Online Resources to Improve the Teaching and Learning of Differential Equations: Encouraging the Wide-Spread Use of Modeling and Computing

Harvey Mudd College, Claremont CA

Investigators

Abstract

Mathematical Sciences (21) This project is improving the teaching and learning of ordinary differential equations (ODEs) by encouraging the wide-spread adoption of modeling projects and computer experiments in ODE courses by: (a) creating a digital library of resources and an online community for ODE instructors to find, share, discuss, and evaluate resources for teaching ODEs; (b) completing the development of a robust, flexible, platform-independent numerical solver that is being freely distributed over the Internet and can carry out computer experiments designed to help students learn about ODEs; and (c) training ODE instructors in the effective use of modeling projects and computer experiments via short courses at mathematics meetings. This project builds on the previous accomplishments of the Consortium of Ordinary Differential Equations Experiments (CODEE). Intellectual Merit: Because dynamical systems lie at the heart of scientific inquiry, courses in ODEs are an integral part of any science, technology, engineering, or mathematics (STEM) undergraduate degree program. To become proficient modelers that allow them to tackle authentic research and industrial problems, students should be immersed in mathematical modeling. Modeling projects help students develop communication, team-building, and critical thinking skills. Students are being prepared in the appropriate use of numerical ODE solvers, as most differential equations of practical interest do not have analytic solutions. Modeling is now a common theme in many introductory ODE textbooks, and the educational value of software to numerically calculate and visualize the solutions of ODEs is increasing. However, resources are not currently available to conveniently bring high-quality modeling projects and computer experiments to a wide audience of STEM students. Indeed, these types of educational materials currently appear in isolated places and are published in disparate media. As a result, many instructors who want to incorporate modeling in a meaningful way in their courses spend a great deal of time and effort to overcome barriers. This project is reducing these barriers as much as possible. Broader Impact: Successful students in the interdisciplinary research environment of today are those who can appreciate the wide applicability of differential equations and understand the techniques that can be used to attack them. Wide-spread adoption of innovations in the teaching and learning of ODEs affects the preparation of a great number of future scientists, not just mathematicians. Since modeling skills are increasingly being sought by employers, project activities improve the employability of these future scientists and engineers. This project combines the efforts of scientists, engineers and mathematicians to bring modeling projects to any student, creates a community of instructors interested in the teaching and learning of ODEs and encourages them to collaborate on the creation of new learning materials, encourages mathematics education specialists to conduct research on the teaching and learning of ODEs, gives undergraduate faculty a venue for publishing their models, and raises the awareness of instructors about the merits of modeling projects and computer experiments in ODE courses.