Undergraduate students’ understanding of the application of integral calculus in kinematics - Tatira, Benjamin (Eurasia Journal of Mathematics, Science and Technology Education, 2025)
In calculus, students can integrate functions that require procedures or algorithmic rules, but they grapple with contextual problems involving real-life motion of physical bodies. When undergraduate students learn the application of integration, they are expected to comprehend the concept of integration and apply it to optimization. This study used the action-process-object-schema (APOS) theory to determine undergraduate students’ construction of the application of integral calculus to kinematics. This study was qualitative and involved a case study of 150 secondary mathematics students registered for a Bachelor of Education degree at a university in South Africa. Data were collected through a written test by all the students and semi-structured interviews with eight students. The eight students were selected purposively, and the interview questions were meant to clarify some of the responses raised in the test. The content analysis of the written responses was done to reveal the stages of students’ concept development of kinematics. The findings revealed that students had significant challenges performing second- and third-level integration. These involve substituting the initial conditions at least once to find the constant integration for each level. Furthermore, students’ connection with displacement, velocity and acceleration concepts was weak, coupled with their failure to consider the point when the object was momentarily at rest.