Many of the struggles students face in postsecondary mathematics courses arise from their rote memorization of mathematical concepts, rather than having developed a relational understanding of these concepts. A relational understanding of mathematical concepts could allow students to form generalizations and extend the ideas they understand to new similar concepts. This study investigated how argumentation in a calculus-based undergraduate mathematics classroom can be used as a cognitive tool to mediate mathematical generalization. A classroom teaching experiment was conducted with twenty-nine students who were registered in two sections of a senior level undergraduate mathematics course. Formal instruction for the study took place during four teaching episodes in which the Teacher-Researcher (TR) modeled argumentation in her presentation of course content to emphasize why she made the steps she did when constructing Riemann sums and extending the ideas to other concepts. The concepts were approached first graphically. Then these ideas were extended by constructing informal equations, followed by constructing formal equations, and then followed by implementing these equations into Excel. For each teaching session, the students participated in class activities and related homework tasks where they were asked to justify their work. Following the four teaching sessions, each student participated in two one-to-one interviews where they worked through the concepts involved in Riemann sums and related topics. As in the class activities, students were asked to approach the topics graphically, using informal equations, using formal equations, implementing these equations into Excel, and, lastly, by applying these ideas to an area of the individual students’ interest. The interviews and written work of the students were analyzed under the lens of Vygotsky’s zones of proximal development and levels of generalization, along with Toulmin’s argumentation model. Three case studies were selected based on the types of learning demonstrated by the students: visual learners, visual and symbolic learners, and non-visual learners. Each of these cases was further broken into categories based on the similarities and differences in their interview tasks and the key strengths or weaknesses demonstrated in their coordination between visualization and conceptualization in the context of Riemann sums. Results showed that the non-visual learners who either lacked symbolization or only demonstrated procedural symbolization did not attempt to verbalize argumentation and were unable to form meaningful generalizations regarding Riemann sums concepts. However, the other two cases each had students who were able to form meaningful generalizations. The distinction in these cases lies within the sub-categories of the cases with the most polarized results falling within the case of visual learners. The visual learner who used argumentation was able to form generalizations while the visual learner who did not use argumentation was unable to form the needed generalizations. Generalization formation among the visual and symbolic learners appeared more student specific; while students who used argumentation did form generalizations, there were also students who formed generalizations without articulating the use of argumentation. Student feedback during the interviews indicated that many students believed the structure of the tasks and the emphasis on justifying their own thinking had a positive impact on their learning.