9619102 kaput Situations involving rates, accumulation, approximations, and limits occur in every citizen's everyday experience and pervade mathematics, science, and their use across virtually all arenas of human endeavor. Furthermore, the actual content of the Mathematics of Change and Variation (MCV) is sowing at an unprecedented rate in the directions of dynamical systems and nonlinear science. Yet only technical college students in traditional calculus courses normally gain access to even part of the MCV. And to do so they must survive a long series of prerequisites that filters out most of their classmates, especially those from poorer backgrounds and neighborhoods. SimCalc's long-term mission is to render practical and widely available to ALL students the opportunities, experiences and resources they need to develop masterful understanding and skill with the Mathematics of Change and Variation. In this project, the SimCalc team expands upon prior work that (a) identified how to enable learning based on children's prior knowledge and cognitive capabilities with carefully designed activities, representations and devices (b) established the power of the MCV to reorganize and energize traditional mathematics topics, (c) created successful sample lessons in both traditional and novel content, (d) created a technological base for accelerating and deepenin@ learning and (e) proved the feasibility of an approach to MCV for young, inner-city, minority hildren. This project progresses from relatively brief teaching experiments to long-term classroom engagement, and from testing of components in small subsets to full integration of physical, simulation and visualization tools, including inexpensive graphing calculators. This intensive research effort will develop solutions to three critical problems, each an undeniable prerequisite for enabling democratic access to the mathematics of change: A. Classroom-based Research on @arning: How can we best combine the full range of cog nitive, linguistic, kinesthetic and cultural resources that ordinary students bring to us, with the affordances of practical new technologies, to enable extraordinary learning in realistic settings? B. School-based Research on Curriculum Reorganization: How can integrating the MCV with important core mathematics produce the curricular efficiency and power absolutely necessary to make possible the new content needed by students of the next century? C. Component-based Architecture for Enabling Technology: How can highly flexible suites of advanced technologies, which are required to learn the MCV, achieve scalable integration through wide author and developer participation based on common standards and open architectures? A theme cutting across each line of research is adapting to diversity and constraint: student diversity, curricular diversity and pedagogical diversity. Hence SimCalc will base most of its fieldwork in inner city schools and community centers, seeking to engage students typically excluded from advanced mathematics under tighter constraints than obtain elsewhere. We direct our technology development toward an open, modular, plug and play architecture that provides the flexibility, integration, and framework for evolution to adapt to this diversity. Finally, we hold to an overall open project architecture that invites and scaffolds work with research collaborate s and commercial partners. These commercial partners, our interface with the larger community, provide both realistic constraints on the possible, and opportunity for massive national impact. You are invited to visit the SimCalc web site at http://tango.mth.umassd.edu for more information. ***
