Hands-On Laboratory Exercises for Engineering Applications of Mathematics Course
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In Fall 2007, the First-Year Engineering Program (FEP) was started with the intent of increasing student retention and success. One of the main hindrances to retention at a public university engineering program with open enrollment is the unpreparedness of students for rigorous curriculum requirements of the first year. In an effort to help first year engineering students who are one or two semesters behind Calculus I, FEP offers Engineering Applications of Mathematics (E-Math) course, which was inspired by the Wright State model for Engineering Mathematics Education. E-Math aims to teach College Algebra, Precalculus, and introductory Calculus I concepts using self-paced lectures focused on engineering applications and supported by hands-on laboratory exercises. FEP gained permission of the Department of Mathematical Sciences to have E-Math course count as a prerequisite to Calculus I, so successful students who finish the course with a “C” or better are able to enroll in Calculus I next semester.
This paper focuses on hands-on labs that support the mathematical concepts and incorporate immediate applications of these concepts so that students can relate what they learn to real-life situations. Also, most labs require students to turn in a lab write-up, which targets to develop students’ scientific communication skills. There are ten hands-on labs developed for this course; we will discuss the following seven in detail. In One-Loop Circuits Lab (inspired by Wright State), students create a circuit, measure voltage and current, and find the unknown value of resistors using linear trendlines in Excel. In Falling Ball Lab, students use an ultrasonic sensor and the Lego Mindstorm EV3 software to create a quadratic graph of time versus height of a falling ball, and then they analyze their data to approximate the acceleration of gravity. In Pennywise Lab, students are given a clear vial containing an unknown distribution of pre- and post-1982 pennies and asked to incorporate systems of linear equations to determine the number of pre- and post-1982 pennies. In Height of Trees Lab, students are given limited materials, asked to make an apparatus, and apply right triangle trigonometry to measure the height of trees outside of the engineering building. In Wind Turbine Lab, students use Lego wind turbines attached to the Lego Mindstorm EV3 brick to measure rotation time for blades and make velocity calculations. In Orienteering Lab, first students use vectors to describe a path to get to a location on university campus, and as a follow-up they follow another group’s directions to find and identify their location. Students repeat the Falling Ball Lab at the end of the course, but this time, they use derivatives instead of quadratic functions for their analyses and calculations.
We examine the course evaluation survey and end of semester results to evaluate the student response to hands-on labs. We also briefly discuss success of students in E-Math.
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