From a sociocultural perspective, we examine activities generated by genres of tasks to understand how the tasks shape teachers knowledge of technology and mathematical content for teaching. The tasks and activities come from a professional development project that engages the cyberlearning system, Virtual Math Teams with GeoGebra. Working in teams, teachers enhance their understanding of dynamic geometry and how to engage in productive mathematical discussion. We theorize and discuss principles of our task design. We explore a task and the collaborative work of a team of teachers to illustrate relationships between the task design, productive mathematical discourse, and the development of new mathematics knowledge for the teachers. Implications of this work suggest further investigations into interactions between characteristics of task design and learners mathematical activity.