Thank you for these questions.

The first course for the teachers includes planning for implementing some activities with their students and they naturally consider their expectations about what their students are capable of doing, what will engage them, etc. The second course for the teachers provides them an opportunity to improve and reflect on their implementation with their students, as it takes place. And in that context Muteb notes that "the teachers reported shifts in their expectations of their students and beliefs about the usefulness of dynamic geometry. Analysis indicates that some teachers have higher expectations of their students, as one teacher said: “I am having my students work on more complex problems and allowing them to work through their struggles in an attempt for them to persevere.” And another teacher reported: “I now see that dynamic geometry can profoundly influence a student’s level of understanding.” Teachers also noticed that the course informed their instructional discourse and their students discourse. "

As concerns variation in the function of the student talk, this is in fact one of the central concerns of the VMT project. In fact, we’d say the Gerry Stahl’s latest book is devoted to this question in a sense. See http://gerrystahl.net/elibrary/analysis/ . There are eight sessions for the group that he studies, and the analysis of each session is looking at categories of related group discourse practices: collaboration, dragging, construction, tool-usage, dependencies, mathematical discourse, etc. There one can see the evolution of forms of discourse such as questioning, conjecturing, coordinating, reflecting, etc.

Thanks, Stephen. This work is very interesting; I’ll check out the weblink you provide.

The teacher is easily able to perform the same informal assessment in the virtual context by entering the ‘room’. It has some additional affordances because the entire session is available, so that the teacher can look at the work of the group over time, at any point, rather than only touching base at a particular moment. In fact, this is part of the point about the transition in focus from thoughts to thinking. This environment might enable more attention on the thinking activity, because dynamic math and chat both beg for thinking, and because it is all recorded. The challenge of encouraging discussion is probably shaped as much by the focus on collaboration and group cognition as it is by the technology. For the most part we and the teachers provide feedback outside of the actual sessions, rather than during the sessions. It seems important for the students to feel the ownership and safety and investment in their work within the context. We do have colleagues such as Carolyn Rose and her group at CMU who are looking at what can be done with software agents that do some facilitation in an automated way.

Thanks for this question. The activities in the “Construction Game” are sequenced so that the focus of the students can evolve from learning the software to collaboration to dynamic math. Among other things, we are interested in the relationship between the development of competence in each of these domains. We also note that creating an environment in which the students feel relatively unpressured, in charge of their work, engaged with rich and novel tasks appears to contribute to their comfort exploring and quickly learning tools they can use to do the work. We definitely see challenges with the tools where their prior conceptions of geometry (visual verification through measurement) run up against the design and affordances of the dynamic math context.

The activity sequence can be found on GeoGebraTube:
http://tube.geogebra.org/student/b140867

Thank you Joni. I will pass along your best wishes to Wes, who, by the way, is involved, as I am, in the EnCoMPASS project, which has a video here as well.

Thank you for taking a look and sending the feedback. It’s true that we didn’t think of teachers as the likely or prime audience for these videos. More for potential colleagues and funders. But, having said that, it’s also true that this was all we could do in the time we gave ourselves, so we look forward to trying our hand again in other ways. Please don’t hesitate to share if you have thoughts about what you’d like to see.