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The Virtual Math Teams (VMT) Project
“Computer-Supported Math Discourse Among Teachers and Students.” Award DRL-1118773 from the National Science Foundation Discovery Research K-12 (DR K-12) Program for $1,800,000 over 5 years on September 1, 2011. PI: Gerry Stahl; co-PIs: Stephen Weimar, Jason Silverman, Michael Khoo, Sean Goggins; collaborative proposal with Rutgers, PI: Arthur Powell; other senior personnel: Andrea Forte, Jennifer Rode, Loretta Dicker, Annie Fetter, Tony Mantoan, Jay Scott. Original funding proposal: http://GerryStahl.net/publications/proposals/dr2011.pdf.
The new phase of the VMT Project focuses on promoting significant mathematical discourse. The project is now offering a series of online courses to math teachers to support them in using VMT with their math students. See the description of these courses and stipends available to teachers who take these courses and then use VMT in their classrooms or in after-school groups. The courses focus on the understanding of mathematical practices as defined by the new Common Core Standards.As part of this effort, we have integrated a powerful dynamic mathematics application into VMT: the open-source GeoGebra, which integrates geometry, algebra and other forms of math in a dynamic computational environment. We have made GeoGebra multi-user, so that small groups of students can share their mathematical explorations and co-construct geometric figures online. In support of teacher and student use of this collaboration environment, we have developed a set of activities that systematically introduce people to dynamic geometry, including core concepts from Euclid, standard geometry textbooks and the Common Core Standards for Geometry. An essay on dynamic geometry motivates the theory of dragging, constructing and designing dependencies in collaborative dynamic geometry. See:
Stahl, G. (2012). Dynamic-geometry activities with GeoGebra for virtual math teams. Web: http://GerryStahl.net/pub/activities.pdf.
Stahl, G. (2013). "Translating Euclid: Liberating the cognitive potential of collaborative dynamic geometry". Submitted to Journal of Mathematical Behavior. Web: http://GerryStahl.net/pub/euclid.pdf.A list of publications related to this project is available at: http://GerryStahl.net/vmt/drk12pubs.htm or pdf.
Virtual Math Teams (VMT) is a research project that I have directed since its inception in 2003 at the i-School and the Math Forum at Drexel University in Philadelphia. A group of PhD students, Math Forum staff, interdisciplinary faculty and visiting researchers collaborate on the project. We are developing an online service for math students to meet in small groups online to discuss challenging mathematical topics. We study the usage of the technological environment that we designed for this service, using a method of chat interaction analysis that we have refined. The project is guided by theories of collaborative learning, community knowledge building and group cognition, that we are exploring. A popular report on the VMT Project in the iSchool Bridge provides a good introduction: download it here.
Much of the VMT research takes place in weekly data sessions, as pictured here.
The VMT online environment consists of a Lobby and many chat rooms for the collaborative discussion of math. In the Lobby, you can define your profile and browse the profiles of other people. You can send messages to other people. Mainly, you can see what chat rooms are already defined. Most chat rooms are associated with a math subject and an interesting problem or topic to explore and discuss. The chat rooms include a number of shared whiteboards for drawing and organizing ideas. There are also web browsers. Each chat room has an associated wiki page, where you can share your findings publicly. The VMT wiki is open to the world for reading, but you must register in VMT to post information there. You can also create a new chat room and invite people to it.
If you register and log into the VMT Lobby, you can enter the VMT Sandbox room to explore the functionality available there. You can also join a chat room or even create one to invite people to for collaborative online chats. There is an introduction to VMT for students, parents, teachers and researchers at the Math Forum VMT web page. An extensive list of publications related to the VMT project is available (pdf); the best source is "Studying Virtual Math Teams".
After the 6-year IERI grant ended, the VMT project continued through an NSF ALT grant to explore agents in the VMT environment; a list of publications related to the ALT grant is available (pdf). An ONR CKI grant also supported continuing data analysis. During this period, we did a proof-of-concept port of the Open Source dynamic math system, GeoGebra, into the VMT system. This created the first multi-user version of a dynamic mathematics environment.
In September 2011, a 5-year DR K-12 grant revived major work on VMT. For funding details see the web page on Research. This grant allowed us to implement a more robust version of VMT-with-GeoGebra, with Math Forum technical support mainly by Tony Mantoan. Through weekly project meetings, we tried out different curricular approaches and developed a series of activities and tutorials for VMT-with-GeoGebra during 2011-2012.