The construction of the number: a more complex learning than a recitation of the numerical sequence.
When we speak of the construction of numbers, we are talking about the construction of the concept as a whole and this construction inevitably involves manipulation.
The child needs to take objects and move them to build up collections of quantities requested and gradually understand that any number is obtained by adding 1 to the previous number. And it is not because he knows the sequence of numbers up to 50 that the child has constructed this notion, because it is only a simple memorization, important but not sufficient.
Learning to count :
The child will start by counting small quantities: 1, 2 and 3 , then up to 6 and next up to 10.
The child has a great tool to build the number: his hand. And if, as he grows older, he will be asked to become capable of no longer relying on his fingers, it remains an essential tool in kindergarten to build a mental image of the quantities and complements that will then be used greatly for mental calculation (5 is 3 and 2; 10 is 5 and 5...).
And so before knowing how to associate numbers with quantities, the child will count by associating a quantity with a number of fingers represented or with points using the arrangement of the dice.
He will train to build growing collections by adding 1 more object each time.
And he will also make collections corresponding to a requested quantity using different strategies: recitation of the digital nursery rhyme by pronouncing the number for each object placed, or the term to term correspondence which consists in showing the fingers one by one by placing an object at the same time each time.
The difficulty of counting often lies in not counting objects one by one. The child counts too quickly, counts twice the same object or forgets one or more, while knowing very well how to state the sequence of numbers most often. And the larger the quantities requested, the greater the risk of errors.
The construction of mental images of quantities :
The first counting images constructed by the child are those that make it possible to quickly quantify a group of objects by evaluating the quantity as a whole: a little, a lot... Gradually, as the child manipulates, he will fix mental images of the quantities that he will become able to recognize spontaneously: he will be able to show three fingers and recognize the quantity 3 without counting the objects one by one.
This step is important because it will then allow him to proceed with the overcount: add 2 to 4 for example without recounting the first 4 objects but simply counting 5 then 6.
Gradually, the child will build an image of numbers up to 10, a fundamental acquisition since he will then be able to understand the principle of our base 10 numbering: make packets of 10 to build 100, then 1000 etc... And he will understand in parallel the principle of writing numbers in numbers: 10 is a packet of ten objects and zero objects next to it, so it is about ten and zero units.