Methods: Establish the concept of space and improve the imagination of space. There is a complete process from understanding plane graphics to understanding three-dimensional graphics as flying over. Some students make some geometric models of space by themselves and observe them constantly, which is helpful to establish the concept of space. It is a good method. Some students have time to observe and speculate on some three-dimensional figures, distinguish the line, surface line and all-round position relationship among them, and explore various angles and vertical lines, which is also a good way to establish the concept of space.

According to the results of combining practice, observing three-dimensional model or comparing plane geometry, the questions are clearly put forward; There is no need to doubt or deny the explicitly raised question, but it needs to be tested with some sufficient and necessary conditions. It is best to ensure that the following examples are negative and confirmed, and there is no doubt. The content of Euler formula is provided in the form of research topics, from which we can feel and cultivate mathematical thinking methods.

By structural types, we mean from the whole to the part, from high-rise residential buildings to low-rise buildings, understanding and learning professional knowledge, and understanding the concepts and methods implied therein. The so-called specialization refers to the concentration of parallel plane, vertical plane, angle, spacing, uniqueness and other similar issues, and the comparison of their differences to get a general understanding. Special attention should be paid to accumulating countermeasures to solve difficulties. For example, the problem of high school solid geometry is transformed into a plane, or the problem of finding the distance between a point and a plane, or the problem of finding the distance between a parallel line and a plane, and then finding the distance between a point and a plane; Or converted to volume.

The concrete content of parallel lines and planes is the basis of solid geometry in senior high school. A shortcut to learn this part is to confirm the law of hard study, especially some core laws. For example, the three vertical theorems. The content of the law is very simple, that is, the discussion of the relationship between lines, lines and surfaces, and surfaces. The legal documents are generally more complicated or even abstract in the process of leaving school.