A common research method, when the problem under study contains many possible situations, and people can't generalize it, it is necessary to discuss it according to all possible situations of the problem and synthesize the corresponding conclusions in each situation, so as to solve the problem (people often call it "case discussion method").

Principle of classification discussion: each level of classification is carried out according to the same standard; Classification should be gradual; Mutual exclusion at the same level, no leapfrog.

Classified discussion thinking

Every mathematical conclusion has its own conditions, and the use of every mathematical method often has its scope of application. Among the mathematical problems we encounter, some conclusions are not unique, and some conclusions cannot be studied in a unified form in solving problems.

The known quantities of some problems are given in the form of letters, so the different values of letters will also affect the solution of the problems. From the above problems, we can see that their problem-solving methods and transformation methods are consistent, that is, the problems studied are divided into several categories according to the characteristics and requirements of the topic and transformed into several small problems to solve. This mathematical idea of classifying according to different situations and then studying and solving them one by one is called classified discussion thought.