Conversational technologies such as email, chat rooms, and blogs have made the transition from novel communication technologies to powerful tools for learning. Currently virtual worlds are undergoing the same transition. We argue that the next wave of innovation is at the level of the computer interface, and that mixed-reality environments offer…

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…