Teaching the limits of functions using The Theory of Didactical Situations and Problem-Based Learning

The concept of limit plays a central role in the foundation of modern mathematical analysis. However, the concept itself plays a minor role in both upper secondary and undergraduate engineering education, leaving the students with many misconceptions about the concept, resulting in poor performance in calculus and calculus-based engineering courses. Most emphasis in teaching has been on how to calculate the limit instead of on understanding its definition. In this paper, we will use the frameworks of Brousseau’s theory of didactic situations (TDS) and Problem-Based Learning (PBL) to suggest a method to teach engineering students the concept of limit and explain its formal definition. The purpose is to enable the students to generate a precise definition of limit of a function that captures the intended meaning of the conventional ε-δ definition. Moreover, we will argue that TDS bears many similarities with PBL, as both frameworks require that the students act and engage in non-routine and realistic problems.