Computing with R for Mathematical Modeling

国家和全球面临的问题的深度和复杂性越来越需要复杂的计算解决方案。寻找在高中课程中无缝构建计算思维的方法是让学生为未来做好准备的一种方式。由于大多数学校不提供计算机科学课程，将计算思维融入现有的高中课程可能更适合为学生准备工作中的这一差距提供解决方案。该项目将使用开源统计程序R开发一个强大的基础设施，以支持将计算思维注入高中数学课程。将开发三个整合计算思维实践的在线课程模块：a)解释分类和定量数据，b)进行推理和证明结论，以及c)线性、二次和指数模型。拟议的在线学习平台将提供对计算资源、学习资源和教师支持的广泛访问。该项目由STEM计算计划资助，该计划旨在通过将计算思维和计算活动应用于从高中到高中的幼儿教育中STEM学科教学和学习中，解决计算STEM领域的新挑战。将数学与日常问题解决联系起来，数学建模是一个迭代的循环过程，涉及识别和选择表示情况的变量，选择描述变量及其关系的数学表示，执行数学运算以得出结论，针对情况解释和验证结论，并反复改进模型。本着同样的精神，计算思维是根据计算机可以执行的计算步骤和算法来制定问题和解决方案的过程。这两种做法的目的都是将现实世界与模型世界联系起来，无论是数学上的还是计算上的，以创造问题的解决方案。本项目关注的是这两个战略的耦合。例如，该项目的一个重点是调查耦合策略的变化如何影响学习。这个项目将系统地操纵设计模式，并比较学生在三个实地测试中的学习结果和学习过程与模块A。计算数学建模周期中的步骤可以分组为初始任务类的子集，以降低处理整个周期的复杂性；然而，这样做可能会降低任务的真实性和丰富性水平。在参与度和认知负荷控制之间找到一个良好的平衡将是这一阶段研究的重点。

The depth and complexity of the problems facing the nation and globe increasingly demand complex, computational solutions. Seeking ways to seamlessly build computational thinking in to high school curricula is one way to prepare students for this future. Because computer science courses are unavailable in most schools, integrating computational thinking into existing high school courses may be better suited to provide a solution to this gap in students' preparation. This project will develop a robust infrastructure using the open source statistical program R to support the infusion of computational thinking into high school mathematics courses. Three online curriculum modules will be developed that integrate computational thinking practices: a) interpreting categorical and quantitative data, b) making inferences and justifying conclusions, and c) linear, quadratic, and exponential models. The proposed online learning platform will provide wide access to the computing resources, learning resources, and teacher supports. The project is funded by the STEM+Computing program, which seeks to address emerging challenges in computational STEM areas through the applied integration of computational thinking and computing activities within disciplinary STEM teaching and learning in early childhood education through high school (preK-12).Linking mathematics to everyday problem solving, mathematical modeling is an iterative cyclic process that involves identifying and selecting variables to represent a situation, choosing mathematical representations to describe the variables and their relationships, performing mathematical operations to draw conclusions, interpreting and validating the conclusions against the situation, and iteratively improving the model. In the same spirit, computational thinking is the process of formulating problems and solutions in terms of computational steps and algorithms that can be executed by computers. Both practices aim to connect the real world with the model world, either mathematical or computational, to create solutions to problems. This project focuses on the coupling of these two strategies. For example, one focus of the project is an investigation of how variations of coupling strategies impact learning. This project will systematically manipulate design patterns and compare students' learning outcomes and learning processes across three field tests with Module A. The steps in a computational mathematical modeling cycle can be grouped into subsets for initial task classes to reduce the complexity of dealing with the entire cycle; however, doing so may decrease the level of authenticity and richness of the tasks. Finding a good balance between engagement and cognitive load control will be the focus of this phase of the study.