Increasing retention among first-year engineering students through a hands-on calculus module

To increase understanding and accessibility of the field of engineering by the public, it is in the interest of engineering programs at the university level to increase retention levels of engineering students, with a higher priority given to underrepresented groups of students. Some universities report that many first-year engineering students leave engineering programs not because of the difficulty of the engineering classes, but because of the difficulty of the prerequisite or corequisite advanced calculus classes. These classes are often taught through mathematics departments and incorporate little to no engineering context. The goal of the Science, Technology, Engineering, and Mathematics Talent Expansion Program at The University of Texas at Austin is to develop and incorporate engineering modules into the calculus course sequence so that engineering students will have opportunities to directly apply what they are learning in calculus to engineering topics. In this report we discuss the process for selecting a calculus topic that is historically challenging for students--solids of revolution--and the creation of an engineering module to help students better understand how calculus is applicable to this topic. The module will center on the engineering design process and is appropriate for first-year engineering students enrolled in calculus I or II, or its equivalent. This module was submitted to current graduate engineering students to obtain feedback. The results are then discussed and suggestion made to improve its efficacy in a calculus class for engineering students.