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Redesigning the Calculus Curriculum for Engineering Students

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Conference

2018 ASEE Annual Conference & Exposition

Location

Salt Lake City, Utah

Publication Date

June 23, 2018

Start Date

June 23, 2018

End Date

July 27, 2018

Conference Session

Mathematics Division Technical Session 2

Tagged Division

Mathematics

Page Count

10

Permanent URL

https://peer.asee.org/30922

Download Count

60

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Paper Authors

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Stacie Pisano University of Virginia

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After receiving a Master of Science in Electrical Engineering from Stanford University, Stacie Pisano worked as an Electrical Engineer and Technical Manager at AT&T and Lucent Technologies Bell Laboratories for 16 years, designing and developing telecommunications equipment for the business market. After moving to Charlottesville, VA, she had the opportunity to teach Multivariable Calculus for UVA SEAS, and she was hooked. She has been teaching Applied Math from that point on and enjoying every minute.

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Hui Ma University of Virginia

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Hui Ma received her Ph.D. in applied mathematics from the University of Alabama at Birmingham in 2012. In her current role as an APMA faculty member at UVA, she teaches applied math courses to engineering students. Her goals in teaching are to help students develop the confidence in their own ability to do mathematics and to make mathematics a joyful and successful experience.

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Bernard Fulgham University of Virginia

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Bernard Fulgham received his PhD in Mathematics in 2002, writing his thesis in the field of non-associative algebras with advisor Kevin McCrimmon. He began teaching Applied Mathematics at the University of Virginia in August 2004 and became an assistant professor in 2018.

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Gianluca Guadagni University of Virginia

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PhD in Mathematics University of Virginia.

Assistant Professor, Applied Mathematics, Department of Engineering and Society, School of Engineering and Applied Sciences, University of Virginia.

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Diana D Morris University of Virginia

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I am a lecturer at the University of Virginia, and enjoy teaching a variety of math courses to undergraduates.

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Monika Abramenko University of Virginia

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I studied math in Frankfurt and finished with the German "Diplom" in Mathematics in 1993. For several years I worked at a bank in Germany. In 2001 I came to the US with my family and started teaching financial math at the Math Department, UVa. After a couple of years I became a lecturer in the Engineering Department at the University of Virginia where I am teaching now full time.

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Abstract

For better or worse, our university’s school of engineering assumes that most (if not all) incoming students should begin with Calculus II. In addition, there is an increasing number of students who begin their college math with multi-variable calculus. In the Fall 2017 semester, less than 15% of our incoming students began with Calculus I. As a result of this trend away from Calculus I, most of our degree programs now assume that students complete calculus by the end of their first year. Unfortunately, much of the second year schedule is structured around this assumption, which can create difficulties for students that took Calculus I in the fall semester of the previous year. (Note that these students must take three semesters of calculus and are therefore unable to complete the calculus requirement by the end of their first year.) These systemic forces result in an unhealthy dynamic that generates many negative feelings and poor decisions: (1) incoming students that enroll in Calculus I are often afraid of falling behind their peers, while (2) many incoming students that struggle with Calculus II won’t move to Calculus I because they’re also afraid of falling behind.

It’s our opinion that many more of our students would benefit from beginning with Calculus I rather than Calculus II. Unfortunately, this isn’t likely to happen any time soon, for many of the reasons described above. As a consequence, we’ve responded to the problem by developing a new two-semester sequence for students that should begin with Calculus I. We hope to eliminate worries/pressures related to “falling behind their peers” and even some of the stigma that students can sometimes feel. (Engineering school can be a very competitive place!)

This new sequence includes the most essential elements of single-variable and multi-variable calculus. We’ve kept many topics often skipped in high school (e.g., hyperbolic trigonometric functions, related rates, optimization, Newton’s method, work, force of a fluid), but we’ve also “trimmed the fat” by eliminating some less essential topics (e.g., trigonometric substitution). In addition, many topics have been stream-lined. For example, our coverage of trigonometric integrals has been reduced to the forms they will encounter most in their future engineering courses, and we cover infinite series with a focus on applications of power series rather than covering each and every convergence test [2] [3].

This is the second step in a three-year plan to redesign our calculus sequence. Ultimately, we hope to develop three tracks which target engineering students of different skill levels. The advanced track was launched in 2016-2017, and our preliminary results were reported at the 2017 ASEE conference [1]. As an ongoing project, we continue to investigate the impact of the redesign on student learning. In this paper, we will present the main features of the implementation of this new track and examine some preliminary results. This will include a comparison of student performance in all three tracks relative to their performance on an initial assessment of their pre-calculus preparation. Furthermore, the changes and improvements made for the advanced track will also be discussed.  

[1] Authors’ paper, 2017. [2] Colson P, Roegner K. "Redesigning the Calculus Sequence for Engineering Students". Proceedings of Mathematical Education of Engineers joint Conference with IMA April 2008 
 [3] Keynes HB, Olson AM, OLoughlin D, Shaw D. Redesigning the Calculus Sequence at a Research University. In Calculus Renewal 2000 (pp. 103-120). Springer US.

Pisano, S., & Ma, H., & Fulgham, B., & Guadagni, G., & Morris, D. D., & Abramenko, M. (2018, June), Redesigning the Calculus Curriculum for Engineering Students Paper presented at 2018 ASEE Annual Conference & Exposition , Salt Lake City, Utah. https://peer.asee.org/30922

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