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

点击翻译按钮获取中文摘要

Today's digital environment is filled with a continuously increasing amount of data stored as images and signals, and 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 to motivate student research as well as to generate a deeper student understanding and appreciation of the mathematical theory needed to solve these problems. Modules 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. 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 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 research collaboration. The project team will conduct research to assess how this hands-on data driven approach affects appreciation of the mathematical concepts involved, 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. Research methods will include the incorporation of beta testing modules and then collecting and analyzing quantitative and qualitative data. The project includes measures of students? knowledge such as course assessments and instruments to measure motivation and self-efficacy related to mathematics. With faculty from four institutions across the country, the project will also study the adaptability to a variety of institutions of the materials and instuctional approach.