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- Performing a multi-stage mathematical and informational task ‟Chaotic mappings” as a means of developing students' creativity
- Sekovanov V.S., Katerzhina S.F., Rybina L.B., Shaposhnikova I.V. Performing a multi-stage mathematical and informational task ‟Chaotic mappings” as a means of developing students' creativity. Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics, 2022, vol. 28, № 3, pp. 125-133. https://doi.org/10.34216/2073-1426-2022-28-3-125-133
- DOI: https://doi.org/10.34216/2073-1426-2022-28-3-125-133
- УДК: 378:51
- Publish date: 2022-09-25
- Annotation: This article describes the method of performing a multi-stage mathematical and informational task ‟Chaotic mappings”, aimed at developing students' creativity. The creative activities that the student performs in the process of solving multifaceted tasks are noted. A scheme is constructed-a plan for the implementation of a multi-stage mathematical and informational task. Examples of chaotic maps on both real and complex planes are given. The aesthetics of the Julia sets are indicated, with the help of which students are invited to create artistic compositions. The integration of mathematics and programming is noted. The creative qualities the students master in the process of performing a multi-stage mathematical and informational task are revealed.
- Keywords: creativity, creative qualities chaos, Julia sets, essential dependence on initial conditions, transitivity, density of periodic points everywhere, continuous dynamical system, discrete dynamical system, attractor
- Literature list: Kronover R.M. Fraktaly i khaos v dinamicheskikh sistemakh [Fractals and chaos in dynamic systems]. Moscow, Postmarket Publ., 2000, 352 p. (In Russ.) Mandel'brot B. Fraktal'naia geometriia prirody [Fractal geometry of nature]. Moscow, Izhevsk, NITs «Reguliarnaia i khaoticheskaia dinamika» Publ., 2010, 656 p. (In Russ.) Minlor Dzh. Golomorfnaia dinamika [Holomorphic dynamics]. Moscow, Izhevsk, NITs «Reguliarnaia i khaoticheskaia dinamika» Publ., 2000, 320 p. (In Russ.) Paitgen Kh. O. Krasota fraktalov. Obrazy kompleksnykh dinamicheskikh sistem [The beauty of fractals. Images of complex dynamic systems]. Moscow, Mir Publ., 1993, 176 p. (In Russ.) Sekovanov V.S. Elementy teorii fraktal'nykh mnozhestv [Elements of fractal set theory], 5-e izd., pererab. i dop. Moscow, Librokom Publ., 2013, 248 p. (In Russ.) Sekovanov V.S. Elementy teorii diskretnykh dinamicheskikh system: uchebnoe posobie [Elements of the theory of discrete dynamical systems: study guide]. Saint Petersburg, Lan' Publ., 2017, 180 p. (In Russ.) Sekovanov V.S. O mnozhestvakh Zhiulia nekotorykh ratsional'nykh funktsii [On the Julia sets of some rational functions]. Vestnik KGU im. N.A. Nekrasova [Bulletin of the N.A. Nekrasov KSU], 2012, № 2, pp. 23–28. (In Russ.) Sekovanov V.S. Chto takoe fraktal'naia geometriia [What is fractal geometry]? Moscow, Lenand Publ., 2016, 272 p. (In Russ.) Sekovanov V.S. O nekotorykh diskretnykh nelineinykh dinamicheskikh sistemakh [On some discrete nonlinear dynamical systems]. Fundamental'naia i prikladnaia matematika; Tsentr novykh informatsionnykh tekhnologii MGU im. M.V. Lomonosova [Fundamental and applied mathematics; Center for New Information Technologies of Lomonosov Moscow State University]. Moscow, Izdatel'skii dom «Otkrytye sistemy», 2016, vol. 21, № 3, pp. 185–199. (In Russ.) Sekovanov V.S., Smirnova A.O. Razvitie gibkosti myshleniia studentov pri izuchenii struktury nepodvizhnykh tochek polinomov kompleksnoi peremennoi [Development of flexibility of students' thinking when studying the structure of fixed points of polynomials of a complex variable]. Vestnik Kostromskogo gosudarstvennogo universiteta im. N.A. Nekrasova [Bulletin of the Kostroma State University named after N.A. Nekrasov], 2016, № 3, pp. 189–192. (In Russ.) Sekovanov V.S. Fraktal'naia geometriia. Prepodavanie, zadachi, algoritmy, sinergetika, estetika, prilozheniia: uchebnoe posobie [Fractal geometry. Teaching, tasks, algorithms, synergetics, aesthetics, applications: study guide]. Saint Petersburg, Lan' Publ., 2019, 180 p. (In Russ.) Sekovanov V.S., Uvarov A.D., Elkin D.V. Izuchenie gladkikh mnozhestv Zhiulia kak sredstvo razvitiia kreativnosti i issledovatel'skoi kompetentnosti studentov [The study of smooth Julia sets as a means of developing creativity and research competence of students]. Iaroslavskii pedagogicheskii vestnik [Yaroslavl Pedagogical Bulletin], 2015, № 3, pp. 70–77. (In Russ.) Sekovanov V.S., Miteneva S.F., Rybina L.B. Vypolnenie mnogoetapnogo matematiko-informatsionnogo zadaniia «Topologicheskaia i fraktal'naia razmernosti mnozhestv» kak sredstvo razvitiia kreativnosti i formirovaniia kompetentsii student. [Performing a multi-stage mathematical and informational task «Topological and fractal dimensions of sets» as a means of developing creativity and forming students' competence]. Vestnik Kostromskogo gosudarstvennogo universiteta. Seriia: Pedagogika, Psikhologiia, Sotsiokinetika [Bulletin of Kostroma State University. Series: Pedagogy, Psychology], 2017, vol. 23, № 2, pp. 140–144. (In Russ.) Sekovanov V.S., Salov A.L., Samokhov E.A. Ispol'zovanie klastera pri issledovanii fraktal'nykh mnozhestv na kompleksnoi ploskosti [Using a cluster in the study of fractal sets on a complex plane]. Aktual'nye problemy prepodavaniia informatsionnykh i estestvennonauchnykh distsiplin: materialy V Vseros. nauch.-metod. konf. [Actual problems of teaching information and natural science disciplines: materials of the V All-Russian Scientific and Methodological Conference], 2011, pp. 85–103. (In Russ.) Smirnov E.I., Sekovanov V.S., Mironkin D.P. Mnogoetapnye matematiko-informatsionnye zadachi, kak sredstvo razvitiia kreativnosti uchashchikhsia profil'nykh matematicheskikh klassov [Multi-stage mathematical and informational tasks as a means of developing the creativity of students of specialized mathematical classes]. Iaroslavskii pedagogicheskii vestnik [Yaroslavl Pedagogical Bulletin], 2014, vol. 2, № 1, pp. 124–129. (In Russ.) Sekovanov V.S. O mnozhestvakh Zhiulia funktsii, imeiushchikh nepodvizhnye parabolicheskie tochki [On sets of Julia functions having fixed parabolic points]. Fundamental'naia i prikladnaia matematika [Fundamental and Applied mathematics], 2021, vol. 23, № 4, pp. 163–176. (In Russ.) Sekovanov V.S. Golomorfnaia dinamika: uchebnoe posobie dlia vuzov [Holomorphic dynamics: a textbook for universities]. Saint Petersburg, Lan' Publ., 2021, 168 p. (In Russ.) Shreder M. Fraktaly, khaos, stepennye zakony (miniatiury iz beskonechnogo raia) [Fractals, chaos, power laws (miniatures from the infinite paradise)]. Moscow, Izhevsk, NITs «Reguliarnaia i khaoticheskaia dinamika» Publ., 2001, 528 p. (In Russ.) Shuster G. Determinirovannyi khaos [Deterministic chaos]. Moscow, Mir Publ., 1988, 240 p. (In Russ.)