When undergraduate students learn the application of differentiation, they are expected to comprehend the concept of differentiation first, make connections between particular constructs within differentiation and strengthen the coherence of these connections. Undergraduate students struggle to comprehend kinematics as a rate of change in their efforts to solve contextual problems. This study sought to explore undergraduate students’ construction of connections and the underlying structures of these relationships as they learn calculus of motion. The action-process-object-schema and Triad theories were used to explore undergraduate students’ construction of connections in differentiation and the underlying structures of these relationships as they learn the calculus of motion. This study was qualitative which involved a case study of 202 undergraduate mathematics students registered for a Bachelor of Education degree. Data were collected through an individual written test by the whole class and semi-structured interviews with ten students purposively selected from the class. The interviews were meant to clarify some of the responses raised in test. The findings revealed that students’ challenges in differentiating the given function were insignificant, but they need help to make connections of differentiation to its application to kinematics. Furthermore, students’ coherence of the connection among displacement, velocity and acceleration was weak, coupled by their failure to consider the point when the object was momentarily at rest (which is central in optimization). The results of this study have some implications for instructors. The teaching of calculus and other 456 mathematical concepts should connect to the real-life application of those concepts so that 457 students can make meaningful interrelationships thereof. Kinematics for differentiation paves way for kinematics under the application of integration hence students’ optimal conceptualization is of utmost importance.
