Begreppslig och proceduriell förståelse i grundläggande matematikkurser för blivande ingenjörer Conceptual and procedural understanding in mathematics courses for engineering students Traditionally, engineering demands from mathematics consisted primarily of fluent use of the techniques of mathematics. The approach in teaching basic mathematics courses for engineering students has therefore been fairly technical and mechanical. With the increasing availability of mathematics software the question arises whether this approach in teaching mathematics to engineers is still relevant. The main objective with this project is to investigate the current needs that engineers have of mathematics. Should we carry on teaching mainly manipulation skills, or should the emphasis move towards a conceptual elaboration of mathematical content to develop a deeper understanding of key concepts? We plan a three-year project involving the University of Pretoria in South Africa and Linköping University in Sweden to identify an appropriate approach to be recommended for basic mathematics courses for engineering students: should the emphasis be on development of conceptual or procedural mathematical skills? Target groups of study will include junior and senior engineering students, colleagues from the engineering faculty, and practising engineers in both countries. An instrument has been developed to measure procedural and conceptual thinking used by students solving mathematical problems. Project findings will reflect in the teaching approach in basic mathematics courses for engineering students at both institutions and may also impact on the curricula of other institutions. Traditionally, engineering demands from mathematics consisted primarily of fluent use of the techniques of mathematics. To supply in this requirement, the approach in teaching first and second year mathematics courses for engineering students has been fairly technical and ‘mechanical’. With the increasing availability of mathematics software programmes, in particular the availability of computer algebra systems such as Mathematica, Maple and others, the question arises whether this mechanical approach in teaching mathematics to engineers is still relevant - most of the mechanical symbolic manipulation can now be done using computers or even graphic and symbolic calculators. The main objective with this project is to investigate the following question: What are the current needs that engineers have of mathematics? Should we carry on with educating students mainly with fluent manipulation skills, or should the emphasis move towards a more conceptual elaboration of the mathematical content and ideas to develop a deeper understanding of key mathematical concepts? We plan a three-year project involving the two universities, the University of Pretoria in South Africa and the Linköping University in Sweden in a joint research project to identify an appropriate educational approach that should be recommended for first and second year mathematics courses for engineering students. The overarching research question of the study is: Should undergraduate mathematics courses for engineering students be presented with the emphasis on development of conceptual or procedural mathematical skills? Results expected during the contract period include investigating the need for a change in approach in the early mathematics courses for engineering students. Target groups in the research project at both institutions will include - junior engineering students at both institutions to find out about the level of development of their conceptual and procedural thinking skills - senior engineering students at both institutions to investigate their experience in what type of mathematics is needed for their engineering subjects - colleagues from the engineering faculty at both institutions to investigate their view on what type of mathematics is needed for engineering students - practising engineers in both countries to investigate their view on what type of mathematics is needed for engineering students. The team was fortunate to have been awarded a planning grant for this project by SIDA/NRF for 2007-2008. The planning period 2007-2008 is being used to develop an instrument that will measure the relevant amounts of procedural and conceptual thinking that students employ in solving mathematical problems and which will be used in the project. Progress in the planning phase include - a pilot run that was completed at the University of Pretoria involving 739 students, and which will be conducted in Linköping University in May 2008. - three meetings between team members during which the research design was developed. - Owe Kågesten and Johann Engelbrecht attended the Delta’07 conference on the ‘Teaching and Learning of Undergraduate Mathematics and Statistics’ in Calafate, Argentina in November 2007 during which time further collaborative work was done on the project. - a paper ‘Conceptual and procedural thinking in undergraduate mathematics for engineering students’ was presented at the Delta’07 conference on the ‘Teaching and Learning of Undergraduate Mathematics and Statistics’ in Calafate, Argentina in November 2007. The findings of the investigation will be implemented to reflect in the approach that is followed in early mathematics courses for engineering students at both institutions. Furthermore, the results of this study may have serious implications in the engineering curricula of not only the two institutions involved, but since the results will be published internationally, many other institutions may be impacted by these results.