doktorska disertacija
Matej Forjan (Author), Vladimir Grubelnik (Mentor), Marko Marhl (Co-mentor)

Abstract

Tema doktorske disertacije sodi na področje didaktike fizike. Predstavljena je teoretična analiza ključnih omejitev, ki se pojavljajo pri prenosu matematičnega modeliranja dinamičnih sistemov v pouk fizike v srednjih šolah. V želji raziskati, v kolikšni meri sedanji pouk fizike spodbuja razumevanje modelov in modeliranja, analiziramo učni načrt in tri najpogosteje uporabljene učbenike za gimnazijsko fiziko. Osredotočimo se predvsem na zastopanost posameznih faz modeliranja pri rešenih primerih v učbenikih ter na predstavitev nekaterih poenostavitev in idealizacij, ki se jih na področju srednješolske fizike pogosto poslužujemo. Pokažemo, da eden od učbenikov v večini primerov korektno in smiselno predstavi poenostavitve v tekstu, medtem ko druga dva polovice analiziranih poenostavitev ne pojasnita. Prav tako se izkaže, da velika večina rešenih primerov v vseh učbenikih eksplicitno ne izpostavlja privzetih predpostavk, na podlagi česa lahko zaključimo, da pri pouku fizike v srednji šoli pri dijakih ne razvijamo v zadostni meri občutka za privzemanje poenostavitev in idealizacij, ki pa so ključni del faze konceptualne faze modeliranja. Za vpeljevanje modeliranja dinamičnih sistemov je pomembno tudi predznanje dijakov, zato izvedemo empirično raziskavo o tem, v kolikšni meri so dijaki v gimnaziji sposobni razumeti časovni razvoj nekaterih dinamičnih sistemov s področja fizike. Rezultati raziskave pokažejo pri dijakih zelo šibko razumevanje dinamike sistemov, v katerih se nahajajo povratne vezave in to ne glede na letnik ali zaključeno oceno pri fiziki in matematiki. Pri modeliranju dinamičnih sistemov pri pouku fizike v srednji šoli naletimo tudi na omejitve, ki so posledica pomanjkljivega matematičnega znanja dijakov, saj le-ti analitičnega reševanja diferencialnih enačb ne obvladajo. Pokažemo, da je pri obravnavi enodimenzionalnih dinamičnih sistemov smiseln geometrijski pristop k reševanju diferencialnih enačb, medtem ko se pri dinamičnih sistemih višjih dimenzij matematičnim omejitvam izognemo z uporabo grafično orientiranih programov za modeliranje. Ker pri reševanju štiri in več dimenzionalnih dinamičnih sistemov lahko naletimo na probleme pri numeričnem reševanju, pokažemo tudi, kako jih presežemo. Na primeru elektrostatičnega nihala prikažemo postopek modeliranja realnega dinamičnega sistema, pri čemer posebej poudarimo posamezne faze modeliranje in način preseganja omejitev, na katere pri razvoju modela naletimo.

Keywords

izobraževanje;fizika;didaktika;poučevanje fizike;poenostavljeni modeli;metoda modeliranja;dinamični sistemi;empirična raziskava;grafično orientirani programi za modeliranje;disertacije;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: M. Forjan]
UDC: 37.091.3:53:519.673(043.2)
COBISS: 21513480 Link will open in a new window
Views: 1384
Downloads: 155
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Other data

Secondary language: English
Secondary title: The limitations of mathematical modeling in high school physics education
Secondary abstract: The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don%t know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems geometrical approach to solving differential equations is appropriate, while in dynamical systems of higher dimensions mathematical constraints are avoided by using a graphical oriented programs for modeling. Because in dealing with dynamical systems with four or more dimensions we may encounter problems in numerical solving, we also show how to overcome them. In the case of electrostatic pendulum we show
Secondary keywords: education;physics;didactics;teaching physics;simplified models;modeling method;dynamical systems;empirical investigation;graphic oriented modeling programs;dissertations;
URN: URN:SI:UM:
Type (COBISS): Dissertation
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za fiziko
Pages: 211 str.
ID: 8752505