Interactive Simulation Software to Enhance ODE Instuction

提案号：9361287 PI姓氏：Marchal计算机的创新使用为显着改善常微分方程（ode）的学习和教学提供了机会。挑战在于确定一种教学工具来解决ODE教学中普遍存在的严重问题——学生缺乏分析和构建数学模型以及解决复杂问题所必需的概念框架。为此，IntelliPro建议研究将数学模拟、图形动画和超媒体相结合的可行性，以创造一个引人入胜的多媒体学习环境，从而显著提高学生对ode的理解和使用知识。研究人员设想了一个强大的、易于使用的、在教学上有意义的交互式模拟，一个计算机“实验室”，它将允许学生检查线性和非线性系统的特性，探索和构建现实的数学模型，并将对ode解的行为的直观理解应用于假设和实际情况。为了确定技术可行性，IntelliPro将(a)确定教学策略和基本内容材料，(b)设计软件结构并实施概念验证模型，以及(c)评估软件设计、数学教育和产品开发，并将进行研究。* * * y

Proposal Number: 9361287 PI Last Name: Marchal The innovative use of computers offers an opportunity to dramatically improve the learning and teaching of ordinary differential equations (ODEs). 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. In response, IntelliPro proposes to investigate the feasibility of combining mathematical simulation, graphic animation, and hypermedia to create an engaging multimedia learning environment to significantly 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, IntelliPro will (a) identify an instructional strategy and essential content material, (b) design a software structure and implement a proof-of-concept model, and (c)evaluate the software design, mathematics education, and product development, will conduct the research. ***y