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Why do you say that children's mathematics begins with actions and gradually internalizes into mental arithmetic?
This is the research result of Piaget's theory of stages of children's cognitive development. Mathematics is the gymnastics of thinking. The development of children's thinking at the age of 0-2 needs to start with motion perception, and children at the age of 2-5 need to think with objects or images. At the age of 5-7, it gradually transits to abstract logical thinking, and at the age of 7- 12, it continues to develop logical thinking, which is called mental arithmetic.