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

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 relationship sbetween [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 point softhe graph of f(y) with the horizontal axis and the number of equilibrium solutions, the sign of f(y)and monotonicityof solution curves,phase lineand labling of equilibriumsolutions.