(1) is conducive to the systematization, systematization and generalization of the learned knowledge, making the learned knowledge clear, focused and easy to remember;

(2) is conducive to improving the ability to solve problems;

③ It is helpful to deepen the understanding of mathematical knowledge and master the methods of analyzing, summarizing, sorting out materials and studying problems;

(4) It is beneficial to cultivate their interest in learning, thus improving their thinking quality and gradually forming good study habits.

For example, when learning to analyze the "straight line" in geometry, how to prove that "three points are on a straight line" on the surface of a nail can be summarized in the following ways:

① Find the distance between two points on the plane so that AB = BC+CA;

(2) Using the constant fraction point formula, when one point is used as the constant fraction point of the other two points, the г value obtained by substituting the abscissa in the line segment constant fraction point formula is equal to the г value obtained by substituting the ordinate;

(3) First, find the linear equation of any two points, and then verify that the third point is on a straight line;

(4) the slopes of any two connecting lines are equal and both pass through the same point, such as KAB=KBC, and both straight lines pass through point B;

⑤ First solve the linear equation of any two points, and then verify that the distance from the third point to this straight line is 0. In this way, we can infer what we have learned. This kind of training of multi-solution ability is of great help not only to our study in school, but also to our society, which can urge us to use our brains when encountering difficulties and properly solve every specific problem.