Despite the standardization of calculus education as a Calculus and Analytic Geometry course after the 1950s, curriculum updates have been slow to penetrate the undergraduate mathematics classroom practice, taking decades to manifest. Common struggles with the teaching and learning of calculus, such as relying on a procedural understanding of calculus topics, echoed those documented in the literature and highlight a common challenge for many students. The derivative, one of the central ideas of the calculus curriculum, remains difficult for some students to conceptualize due in part to its multifaceted nature and the manner in which mathematics is taught at the undergraduate level (e.g., a lecture model, which stands in contrast to more active learning models that are more familiar to students in secondary school settings). The Calculus Reform Movement of the early 1990s initiated various curriculum changes and promoted experimentation with active learning strategies, particularly those that place mathematical discourse at the forefront of the activities, to address these challenges. With the implementation of these discursive learning environments in mathematics classrooms across the country, this prompted my investigation into the derivative-based mathematics that students were learning and the ways in which they were learning such concepts in two specific discursive learning environments at a large research-intensive university in the southeastern United States. Resulting from a commognitive analysis, I present the cases of two highly different activities, fostering both explorative and performative routines among students which led them to draw upon varying aspects of mathematics to reason about the derivative concept. Implications highlight aspects of students' discourse of the derivative concept, such as leveraging only the productive and correct components of a metaphor to reason across contexts. Additionally, this research illuminates the role of documentative routines in discursive learning activities and suggests that instructors should be attentive to the affordances and constraints of such routines. Thus, curriculum designers should adhere to specific goals for discursive learning activities and incorporate routines that promote awareness of processes across the multifaceted classroom discourse and facilitate meaningful documentative routines which serve not only as an assessment but also as a tool to carefully attend to students' sense-making. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]