Mathematics coursework causes significant engineering student attrition. Many students drop out of engineering before even taking their first engineering course, due to failing a prerequisite mathematics course. If the mathematics prerequisites fail so many engineering students, it is prudent to understand what exactly those students ought to be gaining by taking these courses. When asked what their students gain from the math course sequence, many engineering faculty respond that it is not technique mastery, but “mathematical maturity” that matters. We conducted a qualitative thematic analysis of 25 interviews with engineering faculty from 11 disciplines who taught engineering courses that list part of the core engineering mathematics sequence as a direct prerequisite. We examine which mathematical skills, habits, and attitudes constitute “mathematical maturity” for engineering students according to these engineering faculty. We constructed an initial coding scheme from literature on mathematical epistemology, mathematical competencies, and symbol sense, with additional codes allowed to emerge during coding by two researchers.
Some of the findings of this study are presented here. 1) Faculty emphasize that students forget much mathematical content before encountering its applications in engineering courses. Many blame the fact that the engineering application of mathematical content may not come for years after the math course, and the engineering curriculum provides little reinforcement of math skills in the intervening semesters. This issue is particularly acute for complex numbers. 2) Engineering faculty are profoundly ignorant of what is currently being taught in mathematics classrooms. Many confess that they don’t know what is being taught at their own university, in the prerequisites for their own classes. Mismatched expectations may result. 3) Faculty repeatedly stressed that “mathematics is the language of engineering”, but don’t see their students holding the same view. Faculty find their students ability to use mathematics for the communication of precise, intricate ideas inadequate. 4) Faculty observe that students have excessive expectations of the certainty of mathematical knowledge. Faculty see students use excessive decimal digits, react with frustration to rough order-of-magnitude estimation or when presented with imperfect models. Faculty state that novice students seem to expect problem solving to not involve any kind of uncertainty, experimentation, or failure.
These results shed more light on the alignment of the current standard mathematics curriculum with the needs of the engineering students and faculty. This project exists in the context of a larger project examining mathematical education for engineering students and adoption of literature-supported curricula and pedagogy.
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