Many physics and engineering curricula include a course on mathematical techniques. This award assists in the development and testing of a suite of exercises for this type of course so students better understand the motivation for the material and to help students incorporate computer skills within the course. For example, motivational exercises walk students through the steps needed to animate graphics on a screen (for matrices) or to analyze data on star positions to show evidence of orbiting planets beyond our solar system (for Fourier series). In each case the students are led through derivations using familiar mathematics to eventually reach a point where they can see the vital need for a new mathematical technique. The computer assisted exercises lead students in tasks such as comparing exact and approximate solutions to equations or solving complicated equations and plotting the solutions. These exercises help illustrate mathematical principles while simultaneously enhancing student numerical skills in the context of challenging and interesting problems.
Courses of this type pose unique challenges. First, the students often don't use the math tools developed until a year or more after they learn them. Educational research shows that material is retained best when it is learned in a meaningful context and best recalled when it comes up again in a related context. The motivational exercises being developed in this project are therefore expected to improve student retention. In addition, in our digital generation the content of these courses should be frequently updated, since traditional skills (such as solving systems of equations by hand) are often not as important as knowing how to effectively use a computer to solve the problems. The exercises being developed in this project will have a broad national impact as professors are assisted in revising their curricula to teach computer skills alongside traditional math skills.
The materials developed are being made freely available on the Web and presented at national conferences. Moreover, a number of participating faculty members at different institutions are volunteering to use these materials as they are developed. The effectiveness of the exercises are being assessed with tests given in semesters before and after the introduction of the exercises, computational skills are tested before and after the class, and surveys are being utilized to gather student and faculty feedback.
