前操作的思考 IV：数

Piaget's preoperational stage of cognitive development spans from ages 2 to 7. It is marked by the growth of symbolic thinking but is limited in logical reasoning.

During this stage, an understanding of numbers also develops.

Children younger than three can recite numbers up to six when counting, but often fail to grasp that the last number counted represents the total.

Around three to five years, the cardinality principle emerges.

This principle states that the last number counted represents the total number of items in the set.

Similarly, children who grasp this principle recognize that zero is less than one. They may refuse to give an object when "zero balls" is asked.

By age 4, they can compare heights and know that getting another cookie means having more than before.

By age 5, they can count to 20 or beyond and understand the relative number sizes from 1 to 10.

Lastly, most children develop basic number sense by elementary school, like counting and simple addition and subtraction.