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Mechanical Engineering Organized Around Mathematical Sophistication

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2019 ASEE Annual Conference & Exposition


Tampa, Florida

Publication Date

June 15, 2019

Start Date

June 15, 2019

End Date

October 19, 2019

Conference Session

First-Year Programs: Mathematics in the First Year

Tagged Divisions

First-Year Programs and Mathematics

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Paper Authors


Louis J. Everett University of Texas, El Paso

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Dr. Everett is the MacGuire Distinguished Professor of Mechanical Engineering at the University of Texas El Paso. Dr. Everett's current research is in the areas of Mechatronics, Freshman Programs and Student Engagement. Having multiple years of experience in several National Laboratories and Industries large and small, his teaching brings real world experiences to students. As a former NSF Program Director he works regularly helping faculty develop strong education proposals.

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Phillip Cornwell Rose-Hulman Institute of Technology

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Phillip Cornwell is a Professor of Mechanical Engineering at Rose-Hulman Institute of Technology. He received his Ph.D. from Princeton University in 1989 and his present interests include structural dynamics, structural health monitoring, and undergraduate engineering education. Dr. Cornwell has received an SAE Ralph R. Teetor Educational Award in 1992, and the Dean’s Outstanding Teacher award at Rose-Hulman in 2000 and the Rose-Hulman Board of Trustee’s Outstanding Scholar Award in 2001. He was one of the developers of the Rose-Hulman Sophomore Engineering Curriculum, the Dynamics Concept Inventory, and he is a co-author of Vector Mechanics for Engineers: Dynamics, by Beer, Johnston, Cornwell, and Self.

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Yirong Lin The University of Texas, El Paso

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Dr. Yirong Lin is currently an Associate Professor in Department of Mechanical Engineering the University of Texas at El Paso. Before that, he was a postdoc at University of Florida and Arizona State University from 2009 to 2011. He received his Ph.D. degree in Mechanical Engineering from Arizona State University in 2009. Dr. Lin's research interests fall in design, fabrication and characterization of advanced multifunctional material systems for embedded sensing, structural health monitoring, vibration and solar energy harvesting and storage. His research encompasses micromechanics modeling, materials synthesis, structural characterization and device evaluation. The goal of his research is to develop advance structural materials for the next generation ground, aerial and space vehicles with enhanced safety and energy efficiency. He has published or submitted 49 technical articles since 2007 (25 referred journals and 24 conference proceedings). Dr. Lin’s teaching interests lies in Mechanical Design, Solid Mechanics, and Dynamics. Currently, he is advising 4 Ph.D. students, 3 Master students, and 2 undergraduate students. Since 2011, 5 Master students graduated from his group. He was awarded the Best Paper at SAMPE 2008 fall technical conference, Honorable Mentioned Best Student Paper at SMASIS 2009 fall conference and ASME Best Paper in Materials of 2010 at SPIE Smart Materials/NDE 2011 conference. He is a member of ASME, SPIE, SAMPE and AIAA.

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Norman Love University of Texas, El Paso

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Norman D. Love, an Associate Professor in the Department of Mechanical Engineering. Dr. Love earned a B.S. and M.S. in Mechanical Engineering from the University of Texas El Paso and completed his Ph.D. at the University of Oklahoma in the same field. Dr. Love’s research interests lie in the areas of propulsion, energy, and engineering education. He has developed flipped classroom modules and also implements project based learning activities in his class activities.

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There are a number of programs designed to increase the number and diversity of the engineering workforce. The author applauds these efforts. The purpose of this paper is to point out some disturbing trends and to propose a radical approach to reversing them.

Some ideas that seem to be commonly accepted are: (1) the first mathematics course in a typical Engineering program is Calculus. (2) The percentage of students entering the university prepared to take Calculus is declining. (3) Many students from lower socioeconomic groups rely on financial aid. (4) Many financial aid programs require full time enrollment in courses leading to the degree.

So here is the problem, an increasing number of students are not able to make progress in engineering classes directly out of high school because they are not ready for Calculus. Many of the students from targeted groups who are not ready for Calculus are required to take many of the core (English, History etc.) to satisfy full-time status for financial aid. When these students are ready for engineering classes, they often have few non-engineering classes left. Therefore, as they progress into higher-level engineering material, they must take a heavy load of highly technical classes. This often results in lower GPA and possibly failure.

Fortunately, although most engineering courses require Calculus at some point in the class, much of the content in these classes does not require Calculus. For example, although a thorough understanding of Bernoulli’s equation may require calculus, the application of the equation itself requires little more than algebra. If an engineering curriculum can be repackaged based on the required mathematical sophistication, it should be possible to create an engineering degree program that could be entered by virtually anyone leaving high school. As long as the student progresses through mathematics, they should be able to progress through engineering classes too. This will allow them to achieve full time status without “using up” all their core classes. Thus allowing them to save the core class to use when they need to dilute the number of engineering classes in a semester.

There are many advantages of an engineering curriculum organized by mathematical sophistication. First, one might expect more students entering engineering because they can make progress immediately. One would expect greater retention for one reason because the student “sees” the application of engineering early in the curriculum. One might also expect the students to be more intellectually diverse. This means not all engineering students are the math wizards from high school.

This paper proposes a method for designing an engineering curriculum organized by mathematical sophistication and describes how it could be presented to students in an understandable way.

Everett, L. J., & Cornwell, P., & Lin, Y., & Love, N. (2019, June), Mechanical Engineering Organized Around Mathematical Sophistication Paper presented at 2019 ASEE Annual Conference & Exposition , Tampa, Florida. 10.18260/1-2--33098

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