**The Cyber-Math Project**

This empirical proposal for emerging research in cyberlearning of mathematics explores how a broad diversity of students can be involved in online collaborations that promote the development of math reasoning. This significantly extends recent NSF-supported research on virtual math teams (at Drexel) and on mathematical reasoning (at Rutgers) by mixing students from diverse backgrounds in collaborative online groups and by supplementing leading-edge networked communication technologies with dynamic math simulations to support mathematical inscriptions, visualizations, abstractions and representations by groups of students.

This research introduces into the design/test/study cycle computer representation and manipulation of mathematical phenomena, supporting conceptualizations in the domains of algebraic sequences, patterns, combinatorics, probability, social choice problems and geometry. It extends innovative methods of evaluating learning by focusing on the group-level processes that lead to pattern recognition, logical argumentation, intermediate abstractions and multi-modal representations. It further develops recent theories of computer-supported collaborative learning with detailed empirical descriptions of social practices of small online groups that accomplish cognitive math tasks. In particular, it explores these design, methodology and theory issues within a context of systematic student diversity, both socio-economic and geographic-cultural.

The success of cyberlearning requires the extension of research in a number of directions. This project extends previous NSF-supported research by the PIs to its logical next step: to support online math collaboration in culturally diverse small groups. A major challenge in introducing diversity into collaboration is the difficulty of overcoming differences in background knowledge and conceptualizations. The proposed research will explore the use of computer technology to provide relevant online resources and to support conceptualization with dynamic math objects, simulations and representations. This will simultaneously extend a proven tool for individual math learning to small-group cyberlearning.