Analysis of Educational Challenges of Geometric Approach on Autonomus Differential Equations: Task Based Interview

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Abstract

Educational challenges of geometric approach to Differential Equations (DE) is one of the important issues of undergraduate mathematics curriculum. Thus, a study was designed to investigate the breadth and depth of students’ understanding of DE. 17 undergraduate students majoring in science and engineering, participated in the study. The data were collected via task- based interviews. Students were asked to solve a DE using geometric approach and then, compare the response curves with the given slope field and justify their answers. The analysis of the data helped to identify various challenges including their understanding of the relationships between [y, f (y)] and [t, y (t)], the number of roots of f(y) = 0 and the number of equilibrium solutions, the number of intersection points of the graph of f(y) with the horizontal axis and the number of equilibrium solutions, the sign of f(y) and monotonicity of solution curves, phase line and labling of equilibrium solutions.  
 

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Journal of higher education curriculum studies
Volume 6, Issue 12
January 0
Pages 9-34

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