2018 ASEE Annual Conference & Exposition

How is calculus applied in engineering statics?

MOTIVATION

Mathematics courses are a major source of engineering student attrition. Many engineering students drop out before even taking an engineering course. In our previous work examining the mathematical expectations that engineering faculty have of their students, faculty claimed they don’t need most of the calculus that is taught in these high-failure prerequisite mathematics courses. We will investigate to what extent this claim is true.

BACKGROUND

While the mismatch between mathematics content and following engineering coursework is already a concern, it is often studied heuristically by talking to engineering faculty. Few rigorous studies empirically document when students actually need to use calculus knowledge in their coursework.

CONTEXT/Data

This study is a component of a larger effort examining what engineering faculty truly desire out of engineering mathematics education. We mapped how foundational calculus concepts are used to solve assigned problems in topics covered in the widely required Engineering Statics course. We analyzed one full semester of 84 Statics homework problems.

ANALYSIS

To create this mapping, we will use the ‘mathematics-in-use’ technique of Czocher et al. Mathematics-in-use makes an important distinction between “topics” and “concepts” and “skills”. Topics are found in tables of contents, syllabi, or at the top of lecture slides, such as “Derivative rules”. Concepts are lower-level ideas about what an object is, such as “derivatives express a rate of change”. Skills are the sequences of steps used to solve a particular type of problem, such as “how to compute the derivative of a polynomial”. The mathematics-in-use technique involves solving the statics problems in high detail, much more than would be expected from student work or an exam solution. A team of two researchers compared the calculus used in the Statics problems to a list of the skills and concepts in calculus from the mathematics education literature.

DATA

The overlap between engineering statics and calculus is rather weak in the course assignments. Just 7 of 84 problems require calculus knowledge to solve. Many concepts and skills from calculus do not occur at all in statics. Integration in Statics is used more as a pre-defined relationship between variables than as a technique of summing or accumulating, and is mostly avoided through the use of centroids.