Psychology of the Interaction of Understanding and Forecasting Processes in Creative Mathematical Thinking
DOI:
https://doi.org/10.32626/2227-6246.2023-59.118-134Keywords:
creative mathematical thinking, understanding of a mathematical problem, prediction of thinking resultsAbstract
Based on the results of the analysis of research on mathematical thinking, its creative nature has been ascertained. The results of research on creative mathematical thinking were analyzed and the expediency of studying the psychological essence of the interaction of thought processes of understanding and forecasting when solving creative mathematical problems was ascertained.
The aim of the article is to find out the psychological essence of the interaction of thought processes of understanding and forecasting in creative mathematical thinking.
To study the interaction of the processes of understanding and forecasting in mathematical thinking, the method of analyzing students’ search actions during solving creative mathematical problems of different classes was used.
The results of the research. It was established that creative mathematical thinking is a complete system of interrelated actions, with the help of which the thinking mathematical result is achieved. It was established that the processes of understanding mathematical problems and predicting thinking results function throughout the entire process of solving mathematical problems. It was found that the content of search actions aimed at understanding the problem and predicting thinking results depend on the stages of solving the problem (study of the condition, search for a solution, verification of the found solution), in which their procedural and dynamic side is not only manifested, but is also being formed. At the same time, the process of understanding a creative mathematical problem and the process of forecasting are complementary. It is established that the understanding of the condition of the problem forms the content of forecasting actions, and the process of forecasting contributes to the formation of understanding of the mathematical problem. It was established that in the search mathematical process it is not possible to record such a state of understanding of the problem that would ensure the emergence of a hypothesis regarding the solution. It has been found that forecasting, which takes place throughout the entire search process, can generate a solution hypothesis at different stages of the solution, with different states of understanding of the mathematical problem. The hypothesis of solving the problem is an indicator of the state of understanding of the problem, and its approbation contributes to deepening the understanding of the essence of the problem itself. At the same time, the content of the hypothesis, its approval determines the state of understanding of the problem.
Conclusion. The process of the subject’s understanding of a creative mathematical problem and the process of prediction take place throughout all stages of the solution process and are mutually complementary.
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