The Use of Graphic Computer Programs for Mathematical Modelling of Dynamical Systems in Primary School

Vladimir Grubelnik, Lidija Grubelnik
vlado.grubelnik@uni-mb.si, lidija.grubelnik@guest.arnes.si
Fakulteta za elektrotehniko, računalništvo in informatiko, Univerza v Mariboru, Osnovna šola Sladki Vrh, Sladki Vrh

Povzetek

V prispevku pokažemo obravnavo dinamičnih sistemov v osnovni šoli na podlagi pretakanja tekočin. Izkazalo se je, da učenci konec osnovne šole prepoznajo časovno linearno spreminjajoče se količine kot posledico konstantnih tokov. Pojavijo pa se problemi pri razumevanju nelinearnih zvez kot posledica povratnih vezav ter vplivov med spremenljivkami. Pri reševanju omenjenih problemov izpostavljamo vlogo grafično orientiranih računalniških programov, kot so Berkeley Madonna, Daynasys in Stella. Omenjeni programi omogočajo, da časovno spreminjajoče se količine ponazorimo z rezervoarji, dotoke oziroma odtoke pa reguliramo z ustreznimi ventili. Pri delu s programi se je izkazalo, da učenci nimajo težav tudi pri reševanju kompleksnejših primerov, kot je padanje teles z upoštevanjem zračnega upora.

Ključne besede: računalnik, sistemsko mišljenje, matematično modeliranje, dinamični sistemi, osnovna šola.

Abstract

In our research, we indicate the process of dynamic systems in the primary school based on fluid decanting. It was proven that the students at the end of the primary school can recognize fluid changes based on linear modifications in time as a result of constant currents. However, the problems occur in terms of understanding of non-linear connections as a consequence of reverse binding and influence among the variables. At solving these problems, we point out the role of graphic orientated computer programs, such as Berkeley Madonna, Daynasys and Stella. These programs enable that the quantities which change in time can be illustrated with storage tanks, while inflow and outflow can be regulated with suitable valves. The students, working with these programs, showed no difficulties in solving even more complex examples, such as falling of bodies with taking into account the air resistance.

Keywords: computer, system thinking, mathematical modelling, dynamical systems, primary school