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Mathematics in Engineer ing: Identifying, Enhancing and Linking the Implicit Mathematics Cur r iculum

Kar en Willcox, Ger gana Bounova Depar tment of Aer onautics and Astr onautics Massachusetts Institute of Technology

Abstract A study is undertaken to lay out in a structured manner the mathematics skills required of undergraduate students in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. The key objective of the research is to identify barriers to deep mathematical understanding among engineering undergraduates. Data from engineering course syllabi and interviews with engineering and mathematics faculty are combined to form an implicit mathematics curriculum, which lists the mathematical skills relevant to core engineering classes along with the flow of learning and utilization. Several problematic areas are identified, including the concept of a function, linearization, and vector calculus. Interview results show that many engineering faculty have an inadequate knowledge of mathematics class syllabi, and often do not know where or how the skills they require are taught, while mathematics instructors often have a limited understanding of how mathematical concepts are applied in downstream engineering classes. A number of recommendations are made, including increased communication between mathematics and engineering faculty, development of joint resources for problematic areas, and dissemination of a formal catalogue of mathematical skills and resources to engineering students and faculty.

Background Inadequate mathematical skills present a widespread problem throughout engineering undergraduate programs; however, specific, well-documented examples of student difficulties are often lacking, and the exact nature of the difficulty is frequently uncertain. Moreover, there is often little communication between engineering and mathematics faculty dedicated to or addressing mathematics skills related issues. Engineering faculty assume that certain concepts are taught in the mathematics courses, but they are often not familiar with the specifics of the mathematics curriculum, or the methods utilized (for example: terminology and context of use).

The level of mathematics skills of sophomores and juniors at MIT has been identified as a problem by a number of the faculty that teach core subjects in the Department of Aeronautics and Astronautics. This issue manifests itself in a number of ways and, in particular, has a negative impact on students’ ability to grasp engineering subject material. Specific problems are observed during lectures, where questions often arise regarding basic mathematic manipulations. These questions are also posed in the form of “muddy cards” – cards on which students anonymously write down the muddiest part of the lecture.6 Some examples of such muddy cards taken from a junior-level controls class are shown in Table 1. In all cases shown, the question relates to material that a typical junior is expected to know when entering the class. The questions on these cards strongly suggest that lack of mathematical understanding presents a

Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright 2004, American Society for Engineering Education

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Willcox, K., & Bounova, G. (2004, June), Mathematics In Engineering: Identifying, Enhancing, And Linking The Implicit Mathematics Curriculum Paper presented at 2004 Annual Conference, Salt Lake City, Utah. 10.18260/1-2--13246