Development of Creative Qualities of Students when Performing a Multi-Stage Mathematical and Information Tasks "Newton's Method for Complex Polynomials"

DOI: https://doi.org/10.25559/SITITO.019.202301.141-151

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.


 


Author Biographies

Valeriy Sergeevich Sekovanov, Kostroma State University

Head of the Chair of Applied Mathematics and Information Technology, Institute of Physics and Mathematics and Natural Sciences, Dr. Sci. (Ped.), Professor

Vladimir Anatolyevich Ivkov, Kostroma State University

Associate Professor of the Chair of Applied Mathematics and Information Technology, Institute of Physics and Mathematics and Natural Sciences, Cand. Sci. (Econ.), Associate Professor

Alexey Alexandrovich Piguzov, Kostroma State University

Associate Professor of the Chair of Applied Mathematics and Information Technology, Institute of Physics and Mathematics and Natural Sciences, Cand. Sci. (Ped.), Associate Professor

Larisa Borisovna Rybina, Kostroma State Agricultural Academy

Associate Professor of the Higher Mathematics Department, Cand. Sci. (Philos.), Associate Professor

Irina Vadimovna Shaposhnikova, Surgut State University

Associate Professor of the Chair of Applied Mathematics, Cand. Sci. (Eng.)

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Published
2023-03-30
How to Cite
SEKOVANOV, Valeriy Sergeevich et al. Development of Creative Qualities of Students when Performing a Multi-Stage Mathematical and Information Tasks "Newton's Method for Complex Polynomials". Modern Information Technologies and IT-Education, [S.l.], v. 19, n. 1, p. 141-151, mar. 2023. ISSN 2411-1473. Available at: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/945>. Date accessed: 16 sep. 2025. doi: https://doi.org/10.25559/SITITO.019.202301.141-151.
Citation Formats
Issue
Vol 19 No 1 (2023): Modern Information Technologies and IT-education
Section
Educational resources and best practices of IT Education
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