5 Fun Ways to Teach Counting to Preschoolers

Almost every three-year-old can chant to ten. A good proportion of them cannot put out four biscuits when asked. Those two facts sit awkwardly together, and the gap between them is the whole of early counting — reciting the number sequence is a memorised song, and using it to find out how many is something quite different.

Understanding which of those your child can actually do changes what is worth practising, and it is easy to check. Put out five objects and ask how many. Watch what happens.

The four things counting is made of

Researchers break early counting into a handful of principles, and they arrive in roughly this order. Knowing them makes it obvious where a child is stuck.

• The number word order — one, two, three, four in a stable sequence. This is the chanting, and it comes first.
• One-to-one correspondence — exactly one number word for each object, no skipping and no double-counting. Usually three to four.
• Cardinality — the last number you said is the answer. Around four to five, and it is the one most often missing.
• Order irrelevance — it does not matter which object you start with, or how they are arranged. Later still, and it is what lets a child trust their own count.

The cardinality test is the most useful thing in this article. Ask how many, let your child count them, then ask how many again. A child who has cardinality repeats the total. A child who has not counts the whole lot again — because to them, the question is an instruction to count, not a request for a number.

Touch, move, say

The fix for one-to-one correspondence is physical. Counting things a child can pick up and move to a different pile is dramatically easier than counting things fixed on a page, because moving each object is what stops them being counted twice. Buttons, grapes, bricks, coins, steps.

When you finish, say the total out loud as a conclusion rather than leaving it hanging: one, two, three, four — so there are four. That single sentence, repeated over weeks, is what builds cardinality, and almost nobody says it.

Subitising, and why it matters more than counting

Show a child two sweets and they know it is two without counting. Three, usually. Four, sometimes. That instant recognition of small quantities is called subitising, and it turns out to predict later mathematical ability better than counting ability does.

It is also easy to practise. Flash a handful of objects and cover them — how many did you see? Roll a dice and name the pattern without counting the dots, which is why dice and dominoes are genuinely good maths equipment. Children who recognise a dice five as five, rather than counting five dots, have something that makes all later arithmetic quicker.

Counting on, and the five anchor

Watch how your child answers when there are five bricks and you add two more. If they start again from one, they are counting all. If they say five, six, seven, they are counting on — and that is the step that turns counting into arithmetic. It generally appears around five or six and it is worth prompting when you see the chance: you know there are five here, so how many altogether?

Five is the natural anchor for this because it is the fingers on one hand, which is also why fingers are worth encouraging rather than discouraging. A child's hand is their first number line, and it falls away by itself once the facts are secure. Nobody ever stayed on their fingers because they were allowed to use them.

Ways to count that are not counting practice

• Stairs, every single day. Going up counts forward and coming down counts backwards, which is considerably harder and rarely practised.
• Laying the table — how many people, so how many forks. That is one-to-one correspondence with a real purpose, which is the best kind.
• Snacks. Ask for three grapes and count them out. Miscounting has an immediate and keenly felt consequence.
• Board games with a dice. Moving a counter the right number of squares is one-to-one correspondence, and reading the dice is subitising.
• Countdowns to anything — blast-off, bath time, the end of a turn. Counting backwards is genuinely harder than forwards and this is the only context in which children volunteer for it.
• Sharing things out fairly between two people, which is early division and something children care about intensely.

The numerals come last

Recognising the written symbol is a separate job from understanding the quantity, and it is the less important of the two. A child who understands that four means four things but cannot read the numeral is in a much better position than one who can read every numeral to twenty with no sense of what they mean.

When you do introduce the symbols, put them next to the amount. Lay the numeral card down and put that many objects beside it. The connection between symbol and quantity does not make itself.

What not to do

Do not push counting past ten before the first ten are solid. The teens are irregular and confusing in English — eleven and twelve give no clue at all, and thirteen puts the three first — so a child who has raced to thirty has usually memorised a longer song without understanding any more of it.

And do not correct every miscount. A four-year-old who counts five objects as six has still done four of the five things right. Recount it together cheerfully rather than marking it wrong, because a child who has decided that counting is something they are bad at is a much harder problem than a child who counts inaccurately.