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

门罗社区学院、罗伯特莫里斯大学和纽约州立大学布法罗分校的合作项目的目的是利用视觉探索来帮助学生更深入地理解多变量微积分概念，并开展和发表可视化对学生理解这些概念的影响的研究。这个项目将建立在CalcPlot3D多变量微积分探索小程序的成功基础上，这是一个屡获殊荣的交互式Java小程序，已经在美国广泛使用，以促进多变量微积分的教学。CalcPlot3D小程序旨在提高学生对曲面、矢量、矢量场和曲线的几何直觉，从而为学生在随后的STEM课程中更全面地理解工程和物理问题做好准备。本项目将通过创建一系列多变量微积分的可视化概念探索，极大地增强CalcPlot3D的使用，并扩展CalcPlot3D，以促进物理、工程、微分方程和线性代数课程中概念的可视化。它还将填补现有教育研究的空白，解决可视化对学生理解三维概念的影响。来自这些不同机构（社区学院、私立四年制大学、公立四年制大学）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微积分的理解；(2)扩展CalcPlot3D的功能，以适应新的概念探索和解决在微分方程、线性代数、物理和工程中的应用；(3)创建新的可视化应用程序，包括新版本的CalcPlot3D，可以在更多的平台上运行，包括平板电脑和手机；(4)通过可视化和动态概念探索，开展并发表研究，调查学生对多变量微积分概念的理解是如何变化的；(5)通过论文、讲习班和会议传播项目材料，制作项目材料的西班牙语版本，促进用户反馈和研究的交流，扩大用户基础并使其多样化。参与该项目的学生将有助于在科学、技术、工程和数学（STEM）领域培养准备更充分、更多样化的劳动力。

The purpose of this collaborative project from Monroe Community College, Robert Morris University, and the State University of New York (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).