The purpose of this case study was to explore the nature of instructors' gestures as they teach Euclidean transformations in a synchronous online setting, and to investigate how, if at all, the synchronous online setting impacted the instructors' intentionality and usage of gestures. The participants in this case study were two collegiate instructors teaching Euclidean transformations to pre-service elementary teachers. The synchronous online instructors' gestures were captured in detail via two video cameras; one through the screen-capture software built into the online conference platform used to conduct the class and another separate auxiliary camera to capture the gestures that the instructors made outside the view of the screen-capture software. The perceived intentionality of the instructors' gestures was documented via an hour-long video-recorded interview after teaching the Euclidean transformation unit. The findings indicated that synchronous online instructors make representational gestures and pointing gestures while teaching Euclidean transformations. Specifically, that representational gestures served as a second form of communication for the students while pointing gestures grounded synchronous online instructors' responses to student contributions within classroom materials. The findings further indicated the combination of the synchronous online instructors' gestures and language provided a more cohesive picture of the Euclidean transformation as opposed to the gestures alone. Additionally, the findings specified that synchronous online instructors believe the purpose of their gestures was for the benefit of their students as well as for themselves. Finally, the findings highlighted a connection between instructors who previously thought about the potential impact of gestures in the mathematics classroom and intentionally producing gestures. Specifically, critically thinking about gestures within the mathematics classroom before teaching appeared to correspond with more intentional gestures while teaching. Based on these findings, there were three recommendations. The first recommendation was for continued education on gesture as an avenue to communicate mathematical ideas. A professional development workshop may assist collegiate instructors to produce more intentional and mathematically precise gestures. The last two recommendations were for synchronous online instructors to utilize technology that affords students the opportunity to view all of their gestures and for the instructors to explicitly instruct their students to pay attention to their gestures. Knowing that the students can view all of their movements and are specifically looking for gestures might prompt the instructors to gesture with more intentionality and precision. [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.]