创造性数学思维中理解与预测过程交互作用的心理学

L. Moiseienko, L. Shehda
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引用次数: 0

摘要

通过对数学思维研究结果的分析,确定了数学思维的创造性。分析了创造性数学思维的研究成果,确定了在解决创造性数学问题时,研究理解和预测思维过程相互作用的心理本质的方便性。本文旨在探讨数学创造性思维中理解与预测思维过程相互作用的心理本质。为了研究数学思维中理解过程和预测过程的相互作用,采用分析不同班级学生在解决创造性数学问题过程中的搜索行为的方法。研究的结果。创造性数学思维是一个由相互关联的行为组成的完整系统,数学思维的结果是在这些行为的帮助下实现的。认识数学问题和预测思维结果的过程贯穿于求解数学问题的全过程。研究发现,以理解问题和预测思维结果为目的的搜索行为的内容取决于解决问题的各个阶段(研究条件、寻找解决方案、验证找到的解决方案),在这些阶段中,搜索行为的程序性和动态性不仅得到体现,而且正在形成。同时,理解创造性数学问题的过程和预测的过程是相辅相成的。确立了对问题条件的理解构成预测行为的内容,预测过程有助于对数学问题理解的形成。已经确定的是,在搜索数学过程中,不可能记录这样一种理解问题的状态,这种状态将确保出现关于解决方案的假设。研究发现,在整个搜索过程中进行的预测,可以在求解的不同阶段产生一个解假设,对数学问题的理解状态也不同。解决问题的假设是对问题理解状态的一个标志,它的认可有助于加深对问题本身本质的理解。同时,假设的内容,其认可程度决定了对问题的理解状态。结论。主体对创造性数学问题的理解过程和预测过程贯穿于解决过程的所有阶段,并且是相辅相成的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Psychology of the Interaction of Understanding and Forecasting Processes in Creative Mathematical Thinking
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 prob-lems 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 en-tire 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 un-derstanding 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 math-ematical problem and the process of prediction take place throughout all stages of the solution process and are mutually complementary.
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