Related Content Extension: Definition and Development of Mathematical Concepts

Mathematical concept is a form of mathematical thinking, which reflects the quantitative relationship of real objects and the essential characteristics of spatial form. In mathematics, judgment and reasoning, as general forms of thinking, are expressed in the form of theorems, rules and formulas, and mathematical concepts are their basis. Correctly understanding and flexibly using mathematical concepts is the premise of mastering basic mathematical knowledge and operational skills, and developing logical argumentation and spatial imagination.

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.

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.

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