Free on-line learning promises to transform the educational landscape of the United States through a significant broadening of supplemental educational opportunities for low income and minority students who do not have access to high quality private tutoring to supplement their in school education. The proposed solution is to develop a technological augmentation to available human support in a lightly staffed Virtual Math Teams (VMT) environment as well as deploying conversational agents that are triggered by automatically detected conversational events and that have the ability to elicit valuable collaborative behavior such as reflection, help seeking, and help provision. This project brings together expertise in technological development and careful experimentation both in the lab and in the classroom, a track record for large scale deployment of educational materials, and a solid foundation in significant student learning results in collaborative environments. The project builds on results from a pilot project in which the team has built VMT-Basilica, which is a technical infrastructure for supporting collaborative problem solving, as well as having conducted pilot studies with it in an on-line setting with promising results. The VMTs use the infrastructure provided by the Math Forum. This project also contributes to the general development of intelligent agents to aid collaboration in a wide variety of settings where collaboration support is needed. By bringing together research in education environments and in computer based intelligent agents, this project is potentially transformative in both computer science and mathematics education.
The project has the potential to bring mathematics to a national community since the development of these agents will substantially reduce the amount of time a human must monitor VMT collaborations. VMTs operate primarily out of the classroom and act as supplemental work for students learning mathematics. In addition, since the collaboration support provided by these agents is not specific to mathematics problem solving, agent supported collaboration could be expanded to any field where collaboration needs to be supported - from education to business to the military.
" was to experimentally learn broadly applicable principles for supporting the development of student skills in effective collaborative problem solving. The project explored (a) the design of a collaboration environment, (b) the incorporation of dynamic-geometry workspaces, (c) the intervention of conversational software agents and (d) the refinement of curricular guidance. (a) The Virtual Math Teams (VMT) online environment was developed, debugged, tested, fielded and refined through many iterative cycles of design-based research. It is now robust enough for public usage at the Math Forum’s free site. See http://vmt.mathforum.org. (b) GeoGebra—the open-source software for dynamic geometry, developed with NSF support—was incorporated into the VMT environment. This provided the first collaborative, multi-user version of dynamic geometry in the world. See http://geogebra.org. (c) Software agents were tested under various conditions by students working in small teams using the VMT software. Student content included high school combinatorics mathematics, middle school dynamic geometry, middle school biology, college chemistry and college engineering. The experiments with biology students are discussed at length in Productive Multivocality (Suthers, et al., 2013, Springer). (d) Curricular guidance was extensively explored for introducing middle school students to the core concepts of dynamic geometry—see Topics in Dynamic Geometry for Virtual Math Teams (Stahl, 2013). The project resulted in at least 78 publications or presentations—see http://gerrystahl.net/vmt/altpubs.html. This includes a book-length report on multiple aspects of the project: the cognitive history of geometry, the evolution of geometry education, the promise of dynamic geometry, the philosophy of the project, the methodology of the project, the findings of the project and the educational vision that results. The book is called Translating Euclid (Stahl, 2013, Morgan & Claypool) and is available in e-book and paperback formats. Presentations on the project disseminated the findings in the mathematics education community, the GeoGebra teacher community and the academic fields of the learning sciences, cognitive sciences and computer sciences. The following principles, among others, emerged from this research: (a) An online collaborative-learning environment should support student learning that crosses and integrates learning at the individual, small-group and classroom levels. It should incorporate and integrate digital media that support persistence and sharing, such as text chat, threaded discussion, blogging, email, shared whiteboard, specialized workspaces (like multi-user GeoGebra), social networking and web browsers. (b) Transforming specialized software like GeoGebra into a multi-user version requires fundamental changes in the software architecture. Project staff worked with GeoGebra developers to adapt GeoGebra to support multi-user versions. (c) The major issue with the use of software agents in collaborative learning is invasiveness. Student collaboration is a delicate process, easily interrupted. Agents have to track student interaction closely to know when and how to intervene. Agents should not be designed to have a dominant role or to pretend to have human cognitive powers or knowledge. (d) Curricular materials are important to guide student discourse in an online setting where there is no teacher playing a central role. The materials should be challenging and should stimulate student creativity. Engaged student groups can interpret the materials appropriately and plan their own responses to the materials. The Virtual Math Teams Project has developed a comprehensive approach to collaborative learning of geometry: an online environment for small teams of students to meet in, a multi-user version of GeoGebra, other appropriate digital tools, and a detailed curriculum with comprehensive resource materials (online apps, a workbook with tutorials). The publicly available system does not currently incorporate software agents; their use has not yet been adequately refined in this context. The project—as described in Translating Euclid—provides a model of design-based research within computer-supported collaborative-learning research. As more students turn to online learning (through home schooling or virtual high schools and after-school activities), VMT provides a model of an online environment for collaborative learning. Collaboration is often the missing ingredient for online learning, but it offers a powerful way to learn and a solution to the isolation that online students so frequently experience. Finally, geometry is often a tipping point for students’ experience with mathematics. A positive experience through VMT’s collaborative version of dynamic geometry can lead to a positive orientation toward STEM topics throughout life.
