Problems with the Requirement to “to Prove” as a Training of Creative Mathematical Thinking

Abstract

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 has been found that questions activate the mental actions of both those who ask them and those who answer them. It is emphasized that the process of solving a creative problem is determined by the performance of algorithmic and heuristic techniques that can and should be developed. They should contribute to the production of various ideas, their qualitative examination and selection. The aim of the article research. To analyze the potential possibilities of the experience of solving problems with the requirement to “to prove” with the active use of cause and effect questions to activate creative mathematical thinking. For this purpose, the method of analyzing students’ searching actions while solving creative mathematical problems was used. The results of the research. It was established that the application of a wide range of questions in the process of solving creative mathematical proof problems activates thinking components: understanding the problem, predicting solution ideas, approbation of thinking results, which become more complementary. 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. It was established that predictive thinking actions, which under the influence of special questions generate a high-quality leading idea for solving the problem, contribute to filling it with content due to the active mental modification of structural elements, the emergence of thought new formations. The possibility of forming the skills of a critical attitude to various kinds of thinking discoveries with the help of their approbation with special questions has been proved. This becomes the basis for building a clear logical chain of reasoning from what is given to what needs to be proved in proof tasks. Conclusions. Solving mathematical proof problems with the active use of cause and effect questions activates creative mathematical thinking.