SBIR Phase II: Interactive Simulation Software to Enhance Ordinary Differential Equation Instruction

9509135马歇尔这一SBIR第二阶段项目旨在设计和实施一个交互式多媒体软件原型，以支持常微分方程式(ODE)课程，并在常微分方程式实验室课程设置中评估其影响。该软件结合了数学模拟、图形动画、数字视频和超幻觉，创造了一个引人入胜的学习环境，建立在当代情境学习和建构主义学习理论的基础上。首席调查员与国家科学基金会资助的ODE实验联盟合作，以(A)确定支持ODE入门课程所需的所有必要数学内容元素，(B)确定支持基于实验室的ODE课程的具体专题，(C)制定软件模块规范，(D)确定和开发支持模块所需的特定应用软件，(E)实施软件模块，(F)在课堂环境中评估原型，以及(G)为商业产品的开发提供建议。该软件的预期好处是，它为学生学习和探索微分方程提供了一种方便和具有挑战性的方式，让他们在物理世界和数学之间架起了一座桥梁。

9509135 Marchal This SBIR Phase II project aims to design and implement a prototype of interactive multimedia software to support Ordinary Differential Equation (ODE) courses and evaluate its impact in an ODE laboratory course setting. The proposed software combines mathematical simulation, graphic animation, digital video, and hypermdeia to create an engaging learning environment that builds upon contemporary learning theories of contextual learning and constructivism. The Principal Investigators work with the NSF-funded Consortium for ODE Experiments to (a) identify all required mathematical content elements required to support an introductory ODE course, (b) identify specific topics to support a laboratory-based ODE curriculum, (c) develop software module specifications, (d) identify and develop application-specific software needed to support the modules, (e) implement the software modules, (f) evaluate the prototype in a classroom setting, and (g) provide recommendations for the development of a commercial product. The anticipated benefit of the software is that it provides a convenient and challenging way for students to study and explore differential equations, giving them a bridge between the physical world and mathematics.