### 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".

__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'.

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