Towards a Framework for how Engineering Students deal with Mathematical Modelling Problems

In order to deal with complex problems related to science and technology in their future profession, it is essential that engineering students develop the ability to translate real world problems into mathematical problems (i.e., mathematical modelling) as well as the ability to systematically deal with non-trivial problems (i.e., problem solving). The aim of the study presented in this paper is to develop a framework for how students deal with problems in mathematical modelling. The study is part of a larger and ongoing project aimed at improving the teaching and learning of mathematical modelling in engineering education. As one of the authors of this paper has developed a course on mathematical modelling and problem solving for engineering students (see Wedelin & Adawi, 2012), this course was the natural context for our study. Empirical data comprised students’ solutions to, and reflections on, a number of mathematical modelling tasks as well as semi-structured interviews with a smaller number of students. Galbraith and Stillman (2006) have developed a framework for identifying student blockages during transitions in the mathematical modelling cycle. However, from our general experience in teaching mathematical modelling, and here supported by the detailed analysis of our data, it is evident that the mathematical modelling cycle is not sufficient to capture the hurdles the students experience when engaging in mathematical modelling tasks. We therefore need to consider a broader framework, including both problem solving and metacognitive strategies. This finding is echoed by Schaap et al. (2011), who investigated how pre-university students create mathematical models. In this paper, we will describe the extended and emerging framework and support each part with illustrative extracts from students’ solutions and the interviews. We will also show how the difficulties that some students had in transferring basic knowledge of mathematics to the mathematising phase in the modelling cycle could be related to the lack of relevant problem solving and/or metacognitive strategies. References Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process.  ZDM, 38 (2), 143-162. Schaap, S., Vos, P., & Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 137-146). New York: Springer. Wedelin, D., & Adawi, T. (2012). Bridging theory and practice: An inquiry-based course in mathematical modelling and problem solving . Paper presented at the International Conference on Engineering Education held at Turku, Finland July 20-August 3.