The present study explores students' understanding of calculus-based kinematics (henceforth, CBK), in which argumentation is taken as the sequence of the modes of fostering reasoning and problem-solving. The investigation stresses the importance of arguments students bring to the learning situation of CBK and recognizes the active construction of meaning which goes on constantly as they interact with their learning environment. The study adopted mixed-methods in which one-group pre-posttest design with supplemental questionnaires and interviews were used. Data included video recordings of pre-posttests activities, as well as students' handwritten work. The pre-posttests evaluated the dependent variables (understanding CBK concepts and solving problems inspired by CBK), the treatment was argumentation. No strong causal relationship is assumed but the analyses of the results tend to show that the treatment improves slightly students' understanding of CBK concepts and their ability to identify relevant knowledge of these concepts for problem-solving. Implications of the findings for educational practice are discussed.