SimCalc: Democratizing Access to the Mathematics of Change

SimCalc：民主化变革数学的获取

• 批准号: 9619102
• 负责人: James Kaput
• 金额: $ 281.61万
• 依托单位: University of Massachusetts, Dartmouth
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-04-01 至 2002-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9619102&HistoricalAwards=false
• 关键词: SimCalc; Democratizing; Access; Mathematics; Change

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. ***

小行星9619102 涉及速率、累积、近似和极限的情况发生在每个公民的日常经验中，并渗透到数学、科学及其在人类奋进的几乎所有领域的使用中。 此外，变化与变分数学（MCV）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发展。 然而，只有技术学院的学生在传统的微积分课程通常获得访问甚至部分MCV。 要做到这一点，他们必须通过一系列的先决条件，过滤出他们的大多数同学，特别是那些来自贫困背景和社区。 SimCalc的长期使命是为所有学生提供实用和广泛的机会，经验和资源，他们需要发展熟练的理解和技能与变化和变化的数学。 在这个项目中，SimCalc团队扩展了先前的工作，（a）确定了如何通过精心设计的活动，表示和设备，基于儿童的先前知识和认知能力进行学习（B）建立了MCV的力量，以重组和激发传统的数学主题，（c）在传统和新颖的内容中创建了成功的样例课程，（d）为加速和深化学习奠定了技术基础;（e）证明了对城市中心和少数族裔青年人实行最低消费额办法的可行性。 该项目从相对简短的教学实验到长期的课堂参与，从测试小子集中的组件到物理，模拟和可视化工具的全面集成，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制定解决方案，每个问题都是实现民主获得变革数学的不可否认的先决条件： A.基于课堂的研究@arning：我们如何最好地联合收割机结合齿轮，语言，动觉和文化资源，普通学生带给我们的全方位，与实用的新技术的启示，使非凡的学习在现实的设置？ B。校本课程重组研究：如何将MCV与重要的核心数学相结合，产生绝对必要的课程效率和力量，使下一个世纪学生所需要的新内容成为可能？ C.基于通用架构的技术支持：如何通过基于通用标准和开放架构的广泛作者和开发人员参与，实现高度灵活的高级技术套件（学习MCV所需）的可扩展集成？ 贯穿每一条研究线的主题是适应多样性和约束：学生多样性，课程多样性和教学多样性。 因此，SimCalc将把大部分实地工作放在市中心的学校和社区中心，寻求在比其他地方更严格的限制下吸引通常被排除在高等数学之外的学生。 我们将技术开发导向开放、模块化、即插即用的架构，提供灵活性、集成性和框架，以适应这种多样性。 最后，我们坚持一个整体开放的项目架构，邀请和脚手架与研究合作伙伴和商业合作伙伴。 这些商业伙伴，我们与更大的社区的接口，提供了现实的限制，可能的，和机会，大规模的国家影响。 请访问SimCalc网站http://tango.mth.umassd.edu获取更多信息。 ***