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.
Dynamical systems lie at the heart of scientific inquiry, which is why courses in ordinary differential equations (ODEs) are an integral part of any science, technology, engineering or mathematics (STEM) undergraduate degree program. Beginning in the 1980s, the teaching of ODEs at some institutions has evolved to include project-based learning, technology, and mathematical modeling. Though we know that many of these active learning strategies improve student learning outcomes, these instructional advances are still not used widely for a variety of reasons including lack of faculty training on these pedagogies and lack of access to materials and software. The goal of this grant was to help accelerate the development and acceptance of effective methods of teaching and learning ODEs. The Community of Ordinary Differential Equations Educators (CODEE) was first formed in the 1990s with the support of two NSF grants. This group organized workshops and published a newsletter with resources and articles for instructors of ODEs courses. In 2007, CODEE received another grant from the NSF to revive the group and continue its work. These funds have allowed CODEE to do three things: (1) create and curate a digital library of resources for the teaching and learning of ODEs, (2) develop a free, intuitive, platform-independent numerical solver called ODE Toolkit (http://odetoolkit.hmc.edu) to help instructors and students can carry out computer experiments and learn about ODEs, and (3) organize workshops and conferences to help train instructors on how to incorporate mathematical modeling, technology, and project-based learning in ODEs courses. CODEE has created an online, peer-reviewed journal called the CODEE Journal (ISSN 2160-5211) that publishes original materials promoting the teaching and learning of ordinary differential equations. These materials include expository works that advance the art and practice of the teaching and learning of ODEs and classroom-ready activities that provide students opportunities to analyze, make predictions and draw conclusions from numerical or analytical solutions to ODEs. Many of these activities are interdisciplinary and involve technology. To date, the CODEE Journal has published 16 articles, 5 collections of projects (each collection multiple projects), and 54 summaries of other papers on the teaching and learning of ODEs. All of the content for the CODEE Journal (and more) is housed at a repository of learning materials at www.codee.org. This web site, which was built on the open-source content management system Plone, became fully functional in December 2009. It complies with the Open Archives Initiative Protocol for Metadata Harvesting so that its contents can be indexed by search engines such as Google Scholar. The CODEE Digital Library also provides instructors with a helpful list of software that they can use to teach differential equations. The grant also enabled CODEE to create ODE Toolkit, a tool for exploring differential equations graphically and numerically. It was designed to be intuitive and easy to deploy in a classroom. Because it is written in Java, it can run on Windows, Mac, or Linux computers. It does not require installation and runs over the web, so that the latest version is always used. The software was written by students at Harvey Mudd College, partly through its Clinic Program. Over the last seven years, these students have turned ODE Toolkit into a mature tool that allows users to quickly interact with differential equations without much training. The ODE Toolkit software has been integrated with the CODEE Digital Library so that articles (PDF files) can contain links that, when clicked, bring up ODE Toolkit with the relevant differential equations loaded for exploration. Finally, CODEE has also organized two minicourses, one workshop, and two conferences to help faculty to learn about how to effectively use modeling projects and computer experiments in their classes. The two minicourses were organized at the Joint Mathematics Meetings, once in January 2012 and once in January 2013. All of the materials from these Minicourses were also archived onto the CODEE Digital Library, where it can be downloaded for free. The first conference, entitled "Differential Equations Across the Collegiate Curriculum," brought college mathematicians around the country to learn together at Gustavus Adolphus College from June 23-26, 2011. The second conference, entitled "Innovations in Teaching Ordinary Differential Equations: A Celebration of Bob Borrelli's Legacy" was held on March 31, 2012 at Harvey Mudd College. CODEE is also proud to have supported 2013 EDGE Program, which took place this summer at New College in Florida. The EDGE Program, funded by the National Science Foundation and National Security Agency, is designed to strengthen the ability of women and minority students to successfully complete graduate programs in the mathematical sciences. The 2013 EDGE Program included sessions on modeling and the teaching and learning of differential equations for mathematics graduate students.
