Abstraction, reasoning and model are the most basic ideas in mathematics. From life to mathematics depends on abstraction, reasoning makes mathematics develop within the discipline, and model is the bridge between mathematics and life. In this way, abstraction points life to mathematics, and reasoning makes mathematics develop, and finally connects life with model.

Professor Shi Ningzhong said: We should look at the world from a mathematical perspective, think about the world with mathematical thinking and express the world with mathematical language. Mathematical vision is abstract, mathematical thinking is reasoning, and mathematical language is model.

This is abstraction. Mathematics is a science that studies quantitative relations and spatial forms.

Without other attributes of the organization, the abstraction is completed only by focusing on the number of objects.

There is such a text in the first grade Chinese of primary school-one big and one small, elephant and cat; One more and one less, a pile of apricots and a jujube. ...

The size in Chinese is somewhat different from that in mathematics. Perhaps, the child has not found the difference, or perhaps, the child already has the corresponding disciplinary thinking ability.

In Chinese, elephants are bigger than cats; In mathematics, through the one-to-one correspondence method, it is found that an elephant corresponds to a kitten, and the quantitative relationship is the same, and then it develops into the same size. This is abstract thinking.

In fact, strictly speaking, it should be like this-6 red flowers and 5 kittens. After one-on-one contact, it was found that there was more than one red flower, so the number of red flowers was more than that of kittens. This sentence is popularly translated into more red flowers than kittens, and then abstracted into 6 greater than 5, which is expressed in mathematical language as 6 > 5.

In fact, this cognitive process is a very long process in the development of human mathematics. In primary school children, this abstract situation may have been unconsciously completed in kindergarten, or passed on by parents.

However, to be sure, this kind of abstraction is incomplete and needs to be constantly experienced.

For example, from the point of view of expression quantity, one-half is equal, and when one-half expression rate is converted into specific quantity, there are different quantitative relationships.

Abstraction makes mathematics come into being in life, reasoning develops in disciplines, and models communicate mathematics with life. Think about it this way, mathematics is actually a bit complicated. ...