26
Valeriy S. Sekovanov
Kostroma State University
Vladimir A. Ivkov
Kostroma State University
Larisa B. Rybina
Kostroma State agricultural Academy
Yuliya A. Sobashko
Kostroma State University
Performing a mathematical and informational task “Research of the dynamics of rational functions of a complex variable as a means of developing students' creativity”
Sekovanov V.S., Ivkov V.A., Rybina L.B., Sobashko Yu.A. Performing a mathematical and informational task “Research of the dynamics of rational functions of a complex variable as a means of developing students' creativity”. Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics, 2020, vol. 26, № 4, pp. 187-195 (In Russ.). DOI https://doi.org/10.34216/2073-1426-2020-26-4-187-195
DOI: https://doi.org/10.34216/2073-1426-2020-26-4-187-195
УДК: 378:81
Publish date: 2020-10-04
Annotation: Multi-stage math and information tasks for students are a kind of creative laboratory in which they show their abilities not only as mathematicians, but also as programmers and artists. Stepwise research on the dynamics of functions of complex variables and their visualisation contribute to the development of students' creativity and the formation of skills in the field of mathematical analysis and programming. This article deals with a multi-stage mathematical and informational task, which is a specially composed sequence of tasks, exercises, problems and didactic situations.
Keywords: mathematical information task, dynamics of rational function, function of complex variable, fixed point, pool of attraction, filling set, creativity
Literature list: Katerzhina S.F., Sobashko Iu.A. Zadachno-modul'noe obuchenie pri izuchenii distsipliny “Matematicheskii analiz” v vuze. Aktual'nye tekhnologii prepodavaniia v vysshei shkole: materialy nauchno-metodicheskoi konferentsii / otv. red. G.G. Sokova, L.A. Isakova [Task-modular training in the study of the discipline “Mathematical analysis” at the university. Actual technologies of teaching in higher education: materials of the scientific and methodological conference, ed. by G.G. Sokova, L.A. Isakova]. Kostroma: KGU, 2019, pp. 24–26. (In Russ.) Minlor Dzh. Golomorfnaia dinamika [Holomorphic dynamics]. Izhevsk, NITs Reguliarnaia i khaoticheskaia dinamika Publ., 2000, 320 p. (In Russ.) Paigen Kh.-O, Rikhter P.Kh. Krasota fraktalov. Obrazy kompleksnykh dinamicheskikh system, per. s angl [The beauty of fractals. Images of complex dynamic systems, Trans. from English]. Mosocw, Mir Publ., 1993. 176 p. (In Russ.) Sekovanov V.S., Babenko A.S., Selezneva E.M., Smirnova A.O. Vypolnenie mnogoetapnogo matematiko-informatsionnogo zadaniia “Diskretnye dinamicheskie sistemy”, kak sredstvo formirovaniia kreativnosti studentov [Fulfillment of a multi-stage mathematical and informational task “Discrete dynamic systems” as a means of forming students' creativity]. Vestnik Kostromskogo gosudarstvennogo universiteta. Seriia: Pedagogika. Psikhologiia. Sotsiokinetika [Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics]. 2016a, № 2, pp. 213–217. (In Russ.) Sekovanov V.S. Kontseptsiia obucheniia fraktal'noi geometrii v KGU im. N.A. Nekrasova [The concept of teaching fractal geometry at the Nekrasov Kostroma State University]. Vestnik Kostromskogo gosudarstvennogo universiteta im. N.A. Nekrasova [Vestnik of Nekrasov Kostroma State University]. 2013a, № 5, pp. 153–154. (In Russ.) Sekovanov V.S. O mnozhestvakh Zhiulia ratsional'nykh funktsii [Julia sets of rational functions]. Vestnik Kostromskogo gosudarstvennogo universiteta im. N.A. Nekrasova. [Vestnik of Nekrasov Kostroma State University], 2012, № 2, pp. 23–28. (In Russ.) Sekovanov V.S. Obuchenie fraktal'noi geometrii kak sredstvo formirovaniia kreativnosti studentov fiziko-matematicheskikh spetsial'nostei universitetov: dis. … dokt. ped. nauk [Teaching fractal geometry as a means of forming the creativity of students of physical and mathematical specialties of universities: DSc thesis]. dis. … dokt. ped. nauk. Kostroma, 2007, 393 p. (In Russ.) Sekovanov V.S. Elementy teorii fraktal'nykh mnozhestv [Elements of the theory of fractal sets]. Kostroma, KGU im. N. A. Nekrasova Publ., 2012, 208 p. (In Russ.) Sekovanov V. S., Ivkov V. A. Mnogoetapnoe matematiko-informatsionnoe zadanie “Strannye attraktory” [Multi-stage mathematics and informational task "Strange attractors"]. Vestnik Kostromskogo gosudarstvennogo universiteta im. N.A. Nekrasova [Vestnik of Nekrasov Kostroma State University], 2013, № 5, pp. 155–157. (In Russ.) Sekovanov V. S., Mironkin D. P. Izuchenie preobrazovaniia pekaria kak sredstvo formirovaniia kreativnosti studentov i shkol'nikov s ispol'zovaniem distantsionnogo obucheniia [Studying the transformation of the baker as a means of shaping the creativity of students and schoolchildren using distance learning]. Vestnik Kostromskogo gosudarstvennogo universiteta im. N. A. Nekrasova [Vestnik of Nekrasov Kostroma State University], 2013, № 1. pp. 190 –195. (In Russ.) Sekovanov V.S., Miteneva S.F., Rybina L.B. Vypolnenie mnogoetapnogo matematiko-informatsionnogo zadaniia “Topologicheskaia i fraktal'nye razmernosti mnozhestv” kak sredstvo razvitiia kreativnosti i formirovaniia kompetentsii studentov [Fulfillment of a multi-stage mathematical and informational task “Topological and fractal dimensions of sets” as a means of developing creativity and forming students' competencies]. Vestnik Kostromskogo gosudarstvennogo universiteta. Seriia: Pedagogika. Psikhologiia. Sotsiokinetika [Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics]. 2017, № 2, pp. 140–144. (In Russ.) Sekovanov V.S., Rybina L.B., Berezkina A.E. O mnozhestvakh Zhiulia funktsii, imeiushchikh parabolicheskuiu nepodvizhnuiu tochku [On Julia's sets of functions having a parabolic fixed point]. Aktual'nye problemy prepodavaniia informatsionnykh i estestvenno-nauchnykh distsiplin [Actual problems of teaching information and natural sciences]. Kostroma, KGU Publ., 2018, pp. 144–150. (In Russ.) Sekovanov V.S., Smirnova A.O. Razvitie gibkosti myshleniia studentov pri izuchenii struktury nepodvizhnykh tochek polinomov kompleksnoi peremennoi [Development of students' flexibility of thinking when studying the structure of fixed points of complex variable polynomials]. Vestnik Kostromskogo gosudarstvennogo universiteta. Seriia: Pedagogika. Psikhologiia. Sotsiokinetika [Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics]. 2016, № 3, pp. 189–192. (In Russ.) Sekovanov V.S., Fateev A.S., Belousova N.V. Razvitie gibkosti myshleniia studentov pri razrabotke algoritmov postroeniia dereva Feigenbauma v razlichnykh sredakh [Development of students' flexibility of thinking when developing algorithms for constructing a Feigenbaum tree in various environments]. Vestnik Kostromskogo gosudarstvennogo universiteta. Seriia: Pedagogika. Psikhologiia. Sotsiokinetika [Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics]. 2016, № 1, pp. 143–147. (In Russ.) Chebun'kina T.A., Katerzhina S.F., Sobashko Iu.A. Neobkhodimost' vkhodnogo kontrolia po matematike v vuze [The need for entrance control in mathematics at the university]. Vestnik Kostromskogo gosudarstvennogo universiteta. Seriia: Pedagogika. Psikhologiia. Sotsiokinetika [Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics]. 2019, № 3, pp. 217–221. (In Russ.)
Author's info: Valeriy S. Sekovanov, Doctor of Pedagogical Sciences, Candidate of Physical and Mathematical Sciences, Professor, Kostroma State University, Kostroma, Russia E-mail: Sekovanovvs@yandex.ru
Co-author's info: Vladimir A. Ivkov, Candidate of Economic Sciences, Associate Professor, Kostroma State University, Kostroma, Russia E-mail: ivkov_wa@mail.ru
Co-author's info: Larisa B. Rybina, Candidate of Philosophical Sciences, Kostroma State Agricultural Academy, Karavayevo, Kostroma district, Kostroma Region, Russia E-mail: larisa.rybina.2014@mail.ru
Co-author's info: Yuliya A. Sobashko, Candidate of Technical Sciences, Kostroma State University, Kostroma, Russia E-mail: kgtu-sobashko-ya@mail.ru