Abstract: This is an experimental study on thinking flexibility or divergentthinking in mathematical operation in schoolchildren in combination of crossresearch with vertical research.The study shows: 1. In the development of thinking flexibility of operation in school-children, the factor of age characteristics is demonstrated, but it developssteadily, that is, no critical period was found in this study. 2. Thinking flexibility of operation develops in eduction. Good teachingmeasures in mathematics can develop thinking and improve the quality ofmathematical teaching. 3. Divergent thinking is a generalization process. Divergent thinkingand convergent thinking are both aspects in the process of dialectical unityof thinking. Convergent thinking is a basis of divergent thinking; divergentthinking is the development of convergent thinking, both of them areimportant in teaching practice.

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