One thing, one word
How Does Counting Work?
Counting is matching each object to exactly one number word, in order.
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Step 1 of 5
Rule one: one word per object.
Every object gets exactly one number word. Skip an object and you undercount; say two words for one object and you overcount.
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Step 2 of 5
Rule two: always the same order.
Any words would do, so long as everyone uses the same ones in the same order. One, two, three, four — the words must come in the same order every time. This is why children chant the sequence long before they can use it.
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Step 3 of 5
Rule three: the last word is the answer.
Counting five apples, the answer is not the whole chant — it is the final word, five. Young children often miss exactly this step.
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Step 4 of 5
The order you count in does not matter.
Count the apples left to right, or right to left, or scattered about — you always get five. The total belongs to the group, not the path.
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Step 5 of 5
You can count anything.
The rules do not care what is being counted Objects, steps, sounds, days, even things you cannot see. This is why counting is powerful — the rules do not care what is being counted.
Some languages have counting words only up to three, then 'many'. The rules still work — the vocabulary just stops.
The short version
One word per object, always in the same order, and the last word is the answer — that third rule is the one young children miss. The path does not matter: the total belongs to the group, not to the route you took through it.
Try it yourself
Count a handful of coins, then shuffle them and count again. The total is the same however you move them.