Analysing engineering students’ understanding of integration to propose a genetic decomposition

Abstract

This paper reports on a study which explored engineering students’ understanding of the techniques of integration in calculus. There were 30 first year engineering students who participated in the project. The concepts were covered as part of a mathematics course at a university of technology in South Africa. Activity sheets, constructed with tasks based on integration were administered to the participants. Their written responses, which were used to identify the mental constructions of these concepts, were analysed using APOS (Action-Process-Object-Schema) theory and interviews were carried out to clarify the written responses. The discussions and written work indicated that students exhibit procedural tendencies in integration and that students could not define both definite and indefinite integrals. These findings raised some didactical implications for higher education and also provided applications of genetic decomposition design and modification.