SimCalc: Democratizing Access to the Mathematics of Change

9619102种涉及速率、累积、近似和极限的Kaput情形发生在每个公民的日常经验中，并渗透到数学、科学以及它们在人类努力的几乎所有领域的使用中。更进一步，《变与变数学》的实际内容正以前所未有的速度向动力系统和非线性科学方向播种。然而，通常只有参加传统微积分课程的技校学生才能接触到MCV的一部分。要做到这一点，他们必须通过一系列的先决条件，过滤掉他们的大多数同学，特别是那些来自贫穷背景和社区的同学。SimCalc的长期使命是为所有学生提供实践和广泛可用的机会、经验和资源，以培养他们对变化和变分数学的精通理解和技能。在这个项目中，SimCalc团队在以前工作的基础上进行了扩展，(A)确定了如何通过精心设计的活动、表征和设备来实现基于儿童的先验知识和认知能力的学习，(B)确立了MCV的力量，使传统的数学主题重新组织和充满活力，(C)创建了传统和新内容的成功范例课程，(D)为加速和深化@学习创造了技术基础，(E)证明了针对儿童、市中心和少数族裔儿童的MCV方法的可行性。这个项目从相对简单的教学实验到长期的课堂参与，从测试小部件到完全集成物理、模拟和可视化工具，包括廉价的图形计算器。这项密集的研究工作将为三个关键问题找到解决方案，每个问题都是实现民主获取变化数学的不可否认的先决条件：a.基于课堂的@Arning研究：我们如何最好地将普通学生带给我们的全方位的学习、语言、动觉和文化资源与实用新技术的支持结合起来，使我们能够在现实环境中进行非凡的学习？B.课程重组的校本研究：如何将MCV与重要的核心数学整合起来，产生绝对必要的课程效率和力量，使下个世纪的学生可能需要的新内容？C.支持技术的基于组件的体系结构：学习MCV所需的高度灵活的高级技术套件如何通过基于公共标准和开放体系结构的广泛作者和开发人员参与来实现可扩展的集成？贯穿每一研究领域的一个主题是适应多样性和限制：学生多样性、课程多样性和教学多样性。因此，SimCalc将把大部分实地考察工作放在市中心的学校和社区中心，寻求让通常被排除在高等数学之外的学生在比其他地方更严格的限制下参与进来。我们将我们的技术开发引向开放、模块化、即插即用的架构，为适应这种多样性的演进提供灵活性、集成性和框架。最后，我们坚持全面开放的项目架构，邀请并搭建平台，与S和商业合作伙伴进行研究合作。这些商业伙伴是我们与更大社区的接口，既为可能的可能性提供了现实的限制，也为大规模的国家影响提供了机会。如需更多信息，请访问SimCalc网站http://tango.mth.umassd.edu。***

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. ***