"Analogy is a great guide" (Paulia, a math educator). Analogy is to transfer the properties and methods of one object to another through the similarity between two objects, so it is a reasonable reasoning from one object to another and an unconventional and free association. Analogical reasoning is an important way of rational reasoning. It has gradually become the focus of attention of mathematics proposers in the college entrance examination. In order to help teachers and students better understand and master the effective ways of rational reasoning, this paper makes a simple classification example of three college entrance examination questions involving analogical reasoning in recent years, hoping that front-line teachers and students can get some enlightenment from it.

Comments: This question is a test question for reasoning and exploring problems through reverse analogy. On the condition of the correct conclusion of the problem, a new problem can be obtained, which is called the "inverse" problem. In fact, the reverse exploration of the relationship between conditions and conclusions is the essence of this problem. When answering this question, make full use of the reasoning method of reverse thinking, explore and put forward a question, and then make a correct answer, which embodies the research mode of asking and solving problems. Facts have proved that raising a problem is more meaningful and valuable than solving a problem. It is worth noting that the scoring standard of this question is very special, and it is no longer based on correctness as the only principle, but on the "quality" of the self-made proposition.

Conclusion: Analogy is a creative imitation and a leap of thinking from one thing to another. In the teaching of open questions, guiding students to compare their own questions with familiar information and make multi-directional association can extend, popularize or transfer the substructure of formulas, algorithms, problem-solving methods and conclusions, explore the unknown from the known and explore new knowledge from the old knowledge, which is conducive to cultivating students' innovative thinking ability.

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