Collaborative Research: Data-Driven Applications Inspiring Upper-Division Mathematics

今天的数字环境充满了以图像和信号形式存储的持续增长的数据量。事实上，美国的学生迫切需要准备好进入职场，具备研究和解决当前现实生活问题的能力--其中许多问题是由数据驱动的。来自马里兰圣玛丽学院(Lead Institution)、亨德里克斯学院、凯尼恩学院和华盛顿州立大学的研究人员将合作(1)向本科生高级数学课程的学生介绍当前科学、工业和政府领域的前沿研究和实际数据问题，(2)引导这些学生培养解决问题、协作和研究技能，这些技能在当今的工作环境中是如此关键。该项目的重点将是创建一系列以应用数据为导向的教学模块，以图像和数据分析问题为中心，包括图像去噪和去模糊、数据集群、数据配准、射线重建、气候模拟、扩散和波传播。这些单元将激励学生进行研究，并使学生对解决这些问题所需的数学理论有更深的理解和欣赏。该项目的目标是：(I)设计、开发、实施、评估和调整(根据需要)可移植的模块，以连接高分实数分析和线性代数的计算和理论方面；(Ii)建立一个专业网络，用于课堂测试和评估项目模块和教学策略；以及(Iii)为学生研究合作提供和利用各种场所。项目团队将进行研究，以评估这种动手数据驱动的方法如何为学生导向的学习提供新的途径，帮助学生为需要研究和数据技能的劳动力做好准备，提高学生的参与度和学习能力，并激励学生在理论和应用数学方面继续研究生学习。项目研究方法将包括纳入测试版，测试模块，然后收集和分析定量和定性数据。这项研究将包括对学生知识的测量，如课程评估，以及测量与数学相关的动机和自我效能的工具。该项目还将与来自全国四个机构的教师一起，调查材料和教学方法对各种机构的适应性。

Today's digital environment is filled with a continuously increasing amount of data stored as images and signals. Indeed, there is a critical need in America for students to be prepared to enter the workforce with the ability to research and solve current real-life problems - many of which are data-driven. Investigators from St. Mary's College of Maryland (Lead Institution), Hendrix College, Kenyon College, and Washington State University will collaborate to (1) introduce current cutting-edge research and practical data problems from science, industry, and government to students in undergraduate upper-division mathematics courses and (2) lead these students to develop the problem-solving, collaborative, and research skills that are so crucial in today's work environment. The focus of this project will be to create a body of applied data-driven instructional modules that will center on image and data analysis problems, including image denoising and deblurring, data clustering, data registration, radiographic reconstruction, climate simulation, diffusion, and wave propagation. These modules will motivate student research as well as generate a deeper student understanding and appreciation of the mathematical theory needed to solve these problems. The goals of the project are to: (i) design, develop, implement, assess, and adjust (as necessary) transportable modules to connect the computational and theoretical sides of upper division Real Analysis and Linear Algebra; (ii) establish a professional network for classroom testing and assessment of project modules and instructional strategies; and (iii) provide and utilize varied venues for student research collaboration. The project team will conduct research to assess how this hands-on data driven approach provides new avenues for student-directed study, helps prepare students for a workforce in need of research and data skills, improves student engagement and learning, and inspires students to pursue postgraduate study in theoretical and applied mathematics. Project research methods will include the incorporation of beta testing the modules and then collecting and analyzing quantitative and qualitative data. The research will include measures of students' knowledge, such as course assessments, as well as instruments to measure motivation and self-efficacy related to mathematics. With faculty from four institutions across the country, the project will also investigate the adaptability, to a variety of institutions, of the materials and instuctional approach .