Incorporating EFFECTs into content-rich courses: A journey

Abstract

Many foundation courses in mathematics are considered "content-rich," meaning they must cover a significant amount of material to introduce tools and methods that will be used in subsequent courses. These courses are tightly scheduled surveys of multiple topics; all of which are considered "essential". The presumption is that students will build skills and develop expertise in these foundation topics and be able to recall and use them when required, at a later date, in a future course. Anecdotal evidence suggests that frequently students will do well in the initial course but retain little familiarity with the content in later courses, when context, application, and sometimes even notation can be quite different. This is often true for engineering students with respect to the Calculus sequence. In courses such as Calculus, concepts and solution methods are typically presented within a mathematical context. While some students can recognize the underlying structure and the mathematical construction, others have trouble identifying patterns or parallel thought structures, which makes it difficult for them to generalize the concept to a range of problem types. For example, students in an Introduction to Mathematical Statistics course were reported to claim they do not know how to integrate a probability distribution over a region. The pre-requisite for the course is Multivariable Calculus, which most certainly covers this topic, but the problem "feels" different to students in the later course because the notation and setting have changed and the purpose is specific to statistics rather than the more abstract concepts of the area of a two-dimensional region and anti-derivatives.