The innovative use of computers offers an opportunity to improve the learning and teaching of ordinary differential equations (ODEs) dramatically. The challenge is to identify an instructional tool that addresses a serious and prevalent problem common to ODE instruction-students' lack of a conceptual framework necessary to analyze and build mathematical models, and to solve complex problems. Researchers are investigating the feasibility of combining mathematical simulation, graphic animation, and hypermedia to create an engaging multimedia learning environment to enhance students' understanding and working knowledge of ODEs. The researchers envision powerful, easy to use, and pedagogically meaningful interactive simulation, a computer laboratory that will allow students to examine the properties of linear and nonlinear systems, explore and construct realistic mathematical models, and apply intuitive understanding of the behavior of solutions of ODEs to hypothetical and practical situations. To determine technical feasibility, researchers are: (1) identifying an instructional strategy and essential content material, (2) designing a software structure and implementing a proof-of-concept model, and (3) evaluating the software in field settings. A professional team with expertise in simulation and multimedia, instructional software design, mathematics education, and product development is conducting the research.The potential commercial application as described by the awardee: Research will result in a feasibility analysis and design specification for interactive simulation, to be used as the starting point for commercial prototype development and validation. Technical innovations will provide the foundation for a variety of new software products to invigorate mathematics, science, and engineering education.
