Стратегія реконструювання як мисленнєвий механізм розв’язування творчої математичної задачі

Abstract

The article deals with the issues of psychological essence of mechanisms forsolving a creative mathematical problem.According to the results of the analysis of research in mathematical thinking,its creative character has been stated and an approach to its study hasbeen identified through the analysis of dominant mental activities in solvingcreative mathematical problems. The author has distinguished three componentsof the process: the process of understanding, the process of forecastingand approbation process. It has been established that reconstructing actionsoccur throughout all components of the process of creative mathematicalthinking, and the analysis of reconstructing in such processes has been carriedout.It has been found out that in some cases the mental actions of reconstructingbecome mental tendencies and can take place during either one processcomponent or several components, turning into prevailing mental trends,and lead to the effectiveness of the search process. The emphasis has been puton the significance of subjective confidence in quality of the obtained result, inpossibility of reconstructing of mental actions with the use of reconstructing.It has been proved that in case when the tendency for reconstructingprevails throughout all the process components and the subject receives thesubjective confidence in the correctness of his actions, this tendency is transformedinto a mental strategy of reconstructing, which provides a positive resultof the mental search process aimed at solving a creative mathematicalproblem.