Computing with R for Mathematical Modeling

使用 R 进行数学建模计算

• 批准号: 1742083
• 负责人: Jie Chao
• 金额: $ 185.1万
• 依托单位: Concord Consortium
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-15 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1742083&HistoricalAwards=false
• 关键词: Computing; Mathematical; Modeling

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.

国家和地球仪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。 寻求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，因此将计算思维融入现有的高中课程可能更适合为学生准备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。 将开发三个在线课程模块，整合计算思维实践：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。 建议的在线学习平台将提供广泛的访问计算资源，学习资源和教师支持。 该项目由STEM+Computing计划资助，旨在通过在幼儿教育到高中（preK-12）的学科STEM教学和学习中应用计算思维和计算活动，解决计算STEM领域的新兴挑战。将数学与日常问题解决联系起来，数学建模是一个迭代循环过程，它涉及识别和选择变量来表示情况，选择数学表示来描述变量及其关系，执行数学运算以得出结论，针对所述情况解释和验证所述结论，以及迭代地改进所述模型。 同样，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。 这两种实践都旨在将真实的世界与数学或计算的模型世界联系起来，以创建问题的解决方案。 本项目的重点是这两个战略的耦合。 例如，该项目的一个重点是研究耦合策略的变化如何影响学习。 这个项目将系统地操作设计模式，并通过模块A的三个实地测试来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。在参与和认知负荷控制之间找到良好的平衡将是本阶段研究的重点。

项目成果

Getting Started Getting Students Modeling: Designing and Facilitating Open-ended Math Modeling Experiences

开始让学生建模：设计和促进开放式数学建模体验

• 发表时间: 2019
• 期刊: The Mathematics Education for the Future Project. Proceedings of the 15th International Conference
• 作者: Galluzzo, Benjamin;Kavanagh, Karen
• 通讯作者: Kavanagh, Karen

Mathematical modeling with R: embedding computational thinking into high school math classes

使用 R 进行数学建模：将计算思维融入高中数学课程

• DOI: 10.1145/3380956
• 发表时间: 2020
• 期刊: ACM Inroads
• 作者: Wiedemann, Kenia;Chao, Jie;Galluzzo, Benjamin;Simoneau, Eric
• 通讯作者: Simoneau, Eric

Integrating Computational Thinking in STEM Education: A Literature Review

将计算思维融入 STEM 教育：文献综述

• DOI: 10.1007/s10763-021-10227-5
• 发表时间: 2021
• 期刊: International Journal of Science and Mathematics Education
• 影响因子: 2.2
• 作者: Wang, Changzhao;Shen, Ji;Chao, Jie
• 通讯作者: Chao, Jie