The role of the relationships between the solution function and its variation in the solution scheme of systems of differential equations
DOI:
https://doi.org/10.23925/1983-3156.2023v25i2p439-458Keywords:
Systems of differential equations, Calculus, APOE theory, Dynamical systems, Parametric functions, SchemeAbstract
This article contributes to the knowledge about the learning of systems of differential equations from the point of view of dynamical systems. It analyzes the evolution of the Schema of dynamic systems of two variables in university students, after finishing a course of dynamic systems designed with the Action Process Object Object Schema (APOE) theory as a support for the design of activities used throughout the course. In particular, this study focuses on how students give meaning to the strategies used to represent and interpret systems of differential equations and the relationships they establish between the structures that make up the Systems of Equations Schema and in particular the relationships between the function and its derivative through the different representations used to study them. This work also contributes to enrich the notion of Schema and interaction between Schemas of the APOE theory, as well as to the analysis of the relationships between the different concepts involved in and between the different representations of the solutions that play a role in the context of systems of differential equations and, importantly, in the understanding of parametric functions.
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