ANALYSIS OF DIFFERENTIAL EQUATIONS APPLICATIONS FROM THE COORDINATION CLASS PERSPECTIVE

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ANALYSIS OF DIFFERENTIAL EQUATIONS APPLICATIONS FROM THE COORDINATION CLASS PERSPECTIVE

Abstract

In recent years there has been an increasing interest in mathematics teaching and learning at undergraduate level. However, many fields are little explored; differential equations being one of these topics. In this study I use the theoretical framework of Coordination Classes to analyze how undergraduate mechanical engineering students apply their knowledge in the context of system dynamics and what resources and strategies they used; in this subject, students model dynamics systems based on Ordinary Differential Equations (ODEs). I applied three tasks in different contexts (Mechanical, Electrical and Fluid Systems) in order to identify what information was relevant for the students, readout strategies; what inferences students made with the relevant information, causal nets; and what strategies students used to apply their knowledge in those contexts, concept projections. I found that the core problem at projecting their knowledge relied on the causal nets, coinciding with diSessa and Wagner’s conjecture (2005). I also identified and characterized three strategies or concept projections students used in solving the tasks: Diagram-based approach, Component-based approach and Equation-based approach.

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