BACKGROUNDDemands by engineering faculties of mathematics departments have traditionally been for teaching computational skills while also expecting analytic and creative knowledge-based skills. We report on a project between two institutions, one in South Africa and one in Sweden, that investigated whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than the traditional more procedurally oriented way of teaching. PURPOSE (HYPOTHESIS)We focus on how second-year engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between Swedish and South African groups of students in answering conceptual and procedural mathematics problems. We also compare these students' conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. DESIGN/METHODAn instrument consisting of procedural and conceptual items as well as items on student opinions on the roles of the different types of knowledge in their studies was conducted with groups of second-year engineering students at two universities, one in each country. RESULTSAlthough differences between the two countries are small, Swedish students see procedural items to be more common in their mathematics studies while the South African students find both conceptual and procedural items common; the latter group see the conceptually oriented items as more common in their studies outside the mathematics courses. CONCLUSIONSStudents view mathematics as procedural. Conceptual mathematics is seen as relevant outside mathematics. The use of mathematics in other subjects within engineering education can be experienced differently by students from different institutions, indicating that the same type of education can handle the application of mathematics in different ways in different institutions.

This article reports on a collaboration project between South Africa and Sweden, in which we want to investigate whether the emphasis in undergraduate mathematics courses for engineering students should be more conceptual than the current traditional way of teaching. On the basis of a review of the distinction between conceptual and procedural knowledge, an analysis of student solutions to tasks designed to be solved with a conceptual approach but 'proceduralized' by the students sheds some new light on this classical distinction. It is argued that the distinction can be operationalized in test items in a meaningful way but that caution needs to be taken in interpreting the results considering the complex interdependence of these constructs when doing mathematical work.

One challenge for an optimal design of the mathematical components in engineering education curricula is to understand how the procedural and conceptual dimensions of mathematical work can be matched with different demands and contexts from the education and practice of engineers. The focus in this paper is on how engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between second and fourth year groups of students in their answers to a questionnaire comprising conceptually and procedurally focused mathematics problems. We also compare these students' conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. Our data suggest that when mathematical knowledge is being recontextualised to engineering subjects or engineering design, a conceptual approach to mathematics is more essential than a procedural approach; working within the mathematical domain, however, the procedural aspects of mathematics are as essential as the conceptual aspects.

Engineering students in technical universities in Sweden, as probably in many other countries, tend to treat mathematics as a mechanical subject in which you do calculations and manipulations and there is very little explanation. In order to create deeper understanding, verbal or written explanations by students can be beneficial. In our study we show a possible way of teaching students to reflect about their mechanical solutions to mathematical problems. The method is based on the supplementary written explanations that students may provide in their written examination in what would be a second stage of the examination, a so-called 'home exam'. In our project students were forced to rethink their answers, attending to comments and questions posed by the teacher who marked the scripts and supplying further explanation of his/her work. Judging from the results of the research, this facet of the project was successful. The additional opportunity to reflect on their responses assisted students in developing a deeper understanding of the mathematical concepts and also exposed weaknesses and gaps in their knowledge.

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