How well do students in secondary school understand temporal development of dynamical systems?

Matej Forjan 1 2 * , Vladimir Grubelnik 3
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1 School Centre Novo mesto, Šegova ulica 112, SI-8000 Novo mesto, Slovenia
2 Faculty of Industrial Engineering, Šegova ulica 112, SI-8000 Novo mesto, Slovenia
3 University of Maribor, Faculty of Electrical Engineering and Computer Science, Smetanova ulica 17, SI-2000 Maribor, Slovenia
* Corresponding Author
EUR J SCI MATH ED, Volume 3, Issue 2, pp. 185-204.
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Despite difficulties understanding the dynamics of complex systems only simple dynamical systems without feedback connections have been taught in secondary school physics. Consequently, students do not have opportunities to develop intuition of temporal development of systems, whose dynamics are conditioned by the influence of feedback processes. We present a research study on students' understanding of temporal development of simple dynamical systems. Students participating in the study were attending the final two years of a technical secondary school (gimnazija) program. Based on written equations for the rate of change of some quantity students had to qualitatively determine dynamical development. The study confirmed the initial hypotheses with regard to poor knowledge in the area of dynamical systems, irrelevant of year in secondary school or final grade in physics or mathematics. The results showed that most students understood the development of linear systems without feedback and based on equations, students were able to forecast the dynamical development of changing quantities. Issues arose in understanding systems with feedback connections that influence the nonlinear dynamical development of changing quantity. Especially with negative feedback connections that provide stabilization of changing quantities. The reason could be that in most of the cases they turned towards linear dynamical development of changing quantities. Frequently, they incorrectly concluded that the temporal development of changing quantities is the same to temporal development of current, which determines the state of quantity. As a response in overcoming such issues, we recommend a geometrical consideration of one-dimensional dynamical systems.


Forjan, M., & Grubelnik, V. (2015). How well do students in secondary school understand temporal development of dynamical systems?. European Journal of Science and Mathematics Education, 3(2), 185-204.