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

当今的数字环境充满了以图像和信号形式存储的不断增加的数据量。事实上，美国迫切需要学生为进入劳动力市场做好准备，具备研究和解决当前现实问题的能力——其中许多问题都是数据驱动的。来自马里兰圣玛丽学院（领导机构）、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)向本科高年级数学课程的学生介绍当前的前沿研究和来自科学、工业和政府的实际数据问题；(2)引导这些学生培养在当今工作环境中至关重要的解决问题、协作和研究技能。该项目的重点将是创建一个应用数据驱动的教学模块，该模块将以图像和数据分析问题为中心，包括图像去噪和去模糊、数据聚类、数据配准、放射重建、气候模拟、扩散和波传播。这些模块将激发学生的研究，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（必要时）可移动模块，以连接上层实分析和线性代数的计算和理论方面；（ii）建立一个专业的网络，对项目模块和教学策略进行课堂测试和评估；（三）提供和利用各种场所进行学生研究合作。项目团队将开展研究，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，并激励学生攻读理论和应用数学的研究生学习。项目研究方法将包括对模块进行beta测试，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，以及测量数学动机和自我效能的工具。该项目由来自全国四所院校的教师组成，还将研究材料和教学方法对各种院校的适应性。

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 .