Development of Thinking Flexibility of Students when Calculating the Feigenbaum Constant Using Information and Communication Technologies

Abstract

The proposed article examines the methodology for developing students' thinking flexibility by combining various approaches to the implementation of educational mathematical tasks. The problem of calculating the Feigenbaum constant using symbolic dynamics and using Newton's method is considered. Mathematical models of the computational process are being built. Algorithms and their implementation in the programming language are presented. It is shown that when solving the problem by different methods, we come to the same result. It is assumed that when solving the problem, students are interested in both mathematical research methods and their implementation using programming tools. Flexibility of thinking is formed by combining analytical mathematical research and computational algorithms implemented on a computer. The proposed methodology for conducting training sessions was considered by the authors earlier in the implementation of the implementation of multi-stage mathematical and informational tasks. At each stage of solving the problem, the student can feel himself both in the role of a mathematician-researcher, and in the role of a mathematician-programmer, experimenter. Such integration of mathematical methods and information and communication technologies provides an opportunity to organize creative mathematical and creative information activities of students, aimed at the formation of flexibility of thinking and creative qualities.

Keywords

• creativity
• flexibility of thinking
• feigenbaum's constant
• symbolic dynamics
• point orbit
• newton's method