An investigation into the development of engineering students' conceptual understanding of mathematics
Following widespread concern over an apparent decline in the mathematical skills of engineering students, this study employed survey and observation methods to investigate the ways in which engineering students understand mathematical concepts, and to compare these with the concepts held-by students of mathematics. It was found that the engineering students employ a different vocabulary from mathematics students in discussing mathematics, and that their understanding of mathematical concepts develops differently from mathematics students both in response to teaching (which appears to be a transitory effect) and as their experience gives meaning to the ideas in life outside study. These findings are important in two ways. We need to make the mathematics teachers of engineering students aware of the language and concepts of their students so that the possibility of mutual misunderstanding is reduced, and we as educators need to help engineering students to make these connections in order to ground their mathematics in reality and to use mathematics an Instrument for understanding the world. Compared with the classical mathematical modelling paradigm and the classical empirical modelling paradigm, the method used by engineering students was found to be a hybrid based on the Identification of the type of problem and the application of a "preexisting law. Some misconceptions concerning the behaviour of beams In bending were found to be widely held, by respondents with a range of levels of experience. Whereas the particular misconceptions are not Important in themselves. It Is salutary to realise that expertise in one area of study does not necessarily Inoculate one against misconceptions In a closely related area. A software package was written using the context of mathematical modelling to help students relate concepts In calculus to physical situations. This package was found not to engage the students sufficiently to provoke cognitive change, and suggests that a higher degree of Interactivity Is needed.