Calculus has long been known as a "gateway course" to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional approach called Complex Instruction (CI) and two other peer-led, cooperative learning models, Peer-Led Team Learning (PLTL) and Supplemental Instruction (SI). While the literature on peer-led models of cooperative learning confirms their effectiveness on undergraduate students' academic outcomes in mathematics, this multiple-case study set out to address the following: "What is the nature of undergraduate Calculus I students' participation in the parallel spaces of coursework and complementary instruction?" The analysis of the seven students in this study revealed 17 forms of agentive participation. These forms of participation were further categorized as either nominal, moderate, or highly interactive participatory interactions with tasks, material resources, and other people. Furthermore, some students experienced an expansion period in both instructional spaces as they took on more roles and enacted a growing variation of participation actions. Conversely, withdrawal periods also occurred when students were unable to enact agency because their willingness to act was not sanctioned by the instructor, which would lead to a decline in their participation over time. The findings of this study complement the findings of prior research employing quantitative methods to yield a more holistic understanding of the phenomena that yield the documented achievement outcomes. [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://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]