Analysis of STEM majors' calculus knowledge by using APOS theory on a quotient function graphing problem

Abstract

Success in many engineering and mathematics courses is tied to well-developed calculus knowledge. Several important calculus concepts used in STEM courses include limit, first derivative, second derivative, and asymptote. In this article, undergraduate and graduate engineering and mathematics students' ability to transform an algebraic function to its geometric representation is analyzed. Participants were either enrolled or recently (two week period) completed a Numerical Methods/Analysis course during the data collection period. Video recorded and written responses to graphing a quotient function are analyzed by using Action-Process-Object-Schema (APOS) theory. Participants are asked to sketch the graph of the given quotient function after calculating its limiting values, first derivative, second derivative and asymptotes. Qualitative and quantitative results indicated Mathematics majors' higher success rate among all the participants.