PROJECT OVERVIEW: Background: Computer computational power, networked communication, Internet global access, Web information sources, digital library resources, learning sciences principles and student literacies provide the preconditions for communities of mathematical discourse that can promote deep understanding of mathematics. Specific mechanisms to bring together small groups of students to discuss well-crafted topics with usable software supports are needed to achieve this potential. The Math Forum digital library provided many of the necessary elements, but offered no service that was explicitly for collaborative learning of math online.
Purpose: We are building a student online community along with a technological infrastructure to support virtual math teams small groups of students who meet online to discuss math.
Intervention: The project is developing a student online math discourse community. It is constructing a regular educational service at the Math Forum and implementing software and procedures and training materials. Evaluation proceeds throughout the timeline with chat analysis and other forms of formative assessment fueling each cycle of design-based research.
Setting: The project is online at the Math Forum website. Students from across the US have participated in trials. We are starting to include students in Europe and Asia as well, with the goal of creating teams that bring students from around the world together to discuss math.
Research Design: Students from middle school, high school and early college meet online in teams of 2 to 6. The average team is 3 or 4. Most sessions last about one hour. Some teams participate in multiple sessions, such as four sessions over two weeks.
Early in the project a collaborative classroom session was videotaped in a Philadelphia middle school and the interactions with a group of four girls was analyzed using conversation analysis. Later in the first year, a set of logs from ten chat sessions was coded using a multi-dimensional scheme developed for this purpose and the codes were analyzed statistically. Since then, many sessions have been analyzed using a form of ethnomethodologically-informed chat analysis.
Findings: The project has already demonstrated the feasibility of supporting small groups of students to engage in intensive online discussion of math topics. We have experimented with a range of math topics, from challenging algebra or geometry problems having correct answers, to open-ended mathematical worlds to explore, to opportunities for students to create and investigate their own problems; we have learned the importance of directing student activity through the careful wording of topics and instructions and mentoring. We have begun to define a science of chat analysis in parallel to conversation analysis and to discover a systematics of chat methods. We have described the sequential flow of math chats, driven by math proposal adjacency pairs, resulting in occasional failed proposals, and requiring often complex methods of deictic referencing. These findings have guided our refinement of a software environment including a lobby for group formation, a persistent chat stream, a shared whiteboard, math symbols and graphical referencing tools. Our findings have been presented in many professional publications, some of which are listed below.
The theoretical and methodological background of the project is discussed at length in:
Stahl, G. (2006) Group Cognition: Computer Support for Building Collaborative Knowledge. MIT Press. 524 pages.
Three recent journal articles with detailed analyses of VMT sessions are:
Stahl, G. (2006). Analyzing and designing the group cognitive experience. International Journal of Cooperative Information Systems (IJCIS). Available at: http://www.cis.drexel.edu/faculty/gerry/pub/ijcis.pdf.
Stahl, G. (2006). Group cognition in an online chat community: Analyzing collaborative use of a cognitive tool. Journal of Educational Computing Research (JECR) special issue on Cognitive tools for collaborative communities. Available at: http://www.cis.drexel.edu/faculty/gerry/pub/jecr.pdf.