MEJORAR LA COMPRENSIÓN DE LOS ESTUDIANTES SOBRE LOS CONCEPTOS DE EQUILIBRIO Y ESTABILIDAD DE SISTEMAS DINÁMICOS
Engineering students on control courses lack of an understanding of equilibrium and stability which are crucial concepts in this discipline. The introduction of these concepts is generallybased on the study of “classical” examples from Newtonian mechanics enriched by a controlsystem.Throughout the engineering syllabus, equilibrium and stability are approached in dierentways, at dierent academic stages: at early stages in essentially static ways, in mechanics forexample, and later, by dynamical analysis, in control courses. There is little clarification of thedierences between those ways and how the underlying concepts are linked (Albanese et al.,1998). We assume that it is a major source of confusion and misunderstanding for engineeringstudents.
Several studies have shown that students encounter diculties in understanding simple familiar or academic static cases from mechanics (Palmer, 2001; Ortiz, Heron, & Shaer,2005; Newcomer & Steif, 2008). Some others shown that the understanding of equilibriumand stability is strongly disturbed when the studied systems are placed either in inertial ornon-inertial moving reference frames (Tamayo et al., 2012). For example, the existenceof unstable equilibrium positions is questioned by students when the system looks like apendulum because of the use of a velocity-based approach to explain the behaviour of thesystem.
Our study is based on “timed-static situations” which show students’ ideas and misconceptions about equilibrium and stability through web questionnaires. This approach allows to highlighta rationale based on the dierence between initial an final system configurations. This kind ofrationale is a direct easy-to-use translation of the mathematics definition of stability proposedby Lyapunov (1992) that can be found only in mathematics language in control courses.In fact, few of students’ problems seem to be linked directly to a lack of knowledgesconcerning the mechanical concepts of equilibrium and stability but results from aninappropriate reasoning. While many classical engineering control courses are focused ondeclarative and procedural knowledges (Solaz-Portolés & Lopez, 2003) they can not improvestudents’ understanding of many situations because this implies strategic skills or reasoninglike the one we propose in this study.Our approach involves educational inquiry in order to identify students’ misconceptions aswell as a didactic engineering. In this perspective, we propose an example of innovative teaching experiment that allows students’ conceptual change (Posner, 1978; DiSessa, 1993;Hammer, 1996). This example shows that one could take advantage of well-chosen situationsin order to improve the engineering students’ understanding of equilibrium and stabilityconcepts.
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