Mathematical language, as the universal language to express scientific thoughts and the best carrier of mathematical thinking, contains many contents. Among them, narrative language, symbolic language and graphic language are more prominent, with the characteristics of accuracy, strictness and conciseness. Because mathematical language is a highly abstract artificial symbol system, it often becomes a difficult point in mathematics teaching. Some students are afraid of mathematics, on the one hand, because the language of mathematics is difficult to understand and learn, on the other hand, teachers don't pay enough attention to the teaching of mathematics language and lack training, which makes them unable to master it accurately and skillfully. Now the author talks about his own understanding according to the characteristics of mathematical language and mathematical requirements. Ordinary language is the language used in daily life, which is familiar to students, and the things expressed are friendly and easy for students to understand. The learning of any other language must take the common language as the interpretation system. The same is true of mathematical languages. Through the mutual translation between the two languages, the abstract mathematical language can be used for reference in real life, so that it can be thoroughly understood and used freely.

"Mutual translation" has several meanings:

First of all, it refers to the transformation of ordinary language into mathematical language (that is, mathematization)

For example, equations turn the conditions of literal expression into mathematical symbols, which is a necessary procedure to solve practical problems by using mathematical knowledge.

The concepts of mapping and function are gradually abstracted from concrete correspondence, and the understanding of abstract mathematical language is internalized with the help of common language or concrete examples, such as constructing examples of mapping and function according to their definitions;

The second is to translate mathematical language into common language.

Mathematical practice tells us that if students can retell the definition of the concept and explain the essential attributes revealed by the concept in popular language, then their understanding of the concept will be profound. Because mathematical language is an abstract artificial symbol system, it is not suitable for oral expression, so it is only convenient to communicate if it is translated into ordinary language.

Thirdly, the transformation between different forms of mathematical languages.

Such as natural language representation, symbolic language representation and Wayne diagram representation of sets. Another example is that the function y=f(x) is on [a, b].

"Mutual translation" helps to stimulate students' interest in learning, deepen their understanding of the essence of mathematics and enhance their ability to distinguish. The process of mutual translation embodies the dialectical thought of unity of opposites, which is helpful to the transformation of different concepts and the reduction of problems.

Pay attention to the learning process of mathematics language and arrange teaching reasonably.

The formation of mathematical concepts and symbols generally includes three links: logical process, psychological process and teaching process.