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.
Brian Faulkner's interests include teaching of modeling, engineering mathematics, textbook design, and engineering epistemology.
http://orcid.org/0000-0002-9501-2295
University of Illinois, Urbana-Champaign
[biography]
Dr. Geoffrey L. Herman is a teaching assistant professor with the Deprartment of Computer Science at the University of Illinois at Urbana-Champaign. He also has a courtesy appointment as a research assistant professor with the Department of Curriculum & Instruction. He earned his Ph.D. in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign as a Mavis Future Faculty Fellow and conducted postdoctoral research with Ruth Streveler in the School of Engineering Education at Purdue University. His research interests include creating systems for sustainable improvement in engineering education, conceptual change and development in engineering students, and change in faculty beliefs about teaching and learning. He serves as the Publications Chair for the ASEE Educational Research and Methods Division.
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