Applied Mathematical Problem Solving: Principles for Designing Small Realistic Problems

Book chapter, 2015

We discuss and propose principles for designing problems that let engineering students practice applied mathematical problem solving. The main idea is to simplify real-world problems to make them smaller, while retaining important characteristics such that the solution to the problem is still of practical or theoretical interest, and that the problem should invoke non-trivial modelling and problem solving activities. We formalize our analysis in three dimensions of learning, which provide a basis for reflection beyond just solving the problem. We further discuss the benefits of being able to consider a large and highly varied set of smaller problems for discerning problem solving patterns, and give examples of such problems. We finally discuss the relationship with other proposed ways of designing problems.