Collaborative Research: Improving Conceptual Understanding of Multivariable Calculus Through Visualization Using CalcPlot3D

协作研究：使用 CalcPlot3D 通过可视化提高对多变量微积分的概念理解

• 批准号: 1525216
• 负责人: Deborah Moore-Russo
• 金额: $ 7.55万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1525216&HistoricalAwards=false
• 关键词: Collaborative; Research; Improving; Conceptual; Understanding

The purpose of this collaborative project from Monroe Community College, Robert Morris University, and the State University of New Your (SUNY) at Buffalo is to use visual exploration to help students develop a deeper understanding of multivariable calculus concepts and to conduct and publish research on the effects of visualization on student understanding of these concepts. This project will build upon the success of the CalcPlot3D multivariable calculus exploration applet, an award-winning, interactive Java applet that is already widely used across the United States to facilitate the teaching and learning of multivariable calculus. The CalcPlot3D applet is designed to improve students' geometric intuition about surfaces, vectors, vector fields, and curves, thereby preparing students to understand more fully engineering and physics problems in subsequent STEM coursework. This project will greatly enhance the use of CalcPlot3D by creating a series of visual concept explorations for multivariable calculus and expand CalcPlot3D to facilitate visualization of concepts in physics, engineering, differential equations and linear algebra courses. It also will fill a gap in the existing educational research by addressing the effects of visualization on student understanding of three-dimensional concepts. Three professors from these diverse institutions (community college, private 4-yr, public 4-yr) will collaborate with faculty across the United States and Mexico to: (1) design and test a series of new visual concept explorations and applications in CalcPlot3D to improve student understanding of multivariable calculus; (2) expand the features of CalcPlot3D to accommodate the new concept explorations and address applications in differential equations, linear algebra, physics, and engineering; (3) create new visualization apps, including a new version of CalcPlot3D, that work on more platforms, including tablets and phones; (4) conduct and publish research investigating how student understanding of multivariable calculus concepts changes through the use of visualization and dynamic concept explorations; and (5) extend and diversify the user base by disseminating project materials through papers, workshops and conferences, by creating a Spanish language version of project materials, and by promoting the exchange of user feedback and research. Students who participate in this project will help populate a better prepared and more diverse workforce in science, technology, engineering, and mathematics (STEM).

该合作项目来自梦露社区学院，罗伯特·莫里斯大学（Robert Morris University）和布法罗州立大学（SUNY）的州立大学（SUNY），是使用视觉探索来帮助学生对多变量的微积分概念有更深入的了解，并对这些概念的可视化影响对这些概念的可视化影响进行研究和发表研究。该项目将基于CalcPlot3D多变量探索小程序的成功，这是一个屡获殊荣的交互式Java小程序，在美国已经广泛使用，以促进多变量计算的教学。 CalcPlot3D小程序旨在改善学生对表面，向量，向量场和曲线的几何直觉，从而使学生在随后的STEM课程中理解更全面的工程和物理问题。该项目将通过为多变量演算创建一系列视觉概念探索并扩展CalcPlot3D来大大增强CalcPlot3D的使用，从而促进物理，工程，工程，微分方程和线性代数课程中概念的可视化。通过解决可视化对三维概念的理解的影响，它还将填补现有教育研究的空白。 这些不同机构（社区学院，私立4年，公共4年）的三位教授将与美国和墨西哥的教师合作：（1）在CalcPlot3D中设计和测试一系列新的视觉概念探索和应用，以提高学生对多变量计算的学生的理解； （2）扩展CalcPlot3D的功能，以适应新的概念探索并解决微分方程，线性代数，物理和工程的应用； （3）创建新的可视化应用程序，包括一个新版本的CalcPlot3D，可在更多平台（包括平板电脑和电话）上使用； （4）进行和发表研究调查学生对多变量演算概念的理解如何通过使用可视化和动态概念探索而改变； （5）通过论文，研讨会和会议，创建西班牙语版本的项目材料以及促进用户反馈和研究的交换来扩展和多样化用户群。参加该项目的学生将有助于填充科学，技术，工程和数学（STEM）方面的更好和更多样化的劳动力。