Teaching and learning mathematical modelling and problem solving: A case study

Engineering students often fail to connect and apply what they have learnt in introductory mathematics courses to other subjects, sometimes leading to the belief that mathematics is not relevant to them. To bridge this gap between mathematical theory and practice, we have designed a course in mathematical modelling and problem solving at Chalmers University of Technology. The main purpose of the present study is to investigate and better understand what challenges engineering students experience when dealing with mathematical modelling problems and what strategies they use to overcome those challenges. Data was collected through semistructured interviews with six students early in the course and the interviews were based on two problems that the students had solved during the course. The data was analysed using basic strategies for qualitative analysis and led to the identification of two central challenges experienced by the students as well as several strategies for overcoming them. The first challenge is that students are not fully aware of the importance of understanding the problem, and the second is that students get stuck because they do not sufficiently consider alternatives in a non-linear solution process. While these issues have little to do with mathematical modelling as such, the modelling problems given clearly reveal these shortcomings, which we see as lacking problem solving skills. Our findings confirm the importance of teaching mathematical modelling and problem solving, and in a more general setting we see cognitive apprenticeship as a promising framework for teaching and learning in engineering education.