Thinking Styles of Understanding Creative Mathematical Problems in the Process of Solving Them

Abstract

The results of research of creative mathematical thinking are analyzed and the expediency of studying its individual differences through the analysis of mental styles of solving mathematical problems is stated. The aim of the article is to identify thinking mathematical styles of students and to analyze the influence of style on the process of understanding the creative mathematical problem. For identifying and determining the essence of mathematical thinking styles, the method of analysis of search actions of subjects during the solution of mathematical problems of different classes was used. The experiment involved 100 students of a technical university, 1000 processes for solving mathematical problems were analyzed. The results of the research. It is stated that mental mathematical style is a holistic system of interconnected actions, by means of which the mental mathematical result is achieved, which distinguishes the activities of one person from another one. The authors identify three thinking styles in creative mathematical process of students: the differential, the integral and the differential-integral. It is established that the thinking style is manifested during all processes micro-stages of understanding. It is proved that the different thinking mathematical styles lead to the formation of different purports of the same problem. It is established that unconscious mental guesses have different meanings in the process of understanding a mathematical problem by students with different styles of mathematical thinking. Conclusions. Thinking mathematical style is manifested throughout the process of understanding a mathematical problem, provides a different content of the search process aimed at understanding a mathematical problem.