SimCalc: Simulations for Calculus Learning

9353507 Kaput他们散文建立，测试和执行学生与一系列引人入胜的模拟和活动，旨在将学生的真实经验与运动，流体流动和其他连续可变的量，首先到图形，然后到更正式的表示工作密切临床分析。最终目的是通过为从中学开始的核心定量数学课程的全球重组提供概念和技术基础，帮助民主化微积分的核心思想。我们的目标不是把微积分作为知识分子和专业精英的一门必修课程，而是作为所有学生的主流课程。虽然我们最初是为那些现在与数学脱节的学生设计和工作的，但我们计划为所有从初中开始到大学微积分的学生创造令人兴奋的活动，在那里我们的材料版本可以作为前端。学生将能够驾驶“MathCars”模拟来创建位置和速度（相对于时间）图形，然后可以下载到便宜的手持设备上进行进一步分析，例如，曲线拟合，斜率或面积近似等。他们还可以通过输入速度数据来重现他们的校车回家之旅，例如，在实际旅程中估计的速度数据。然后，他们可以指定两辆模拟车辆中的一辆的运动是公共汽车的运动，并“跟随”；第二辆公交车，只使用位置图，而不是通常的挡风玻璃视图。或者他们可以跟随显示其位置图形的公共汽车，同时只获得关于他们自己的速度的反馈。他们还将能够在两条车道的轨道上用“玩具车”进行各种各样的实验，用代数方法指定它们的运动，并最终检查其他规则运动，包括谐波和其他周期性运动。利用临床研究方法，我们计划详细研究基于模拟的学习和涉及物理MBL设备的学习之间的关系，不同具体背景（如运动与流体流动）的概念影响差异，以及将具体和图形表征介导的理解转化为形式代数表征编码的理解的渐进过程。我们将把我们的工作与TERC的Memirovsky变化和变异项目结合起来，该项目正在研究物理环境下的学习。在项目的最后18个月，将在几个地点对代表性不足的人群进行第二阶段的课堂测试，随后将对个人和成对进行研究，在初中和高中各级班级以及大学微积分预科和微积分课程中使用丰富模块。＊＊＊

9353507 Kaput They prose to build, test and perform close clinical analyses of students working with a series of engaging simulations and activities designed to link students' real experience with motion, fluid flow and other continuously variable quantities, first to graphical and then to more formal representations. the ultimate intent is to help democratize access to the central idea of calculus by providing the conceptual and technological foundation for a global reorganization of the core quantitative mathematics curriculum from the middle school onward. We aim to treat calculus not as a capstone course for the intellectual and professional elite that follows upon a long series of prerequisites, but as a mainstream strand in the curriculum for ALL students. While we initially design for and work with those students who are now alienated from mathematics in unacceptably high numbers, we plan to create exciting activities appropriate for all students beginning in the middle grades and continuing into university calculus, where versions of our materials can serve as a front-end. For students will be able to drive a "MathCars" simulation to create position and velocity (vs. time) graphs that can then be downloaded to an inexpensive hand-held device to do further analysis, e.g., curve- fitting, slope or area approximating, etc. They will also be able to recreate their school bus trip home by inputting velocity data, for example, estimated during the actual trip. They could then specify the motion of one of two simulated vehicles to be that of the bus and 'follow; the bus in the second, using only position graphs, say, instead of the usual windshield view. Or they could follow the bus displaying its position graph while getting feedback only on their own velocity. They will also be able to run a variety of experiments with 'ToyCars' on a two lane track, specifying their motion algebraically, and eventually examine other regular motion, including harmonic and other periodic motion. Using clinical research methods we plan to examine in considerable detail the relations between simulation-based learning and learning involving physical MBL devices, differences in conceptual impact of different concrete contexts such as motion vs. fluid flow, and the gradual process of transforming understandings mediated by concrete and graphical representations to understandings encoded in formal algebraic representations. We will integrate our work with the Memirovsky Change and Variation Project at TERC, which is investigating learning in physical contexts. A second level of classroom based testing with underrepresented populations at several sites in the last 18 months of the project will follow the research with individuals and pairs, using enrichment modules in both middle and high school classes at all levels, as well as university precalculus and calculus classes. ***