doktorska disertacija
Damjan Osrajnik (Author), Robert Repnik (Mentor), Vladimir Grubelnik (Co-mentor)

Abstract

Kaotični sistemi so kompleksni oscilirajoči sistemi z značilno nelinearno dinamiko. Slednje vodi do otežene obravnave, zaradi česar se kaotični sistemi ne vključujejo v pouk fizike na sekundarni ravni izobraževanja. Osnovni cilj doktorske disertacije je razvoj učnega pripomočka za vpeljavo kaotičnih sistemov v pouk fizike na programu splošne gimnazije. Na podlagi pregleda literature lahko sklenemo, da nezadostno matematično znanje dijakov vodi v poenostavljanje opisa dinamike sistemov, včasih tudi do mere, ko rezultati modela niso več primerljivi z realnim stanjem. Posledično so obravnavani primeri pogosto neavtentični in je učenje fizike osredotočeno na uporabo formul. V teoretičnem delu predstavim matematično modeliranje oscilirajočih sistemov, pri čemer se osredotočim na dvodimenzionalne linearne in nelinearne dinamične sisteme. S stabilnostno analizo pokažem, da so za nastanek oscilacij potrebni dvodimenzionalni sistemi in predstavim, da za prisotnost determinističnega kaosa, sistem mora biti večdimenzionalen, nelinearen in oscilirajoč. Na primerih kaotičnih sistemov v naravi in družbi predstavim nekatere značilnosti kaosa kot je občutljivost na začetne pogoje. Podrobneje predstavim dve metodi za prepoznavanje determinističnega kaosa in sicer metodo izračuna največjega Lyapunovega eksponenta ter vizualizacijsko metodo grafa ponovitev. Nato se osredotočim na akustične sisteme, natančneje na vibrirajoče strune. Na primeru posnetka zvoka tona in akorda A zaigranega na kitari, prikažem časovno vrsto tlačnih sprememb. Za časovno vrsta akorda A se nam na prvi pogled zdi, da ustreza kaotičnemu sistemu, zato to preverimo z metodami za prepoznavo kaotičnega obnašanja. Metoda največjega Lyapunovega eksponenta napačno nakazuje, da gre za kaotičen sistem. To potrdim z uporabo vizualizacijske metode grafa ponovitev za ton in za akord A, ki potrdi, da opazovana dinamika ni kaotična. Teoretični del doktorske disertacije se zaključi z razvojem učnega pripomočka za vpeljavo kaotičnih sistemov v pouk fizike. V ta namen pregledam obravnavo oscilirajočih sistemov pri fiziki in se seznanim z matematičnimi omejitvami obravnave fizikalnih modelov. Študije so že pokazale prednost vpeljave blokovnih shem za razumevanje dinamike sistemov. Z blokovnimi shemami prikažem vzročno posledične relacije med količinami in vizualiziramo, kako količine vplivajo ena na drugo. Na blokovnih shemam temeljijo tudi grafično orientirani računalniški programi. Na podlagi zbranih informacij razvijem učni pripomoček za vpeljavo kaotičnih sistemov v pouk fizike. Učni pripomoček obsega 20 strani dolg učni list s 6. poglavji in 4 videoposnetke z razlago. Učni pripomoček prilagodim v luči omejevanja fizičnih stikov in sicer tako, da je primeren za poučevanje na daljavo, saj omogoča samostojno delo dijaka. Za oceno učinkovitosti razvitega učnega pripomočka izvedem empirično raziskavo, v katero je vključenih 7 srednjih šol, 7 učiteljev fizike in 243 dijakov. Učiteljem fizike posredujem učno gradivo, ki obsega učni pripomoček, inicialni in finalni test znanja za dijake ter lestvico stališč, s katero zbiramo mnenja učiteljev o učnem pripomočku. Z inicialnim testom znanja pridobivam informacije o trenutnem razumevanju dinamike sistemov ter prepoznavanja oscilirajočih in kaotičnih sistemov z namenom dopolniti učni pripomoček. Končni test znanja je namenjen oceni učinkovitosti učnega pripomočka z vidika pridobljenega znanja dijaka. Preverim, v kolikšni meri dijak po uporabi učnega pripomočka razume dinamiko sistemov in fazne prostore ter v kolikšni meri se izboljša prepoznava oscilirajočih in kaotičnih sistemov iz grafičnih prikazov. Z analizo rezultatov finalnega testa potrdim, da se je razumevanje dijakov izboljšalo. Dodatno lahko na podlagi pregleda lestvice stališč potrdim, da je v učnem pripomočku obravnavana tematika zanima, aktualna, a zahtevna. Ocenjujem, da je razvit učni pripomoček učinkovit in primeren za vpeljavo kaotičnih sistemov v pouk fizike na programu splošna gimnazija.

Keywords

disertacije;kaotični sistemi;oscilirajoči sistemi;akustični sistemi;splošna gimnazija;poučevanje fizike;kaos;časovne vrste;učni pripomočki;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [D. Osrajnik]
UDC: 373.5.091.3:53(043.3)
COBISS: 112039683 Link will open in a new window
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Downloads: 4
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Other data

Secondary language: English
Secondary title: Introduction of chaotic systems with an emphasis on acoustics in grammar school physics
Secondary abstract: Chaotic systems are complex oscillating systems with characteristic nonlinear dynamics. The latter leads to difficult treatment, which is one of the reasons why chaotic systems are not included in physics classrooms at the secondary level of education. On the other hand, chaos and chaotic behaviour are of high interest to the public. The main goal of this thesis is to develop a learning tool for the introduction of chaotic systems in the teaching of physics in the general gymnasium program. Based on a literature review, I conclude that insufficient mathematical knowledge of students often leads to the simplification of the description of systems dynamics to the extent that the results of the model are no longer comparable with the results of experimental measurements. As a result, the discussed problems lack authenticity, which leads to focusing only on the use of formulas. In the theoretical part, I present the mathematical modelling of oscillating systems, focusing on 2D linear and nonlinear systems. With stability analysis, I show that 2D systems are necessary for the formation of oscillations and present the requirements for the presence of deterministic chaos, namely that the system is multidimensional, nonlinear, and oscillating. By presenting examples of chaotic systems in nature and society, I show the main characteristics of chaos such as the sensitivity to initial conditions. Two methods for chaos recognition are presented in detail, namely the largest Lyapunov exponent and the visualization method of the recurrence plot. Then I focus on acoustic systems, specifically vibrating guitar strings. The recording of the sound of the tone and chord A is displayed in the time series. For chord A, the time series seems to show chaotic behaviour. Therefore, we apply methods. The largest Lyapunov exponent incorrectly suggests presence of chaos, as recurrence plots for tone and chord A confirm that the observed dynamics are not chaotic. The theoretical part of the doctoral dissertation concludes with the development of learning tool for the introduction of chaotic systems in the teaching of physics in the general gymnasium program. We first review oscillating systems in the physics curriculum and identify the mathematical limitations of students. Studies have shown the advantage of introducing block diagrams to understand systems dynamics. Block diagrams show the causal relationships between quantities and visualize how quantities affect each other. Graphically oriented computer programs are also based on block diagrams. With respect to the collected information, we developed learning tool for the introduction of chaotic systems in physics classroom. The learning tool comprises a 20-page long worksheet with six chapters and four videos. It is also suitable for distance learning, as it allows students to work independently. To assess the effectiveness of the developed learning tool, we conduct empirical research, in which 7 high schools, 7 physics teachers, and 243 students participated. We provide materials including the developed learning tool, initial and final tests for students, and a Likert scale to obtain teachers' opinions. The initial test provides information on the current understanding of systems dynamics and the identification of oscillating and chaotic systems. The final test assesses the effectiveness of the learning tool from the student's perspective. It is of interest to see to what extent students understand and recognize oscillating and chaotic systems. The results confirm students' understanding has improved. By reviewing the Likert scale, we confirm the selected topic is interesting but demanding. We conclude that the developed learning tool is effective and suitable for the introduction of chaotic systems in physics classrooms in the general gymnasium program.
Secondary keywords: dissertations;chaotic systems;oscillating systems;acoustic systems;general gymnasium;teaching physics;chaos;time series;learning tools;Fizika;Kaos (teorija sistemov);Srednješolsko učenje in poučevanje;Gimnazije;Učila in učni pripomočki;Univerzitetna in visokošolska dela;
Type (COBISS): Doctoral dissertation
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko; Oddelek za fiziko
Pages: XIII, 140 f.
ID: 15283563