Undergraduate basic sciences and engineering students’ understanding of the concept of derivative

Abstract

Derivative is one of the most important topics in calculus that has many applications in various sciences. However, according to the research, students do not have a deep understanding of the concept of derivative and they often have misconceptions. The present study aimed to investigate undergraduate basic sciences and engineering students’ understanding of the concept of derivative at Tehran universities on based the framework of Zandieh. The method was descriptive-survey. The population included all undergraduate students of Tehran universities who passed Calculus I. The sample included 604 students being selected through multi-stage random cluster sampling. The measurement tool was a researcher-made test for which the reliability coefficient was obtained using Cronbach's alpha (r=.88). Inspired by Hähkiöniemi’s research, nine tasks on derivative learning were given to the students. The students’ responses were evaluated using a five-point Likert scale and analyzed using descriptive responses. The results indicated that students have no appropriate understanding of the basic concepts of derivatives in numerical, physical, verbal, and graphical contexts. Basic sciences students performed meaningfully were better in understanding the tangent line slope compared to engineering students, while engineering students performed meaningfully were better than basic sciences students in the rate of change.

Literature review on networking of theories developed in mathematics education context

“…In another view of understanding, Rodríguez-Nieto et al ( 2021b) state that quality level 0 mathematical connections (with mathematical errors or inconsistencies) are the causes for which students have difficulty understanding the derivative concept and quality level 2 mathematical connections (based on mathematically consistent arguments) are a guarantee of understanding by students or teachers. Haghjoo and Reyhani (2021) concluded that university students have inadequate understanding of the derivative concept in contexts (numerical, physical, verbal and graphic), for example, they state that the inconsistency between interpretations of slope in mathematic classes (involving difference quotient limit, velocity, rate of change, etc.) and interpretations of rate of change in engineering classes may cause some problems for students in understanding the derivative, additionally, they share similar results with previous research in two directions:…”