Psychological Aspects of Activating the Approbation Process of Creative Mathematical Thinking
Authors:   Ivano-Frankivsk National Technical University of Oil and Gas, Moiseienko Lidiia , Shehda Liubov ,   Ivano-Frankivsk National Technical University of Oil and Gas
Published: December 2024

The purpose of the article is to find out the potential influence of cause and effect questions on the approbation process of creative mathematical thinking in order to activate it.
Methods of the research. According to the results of the analysis of re­search on creative mathematical thinking, it was established that the explor­atory mathematical process is the process of setting and solving a mathematical problem. It was found that the approbation of thinking results accompanies the solution of the problem at all its stages. It is emphasized that the process of solving a creative problem is determined by the performance of algorithmic and heuristic methods, which can and should be formed. They should contribute to the production of various ideas, their qualitative examination and selection.
The results of the research. It was established that the psychological es­sence of the approbation actions of mathematical thinking is the comparative interaction of the knowledge obtained during solving the problem with the existing subjective knowledge system.
The use of a wide range of cause and effect questions when solving creative mathematical problems is established to activate the components of the search process: understanding the problem, predicting solution ideas, approbation of thinking results, turns them into complementary ones.
The approbation actions are found to have different content and psycho­logical significance at different stages of solving mathematical problems.
It was found that special questions ensured the actualization of existing knowledge, experience, and skills, the flow of associations, imagination, which contributes to deepening the understanding of the meaning of a mathematical problem and actualizes approbation actions.
It has been established that there is a significant activation of approba­tion actions when forming a solution to a mathematical problem. Under the influence of special questions, the structural elements of the task are modified, which requires the study of their properties and functional capabilities.
It is proven that the acquired experience of accompanying the search pro­cess with questions turns the approbation of the solution project into a subjec­tively meaningful process aimed at comparing the parameters of the solution hypothesis with the parameters required in the mathematical task.
It was found out that in such conditions, knowledge is formed about a suf­ficient level of inspection quality and the skill to necessarily introduce it into the search process is developed.
Conclusions. Activating a wider range of thinking actions, the acquired skill of forming numerous questions changes the depth and quality of approbation actions that take place throughout the entire solution of mathematical prob­lems, forms the ability to analyze and control one’s own thinking steps, contrib­utes to the formation of subjective confidence in the correctness of the solution found.