Mr. Chen Shengshen once said, "What is mathematics? Mathematics draws conclusions through logical reasoning according to some assumptions. " Analogical thinking method is one of the most typical and useful mathematical reasoning methods. Analogical extension, analogical reasoning and analogical conjecture are the main forms of human abstract logical thinking. From the point of view of formal logic, analogy is based on the fact that two or two objects are the same or similar in some attributes, and one or the other is known to have other specific attributes. It is concluded that another object or another object also has this specific property. The solution to this problem is analogy. Its logical form can be expressed as follows: object A has attributes A, B, C and D; Object B has attributes A, B and C, so object B also has attributes D. Simply put, the structure of analogy method mainly consists of two parts: original image and class image or source and target. Using analogy thinking method can transfer knowledge and sublimate thinking. Based on this, the author uses the analogy thinking method to talk about their analogy extension, analogy reasoning and analogy conjecture in space with several vector conclusions in the plane for colleagues to discuss.

Analogical generalization of the basic theorem of 1 plane vector;

As we all know, there are two very important rules in plane vector addition and subtraction:

(1) triangle rule; (2) parallelogram rule; Using analogy extension, it is easy to get the addition and subtraction rules of two space vectors.

Conclusion: In senior high school mathematics teaching, we teachers should not only be good at using analogy, but also consciously train students in analogy, so that students can make analogy extension, analogy reasoning and analogy guess about the problems they encounter in their life and social practice, and find out the solutions to the problems. This will not only expand their thinking field, but also help to cultivate students' creative thinking and ability. Of course, analogy is sometimes a "double-edged sword". But as long as we think carefully, don't be far-fetched, and keep a high degree of vigilance against the negative transfer of analogy in the action sequence of solving problems, we can promote the "complete success" of solving problems.

refer to

1 Tian Fude. Two properties of triangle interior. Mathematical communication, 2007( 19)

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