Collaborative practices in virtual group work on dynamic geometry tasks

The goal of this study is to explore productive ways to engage students in groupwork using dynamic geometry tasks in online synchronous classroom environments. In particular, we aim to understand the social, mathematical, and technological aspects of student collaboration in virtual spaces. We analyzed how three online groups of students collaboratively worked on dynamic geometry tasks of exploring interactive kaleidoscope applets in Desmos and producing visual representations and written descriptions of geometric transformations used in the applets. The students shared their screens in Zoom as they shared their findings and discussed how to draw and write to represent the kaleidoscopes. We identified three emerging practices of the students collaboratively working on dynamic geometry tasks in online synchronous environments: (a) drawing in response, (b) co-construction, and (c) writing in real time. The emergent practices captured how students socially interacted with others, engaged in mathematical processes, and utilized technology tools. We also discuss inequity in students' participation in collaborative practices in an online environment and possible ways to ensure equitable learning opportunities for online students.