When am I ever going to use this? An investigation of the calculus content of core engineering courses

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How engineering students use domain knowledge when problem solving using different visual representationsBackground: Engineering students commonly learn domain knowledge by engaging with visual representations of it. However, at times they have trouble accessing information from these representations due to the way information is encoded in features of the representation.Purpose: To describe how students engage with representation features, we explored two research questions: 1) What is the interplay between how concepts are encoded within representations, students' use of those concepts, and how students translate between representations during their problem solving and 2) How is the interplay described in Research Question 1 similar and different across students in statics versus those in digital logic? Design/Method: We synthesized findings from two of our prior research studies using the constant comparative method. We describe the effect of representations on students' ability to access and use domain knowledge during problem solving within and across engineering disciplines. Results:We identified three themes that describe how visual representations affect students' reasoning. First, students conflated concepts that were represented using similar features.

Progress through standard mathematics coursework represents a major barrier to engineering student graduation rates. Long prerequisite chains of mathematics courses have high failure rates, and must be passed to enter engineering coursework. This project aimed to investigate the mathematical expectations of engineering faculty, particularly the ambiguous quality of "mathematical maturity" seen in some engineering-mathematics education research during interviews or workshops. This research aims to create a better understanding of how engineering faculty perceive the mathematical needs of their students.Interviews with thirty four engineering faculty members at seven institutions revealed common themes across disciplines and institution types. Engineering faculty members stressed the importance of students' ability to apply mathematics to the physical domain. Engineering faculty stressed the need for students to be able to flexibly represent physical entities in a variety of symbolic and graphical forms. They claimed that the ubiquity of computers changes where students mathematical training should focus its emphasis.The course artifact analysis uncovered substantial mismatch between the mathematics that is taught in calculus courses and how that mathematics is called upon in introductory core engineering courses. Only 8% of homework problems in engineering statics and 20% in circuits used calculus of any kind. What calculus did get used on engineering homework assignments was usually the simplest examples such as polynomials and exponentials.One round of survey data has been collected, investigating student beliefs about mathematics. This first round used two existing instruments from the literature to probe student beliefs about how relevant mathematics was to their engineering studies. Initial results show moderate beliefs in the relevance of mathematics by sophomore engineering students.

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