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Abstract: The subjects of the study were 174 pupils from four classes of the first year primary school, second semester. It took a whole semester time to observe systematically and test the features of their mental process of analysis and synthesis, and the periodic sense of its development as they were working out the two-step applied problems. The primary result of the study indicates that the whole process of its developments is of the following stages:1. When they proceed from one-step to two-step problems, they are short of the ability in analyzing the objects of the later. It is indicated as they are often confused by the two types of problems.2. When they have overcome the contusions encountered in the first step, they begin to be able to analyze and synthesize some of the explicit features of thé two-step problems. However, they are still not able to comprehend fully the subject matter of the problem.3. At this step of the simple type problem exercises, they are able to analyze and synthesize the subject matter of the one type problems. But they are not able to fulfil the requirement for the composite manipulation of the multiple problems.4. Having comparatively acquired the ability of differentiating and generalizing the subject matter of all types of problem exercises, pupils begin to be able to handle it in dealing with composite problems.Generally speaking, all pupils have gone through the different stages as described above, but the time required for each pupil to get over each stage and whether they have expressed themselves outwardly or not, all depends on the conditions of classroom instructions and the talents of the individual pupils respectively.

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