SimCalc: Simulations for Calculus Learning

小行星9353507 他们散文建立，测试和执行密切的临床分析的学生工作与一系列从事模拟和活动，旨在联系学生的真实的经验与运动，流体流动和其他连续变量，首先图形，然后更正式的表示。 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，帮助实现微积分中心思想的民主化。 我们的目标是把微积分不作为一个顶点课程的知识和专业精英，遵循了一系列的先决条件，但作为一个主流的所有学生的课程链。 虽然我们最初的设计，并与那些学生谁是现在疏远数学在不可接受的高数字工作，我们计划创建令人兴奋的活动适合所有学生开始在中间年级，并继续进入大学微积分，在那里我们的材料版本可以作为前端。 对于学生将能够驱动“MathCars”模拟，以创建位置和速度（与时间）图，然后可以下载到一个便宜的手持设备做进一步的分析，例如，曲线拟合、斜率或面积近似等。他们还将能够通过输入例如在实际行程期间估计的速度数据来再现他们的校车回家行程。 然后，他们可以指定两辆模拟车辆之一的运动为公共汽车的运动，并“跟随”第二辆公共汽车，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的公共汽车，同时只获得自己速度的反馈。 他们还将能够在双车道轨道上运行各种“玩具车”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。 使用临床研究方法，我们计划在相当详细的研究之间的关系，基于模拟的学习和学习涉及物理MBL设备，不同的具体情况下，如运动与流体流动的概念影响的差异，以及转化的过程中的理解介导的具体和图形表示的理解编码在正式的代数表示。 我们将把我们的工作与TERC的Memirovsky变化和变异项目相结合，该项目正在调查物理环境中的学习。 在该项目的最后18个月里，在几个地点对代表性不足的人群进行了第二层次的课堂测试，这些测试将遵循个人和配对的研究，在各级初中和高中课堂以及大学的微积分和微积分课程中使用丰富的模块。 ***

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. ***