Exploring students’ understanding of the second derivative within the context of a differential equations course

Abstract

Much research has been conducted on the conceptual understanding of the derivative with a focus on the first derivative. Also, a considerable amount of research work has investigated student’s understanding of the qualitative approach to solving first-order ordinary differential equations (ODEs). This paper explores the role of the second derivative in further understanding the qualitative properties of solutions to a first-order ODE. This exploratory research was conducted in fall of 2022 at an average size university in Lebanon. The participants were students enrolled in an introductory differential equations course. The teaching of this course emphasizes a qualitative approach and therefore a solid understanding of the first and second derivatives is critical to determine the increase/decrease of solutions as well as their rate of increase/decrease. Results show that students’ knowledge of the second derivative is not thorough, but that an exploration of the first derivative can help students expand their understanding, consequently improving their skills to plot solutions to ODEs.