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

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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 .