Zhuangzi said, "Those who can do it are skilled." Stripping off or gorgeous technical "coat", we will see one of their gods-understanding of mathematical concepts. The weighted average algorithm is not difficult for students, just imitate the program. The difficulty lies in why this calculation is done and what value it has. It can be said that all participating teachers design and organize teaching based on these two points, with different designs and unified ideas. Usually, if the understanding of "weighted average" does not reach a certain depth, it is likely that the classroom will become a variant training for students, which runs counter to the inheritance of mathematical spirit.

There is a saying in The Doctrine of the Mean: "Be profound". Mathematical understanding should also be manifested in the macro-construction and micro-exploration of mathematical knowledge. First, pay attention to the process of knowledge occurrence and development, so that knowledge can come alive; Second, we should pay attention to the classification, organization and structure of knowledge to make it orderly; Third, we should pay attention to the horizontal and vertical connection of knowledge, so that knowledge is connected; Fourth, we should pay attention to the "life background" of knowledge and the "mathematization" in life, so as to apply what we have learned from books.

2. Educational concept. Borrow Felix Klein's point of view: Only when the point of view is high can things be clear and simple. Felix Klein also made it clear that "the duty of a math teacher is to make students understand that mathematics is not an isolated subject, but an organic whole." In teaching, "we should pay attention to the relationship between different branches and contents of mathematics, the relationship between mathematics and daily life, and the relationship between mathematics and other disciplines"; Attention should be paid to analyzing the relationship between a unit and a learning section and establishing a network structure diagram. If we can build a "pyramid" structure diagram, the level will be higher; To look at the teaching content from a height, "a competent teacher should master or understand various concepts and methods of mathematics, the process of its development and perfection, and the evolution of mathematics education"; It is necessary to design a unit or even a period of teaching ideas as a whole. For example, in the initial class and review class, a link similar to "introduction" or "overview" is designed to let students have an overall understanding of the knowledge structure, learning content and research methods of a chapter, which can not only stimulate learning enthusiasm, but also improve learning efficiency. However, this observation, although it is also a beginner's class, has not seen the clue, which is regrettable.

Students' learning is a dynamic and continuous process. Students' understanding of mathematics, in a sense, corresponds to the historical process of human cognition of mathematics. Of course, it is by no means that students' cognition should repeat the cognition of human beings in history. Instead, we should teach students according to their cognitive laws, including age and maturity, do the right thing, and stop when it is right; When it is detailed, it is detailed, and when it is slightly, it is slightly; Do not overstep, do not mourn; No mistakes, no mixing. A popular saying is "What mountains sing what songs."

3. Humanistic spirit. Professor Morris Klein, the author of Ancient and Modern Mathematical Thoughts, believes that "the overall characteristics of an era are closely related to the mathematical activities of this era." Mathematics is not only a tool, but also a spirit and a culture. Mathematics has been the main cultural force of human civilization since ancient times, and a history of mathematics is also a person.