Analysis of student's understanding of the concept of derivative with a discrete approach

This paper studies the engineering students' understanding of derivatives with a discrete approach using sequences introduced by Weigand (2014). This approach proposes a step-by-step method of difference sequence for functions defined on Z and Q. This concept was taught as part of a mathematics course in an engineering college at an Iranian university. HomeWorks with questions based on derivatives with a discrete approach were constructed and performed for the participants. Their written answers, which were used to explore the students' mental structures of these mentioned concepts, were analyzed using APOS (Action-Process-Object-Schema) theory. We performed interviews so that the students could explain their written answers. The results show that students tend to adopt an algorithmic approach when solving derivative problems and students' understanding of the meaning of derivative with a discrete approach was mainly procedural. Also according to the observed mental structures, a suggested genetic decomposition for the derivative with a discrete approach is presented.