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。寻找将计算思维无缝融入高中课程的方法是让学生为未来做好准备的一种方法。由于大多数学校都没有计算机科学课程，因此将计算思维整合到现有的高中课程中可能更适合为学生的准备差距提供解决方案。该项目将使用开源统计程序R开发一个健壮的基础设施，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)推断和证明结论；c)线性、二次和指数模型。提出的在线学习平台将提供广泛的计算资源、学习资源和教师支持。该项目由STEM+Computing项目资助，该项目旨在通过将计算思维和计算活动应用于STEM学科的教学和学习中，解决计算STEM领域的新挑战。数学建模将数学与日常问题的解决联系起来，是一个迭代的循环过程，包括识别和选择变量来表示一种情况，选择数学表示来描述变量及其关系，执行数学运算来得出结论，根据情况解释和验证结论，以及迭代地改进模型。同样，计算思维是用计算机可以执行的计算步骤和算法来表述问题和解决方案的过程。这两种实践都旨在将现实世界与模型世界（无论是数学的还是计算的）联系起来，以创建问题的解决方案。本项目侧重于这两种策略的耦合。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。该项目将系统地操纵设计模式，并通过模块a进行三次实地测试，比较学生的学习成果和学习过程。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，以减少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。在投入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.