Connecting with actual things or objects, introducing models and making materialistic explanations of concepts Engels pointed out that "the concepts of number and shape are not found elsewhere, but come from the real world."
Introduction of concepts by analogy? Analogy is not only an important form of thinking, but also an important method to introduce concepts. Take my teaching as an example: when I talk about the introduction of the basic nature of fractions, I guide students to recall the basic nature of fractions through specific examples, and then draw inferences.
Introduce new concepts on the basis of students' original? In the definition of concept, there is a definition called genus plus species difference definition. The connotation of this concept has been exposed in the definition of general concepts.
Introduce concepts from the inherent needs of mathematics itself? In the development of students and mathematics in human history, the concept was introduced in the constant demand. For example, at the beginning, human beings didn't have the concept of counting, so they counted by tying a rope. The introduction of the concept of natural number solves the problem of counting, but natural number can not be satisfied in subtraction, so negative number is introduced.