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Dag Wedelin
Computer Science and Engineering Chalmers, Sweden
Between courses of mathematics, which mostly engage in the mathematics itself, and traditional engineering courses which are often concerned with already existing models and methods, other more elusive competencies such as mathematical modelling and problem solving may fall between the chairs, especially since they are difficult to teach within the scope of the well-defined.
In the Chalmers software engineering programme and related programmes, we address this with a second-year inquiry-based course in mathematical modelling and problem solving. The course is not a project with a single problem, but is based on a set of about 30 reasonably realistic, highly varied and challenging problems, which are solved in pairs.
We will here reflect on some key aspects of this multi-problem approach:
- By providing a variation among problems which are still large enough to be remembered as cases, we enable students to build a familiarity with the scope of mathematical modelling, and also in other ways develop an ability to handle similar variation in unknown future problems.
- Modelling problems are typically ill-structured, and thus provide an excellent opportunity also to teach problem solving in a way that is relevant to engineers. Also here the variation comes into play, since many classical patterns of problem solving become visible. Based on the students' own first-hand experiences, these patterns are explicitly discussed throughout the course.
- Compared to a project, the set of problems provide a controlled environment with more guidance, and with short feedback loops. This is done with a cognitive apprenticeship approach, making both student and expert/teacher thinking visible. This is adapted to the constraints of a large course, where we provide as much individual group supervision as possible, together with collective feedback, where reflection is an important part.
After taking the course, most students express and demonstrate a fundamental change in their abilities to think and work mathematically, in their understanding of the nature of mathematics and its role in their future profession. They also consider it as one of the most important courses in their education.
Wedelin D., Adawi T. (2014). Teaching mathematical modelling and problem solving - a cognitive apprenticeship approach to mathematics and engineering education. International Journal of Engineering Pedagogy 4(5).