The number of fully online asynchronous undergraduate mathematics courses is growing rapidly, making it imperative that the instructional choices that are chosen by instructors and their effects on students' opportunities to learn in the online learning environment be further explored. Therefore, this research aims to understand instructors' choices when teaching an online undergraduate mathematics course, and how these decisions impact students' communication opportunities. This research organized the instructors' decisions and their impacts on students using the community of inquiry framework. The three categories of the community of inquiry framework, teaching presence, social presence, and cognitive presence, were analyzed through course artifacts, an instructor interview, student interviews, student surveys, and course usage data. The primary analysis was performed using the interviews with the other data sources providing further detail and explanation. Four claims were generated while analyzing these data sources. Claim one posits that students tend to have singular preferences of the course's direct instructional elements. Claim 2 proffers that students who chose to work with others report having positive experiences, and those who decided not to work with others report not needing help, with one exception. Claim 3 states that meaningful contact points can be created between the instructor and student using surveys and personalized mass emails; however, most describe learning mathematics in Math 101 as not making them feel a part of a learning community. And claim 4 posits that elements of the teaching presence were more likely to foster participation if they were associated with a grade. The results of this study have implications for both the research and practice communities. The current study's results imply that--even though sizes of online mathematics classes may still grow--there are ways instructors can facilitate high levels of social processes using mass email, surveys, cooperative learning groups, and other online tools. These specific tools should be studied and evaluated for their effects on social presence and cognitive presence on the mass scale. The present study suggests four specific things that instructors should familiarize themselves with that are available today, (a) prescribe opportunities for students to communicate with each other such as having assignments that are completed in cooperative learning groups, (b) communicate with your students through personalized means (e.g., emails, surveys, and Zoom sessions), (c) use feedback from surveys to inform your future teaching practice, and (d) ensure that students observe your communication and direct instruction by tying them to elements associated with grades. [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.]