1, written language: It is accurate and standard to describe mathematical concepts, theorems and problems in written form. For example, in mathematics textbooks, theorems are usually presented in written language, and students need to understand and master the concepts and theorems expressed in these words.

2. Symbolic language: mathematical symbols are used to represent mathematical concepts, theorems and problems, which are concise and abstract. For example, in mathematics textbooks, formulas are usually presented in the form of symbolic language, and students need to understand and master the meanings represented by these symbols.

3. Graphic language: using graphics to represent mathematical concepts, theorems and problems is intuitive and vivid. For example, in mathematics textbooks, geometric figures are usually presented in the form of graphic language, and students need to understand and master the characteristics and properties of these figures.

4. tabular language: use tables to express mathematical data and relationships, which is intuitive and comparative. For example, in mathematics textbooks, statistical charts are usually presented in tabular language, and students need to understand and master the data and relationships expressed in these tables.

The main forms of mathematical language in compulsory education;

1, Accuracy: Mathematical language must be accurate, clear and concise, and vague and ambiguous expressions should be avoided. For example, when describing geometric figures, it is necessary to use mathematical terms and symbols accurately to ensure the accuracy of the language.

2. Logic: Mathematical language needs to follow logical principles, and reasoning and proof must be rigorous and convincing. In mathematics, every conclusion needs a clear derivation process and basis, and there can be no jumping or fuzzy inference.

3. Simplicity: Mathematical language should be concise and clear, avoiding tedious expression. The use of mathematical symbols and formulas can make the language more concise and improve the accuracy of expression.

4. Abstraction: Mathematical language is abstract, which requires students to have certain abstract thinking and logical reasoning ability. For example, in algebra, letters can represent any number, which requires students to understand abstract algebraic concepts.

5. Symbolization: Symbolization is widely used in mathematical languages, such as variables, functions and sets. These symbols have specific meanings and laws, and students need to understand and use them correctly.

6. Visualization: Mathematical languages are often expressed in combination with images, such as plane geometry and solid geometry. Images can help students better understand mathematical concepts and problems and improve their spatial imagination.