This multi-institution, multi-disciplinary project investigates the use of models of collaboration, especially as embodied in collaborative human-computer interface systems, in the augmentation of existing flexible software tools for mathematics education. It draws on prior work and expertise in two complementary fields: (1) mathematics education: the development of representational tools for data and probability, and (2) multi-agent systems research: the development of a theoretical model of collaboration and its deployment in the design of collaborative human-computer interfaces. It simultaneously raises research questions and will contribute to research in both fields. Over the course of three years, the project will develop three pedagogical tools based on techniques for collaborative interface design. These systems will entail the development of new plan-recognition algorithms and human-computer interface designs. They will be tested in several middle school classrooms using the probability modeling software Model Chance. In Year 1, a tool will be created for teachers to provide them with a representation of their students' work organized around possible plans. In Year 2, this resource will be extended to one that can alert teachers to students who may need immediate assistance and provide some representation of how their planning may have gone awry. Finally, in Year 3, the lessons of the previous two years will be brought to bear on the design of a pedagogical module that will interact directly with the student when it senses that he may need some assistance or advice. The intellectual merit of the project resides in the computer science and education research. The broader impact lies in the project's promise for improving mathematics education.
