In order to understand and form a mathematical concept correctly, we must make clear the connotation of this mathematical concept-the characteristics and extension of the "quality" of an object-the scope of the "quantity" of an object. Generally speaking, mathematical concepts reveal their essential characteristics in the form of definitions. But before that, there is a stage of understanding through examples, exercises and oral descriptions. For example, children's understanding of natural numbers and operation results-sum, difference, product and quotient is like this. In the senior grade of primary school, a mathematical concept, that is, the way of defining scores and proportions, began to appear in the text. Some mathematical concepts, such as functions and limits, have to be brewed for a long time before they can be finally expressed in the form of definitions. Definition is a way to accurately express mathematical concepts.

Many mathematical concepts need to be represented by mathematical symbols. For example, dy represents the differential of function Y, and mathematical symbols are a unique way to express mathematical concepts, which plays a great role in students' understanding and forming mathematical concepts. It simplifies and clarifies the thinking process of students mastering mathematical concepts. The definitions of many mathematical concepts are expressed by mathematical symbols, thus enhancing the scientific nature.

Many mathematical concepts also need to be represented by graphics. Some mathematical concepts are graphics themselves, such as parallelogram, pyramid, hyperbola and so on. Some mathematical concepts can be represented by graphs, such as the image of y=x+ 1 Some mathematical concepts have geometric significance, such as the differentiation of functions. The combination of numbers and shapes is another unique way to express mathematical concepts, which visualizes and quantifies mathematical concepts.

In a word, mathematical concepts are gradually formed and developed in the process of human historical development.