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Calculus courses have been attracting the attention of mathematics education researchers over the last decades. Recent publications and special issues dedicated to calculus highlight the diverse roles of calculus courses in the pathways for STEM studies within and across educational levels, as well as issues related to the academic preparation of future STEM professionals, including mathematicians, non-mathematics professionals (NMPs) and teachers. In this paper, we review recent literature, mostly since 2015, to identify and characterize explicit references to such diverse roles of calculus courses. The review highlights an intrinsic tension between two institutional roles of calculus: "scaffolding" and "filtering." We find nuanced yet substantial variation in how the dual role of calculus is experienced and managed across different groups of students and stakeholders. With regard studies on calculus for mathematics students, recent studies attend to changes in the rules underpinning calculus notions and processes, and highlight the scaffolding potential of calculus courses towards abstraction and reasoning. In contrast, studies on calculus for NMPs report that such courses often promote filtering rather than scaffolding and question transferability and relevance of those courses for NMPs. Finally, studies challenge the perception that traditional tertiary calculus courses scaffold school teaching and underline the need for empirical research that would explain the nature of this scaffolding and how it can be realized in practice. We conclude that further empirical research, in particular theory development, is needed to address the diverse roles of calculus at the intersection of institutions, disciplines and communities.

Of the many disciplines that rely on calculus, physics is among those with the strongest connections to this branch of mathematics. For instance, the derivative--one of the key notions of calculus--is used to describe velocity and acceleration, which play a central role in mechanics. In post-secondary education, in particular at the college level, it is not unusual for students to enroll in calculus and mechanics courses in the same year, and even the same term. In mathematics education, however, there is scant research focusing on students' construction of the notion of derivative in a mechanics context, and existing studies offer contradictory views on the effectiveness of using mechanics to teach derivatives. To shed light on the use of derivatives in mechanics and calculus courses, our study focuses on practices involving the use of derivatives to study motion in both courses. We first conducted a praxeological analysis of five differential calculus textbooks and five mechanics textbooks to pinpoint their use of derivatives in the study of motion. This analysis was complemented by interviews with four mathematics teachers and three mechanics teachers, to compare their praxeologies with those of the textbooks. We then identified consistencies and inconsistencies between practices employed in both courses, which may have an impact on students' learning, and formulated recommendations for teaching the notion of derivative in kinematics.