Teaching Mathematical Modelling and Problem Solving - A Cognitive Apprenticeship Approach to Mathematics and Engineering Education

We describe a course in mathematical modelling and problem solving, intended to provide the students with the appropriate skills to deal with real world problems in science and technology. The course is inquiry-based and centered around approximately 30 reasonably realistic, highly varied and challenging problems, which are solved in pairs. The students are supervised in a cognitive apprenticeship environment, where the teacher uses a range of techniques to align student thinking with expert thinking. After taking the course, most students express and demonstrate a fundamental change in their abilities to think 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. We therefore argue that this kind of course, or similar teaching, should be present in the engineering curriculum