Mathematics Education Undergraduates’ Conceptualisation of Non-Homogeneous Differential Equations Using the Method of Undetermined Coefficients - Makamure, Chipo; Jojo, Zingiswa M.; Mkwelie, Nhlanhla (Mathematics Education Journal, 2025)
The topic of ordinary differential equations (ODEs) is widely covered in higher education institutions, however, understanding non-homogeneous differential equations (NHDEs) poses challenges for students due to its complexity. Limited research in second order NHDEs points to the need for more studies on students’ conceptions and understanding of this topic and its basic concepts. This study delved into the conceptualisation of second order NHDEs and their solutions using the method of undetermined coefficients among Bachelor of Science in Education Mathematics student teachers. Employing the APOS Theory, an in-depth test on NHDE was administered to 60 participants from a university in Zimbabwe to identify their underlying challenges. The study revealed that student teachers encountered difficulties in determining general solutions for NHDEs using the method of undetermined coefficients, largely due to insufficient knowledge of basic ODEs concepts such as differentiation of exponentials, trigonometric ratios, solving quadratic equations, and algebraic skills. The findings indicated that the participants primarily utilised reasoning associated with APOS ‘action’ and less of ‘process’, hindering their engagement with higher-level concepts of solving NHDEs. Consequently, enhancing student teachers’ performance and retention in NHDEs classes therefore requires inventive approaches to instruction.