of the group it represents is the building block for learning maths. It will help the children get a 'feel' for the size of much larger numbers, which improves their ability to perform mental arithmetic efficiently and to estimate and check answers. It will also enable a smoother transition to being able to work with decimals and fractions, as you will be able to introduce them as a 'quantity' of less than one.

Early addition and subtraction will also come much more easily if a child has a real sense of quantity and therefore cardinality. If you ask a child to add 4 and 3, many children will start counting "1, 2, 3, 4" and then count on three more "5, 6, 7". This strategy works well, especially for small numbers, but it is much more efficient if the child realises that they can start with (a quantity of) 4 and then add 3 more to it. To begin with, they will realise that they can start at 4, but may still need to count on 3 more (5, 6, 7) before getting to the answer. However, this has already saved them half of the work. Eventually, they will be able to get straight to 7, either from being able to visualise it or from remembering number facts.

Tasks to develop an understanding of counting

Count physical objects in group sizes ranging from 1 to 10
Counting physical objects can be done anywhere and at any time. The more you do it with your children, and the more varied the objects you are counting, the more they will start to associate each of the numbers with a sense of how many there are.

A nice, early years task is to count lots of groups of objects that all contain the same quantity. In the Kiducation UK video below, we used the child's own toys in groups of five. We counted the objects by physically moving them across the table. This helps the child learn the sequence of number names but also allows them to associate each name with the quantity of objects they have moved. It also reinforce what 'five' really means. Each time before counting, ask the child to look at the group and tell you how many they have (they will probably just say "lots" or "not too many" or something of the sort but at least they are thinking about 'how many' there are). After counting ask the same question, reiterating that each of the groups contains five items. The child will start to get a sense of the 'fiveness' of five, as they can physically see and compare all the different groups that contain five items.

Develop understanding of cardinality
Using ten frames is a great idea. You can draw some or make your own. The idea is to ask children to represent numbers using counters; prompting them to consider the number as 'how many' counters they have placed in the ten frame. You can then ask the children  to match the visual representation to the correct numeral. This really helps the child to link the way we write a number to the physical quantity that it represents. It also encourages them to think of '5' (for example) as its own number, rather than as part of a sequence.

Practising to count and developing an understanding of cardinal numbers strongly links to other areas of maths, such as a addition and subtraction. If you give the child physical objects to add and take-away, it is a counting exercise but also develops their understanding of addition as combining two quantities and subtraction as taking one quantity away from another. The important point of this task is that it is the total that you are interested in. When you ask the child to tell you how many they have after adding two groups, they may count the objects (starting at 1) but they only need to tell you the total. If the child is able to understand this then they are beginning to understand cardinality. This, in turn, reinforces that numbers are used to represent quantities and that they are not just a sequence.

Counting by adding more than one each time (such as counting in 2s or 5s) is a great way for children to grasp that counting is not just a sequence of 1, 2, 3, 4, 5... . By counting in 2s, for example, children will notice that the pattern has changed. If they can associate this change in pattern with the fact that they are adding on a quantity of two (instead of one) each time, then they have some awareness that when counting they are actually naming quantities.

Practise number sequence from 1 to 10
Although it is important for children to realise that numbers are simply a way of naming (or writing down) a quantity, they do need to learn and memorise the names and the symbols that we use. They need to know the order in which the numbers appear and which numbers are one more, or one less than others. Because of the nature of our number system and how place value works, the most important numbers for kids to learn are the numbers from 1 to 10 (or 0 to 9).

Learning the names and symbols for the numbers from 1 to 10 can be achieved through constant repetition and practice. There are plenty of online games, apps and worksheets that are great for practising. Whenever possible, adults can also be counting with their kids: when dishing up dinner, buttoning a coat, walking up the steps, swinging on a swing, etc. . If they are used to it, kids will also automatically practise counting on their own. When counting, try to ask questions every now and again that require the child to consider numbers that are one more or one less. If they get used to doing this when counting, it will be easier for them to apply the concept when moving on to addition and subtraction. For example
• when doing up buttons, count out loud, 1, 2, 3 - then undo the last button and ask how many are still done up. The child will be able to associate the last one left done up as the one when you counted "two". They will also notice that this was the number that you said before you said "three".
• when going for a walk, count your steps (1, 2, 3, 4, 5) then ask the child how many steps you will have walked on the next step. They will then associate "six" with being one more than "five".
Tasks such as those above help children to develop an intuitive understanding of 'one less' being the number that you would count before and 'one more' being the next number along. It will also reinforce that numbers merely represent quantities and that you do not always have to count in ascending order from one.

Use pattern recognition to move on to larger numbers
Once kids have a strong grasp on counting from 1-10, and can comprehend the meaning of each number, they are ready to move on to higher numbers. An understanding of place value and the ability to recognise and repeat patterns will enable kids to make their own progression on to larger numbers. They will need help explaining their ideas and they will need to be given the names of new numbers (the teens, twenty, thirty, forty... ) but the rest should come naturally, with little instruction from a teacher. There are numerous tasks and activities for practising, including making number lines, filling in missing numbers, guessing what will come next and counting physical objects. I particularly like using an abacus to count to 100 (with a one to one value for every ball in every row) as it groups the numbers into tens, much like a number square.

Develop understanding of place value
Understanding place value is vitally important for many areas of maths including the ability to count to (and comprehend the size of) much larger numbers. Numbers are simply a way of keeping a record of 'how many' there are and place value plays an important role in how we keep that record. For a more detailed explanation of place value and ideas for tasks to develop understanding, please see my blog 'Understanding Place Value'.

I strongly believe that kids should learn that counting is a way of keeping a record of quantity and that numbers are simply a way of representing 'how many' there are. Children need to learn the order of numbers and how they are written, but learning to count is so much more than memorising a sequence. They need to learn how numbers are linked together and should be able to visualise (at least roughly) the size that each number represents.

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