Literature has established that some learners encountered difficulties solving first order ordinary differential equations (ODEs). The use of error analysis in teaching ODEs is believed to make essential contribution towards calculus knowledge development. This paper therefore focuses on analyzing pre-service teachers’ (PSTs) errors and misconceptions apropos of first order ODEs. The paper analyzed the nature of errors made in a test which was written by PSTs on the above topic. The test comprised various types of first order differential equations such as ODEs with separable variables, exact ODEs, ODEs that needed integrating factors, linear ODEs, and homogeneous ODEs. The purpose was to investigate the challenges faced by PSTs in various types of ODEs and the nature of misconceptions that they had in each particular type. This is a qualitative study that involved 63 PSTs who wrote a test on ODEs after being taught the topic for two weeks. The authors marked the work in order to ascertain the misconceptions and errors exhibited by the participants in the test. The PSTs’ performance in the test was analyzed using the SOLO taxonomy and the Newman’s theory mistake analysis. The study established that the topic was rather difficult for PSTs due to various reasons that included, among others, knowledge gaps in integration rules, algebraic computations and, in rare cases, differentiation, as well as misapplication of the rules of natural logarithms. This research therefore recommends that mathematics teacher educators ought to rather focus on the concept of integration and basic algebra before introducing the topic on ODEs to teachers on training.
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