Современные информационные технологии и IT-образование (Mar 2023)
Development of Creative Qualities of Students when Performing a Multi-Stage Mathematical and Information Tasks "Newton's Method for Complex Polynomials"
Abstract
The proposed article describes the methodology for performing a multi-stage mathematical-informational task "Newton's Method for Complex Polynomials", aimed at developing the creative qualities of students. It notes creative activities that the student performs in the course of solving multifaceted problems. A scheme-plan for the implementation of a multi-stage mathematical and information task has been built. Examples of Julia sets of rational functions obtained by applying Newton's method to polynomials are given. The aesthetics of Julia sets are indicated, with the help of which students are invited to create artistic compositions. The integration of mathematics and programming is mentioned. The creative qualities have been identified, which are formed in students in the process of performing multi-stage mathematical and information task. When performing the tasks, students establish connections between iterations of rational functions of a complex variable and quadratic polynomials, discover for themselves Julia sets having complex fractal structure. They analytically calculate the fixed points of rational functions, determining their character. At the next stages, the study is visualized: with the help of a computer program, the orbits of the points of the studied functions and their Julia set are built. The introduction of color classification for different points allows you to get a more informative image of the fractal. The resulting image at the final stage is used to create some artistic compositions. The proposed method of function study makes it possible to develop flexibility of thinking, intuition, overcome stereotypes of thinking, develop aesthetic ideas, which positively affects the development of students' creative qualities.
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