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（SUNY）布法罗分校的这个合作项目的目的是使用视觉探索来帮助学生更深入地理解多变量微积分概念，并进行和发表关于可视化对学生理解这些概念的影响的研究。该项目将建立在CalcPlot 3D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和学习。 CalcPlot 3D小程序旨在提高学生对曲面、向量、向量场和曲线的几何直觉，从而帮助学生在随后的STEM课程中更全面地理解工程和物理问题。该项目将通过为多变量微积分创建一系列可视化概念探索来大大增强CalcPlot 3D的使用，并扩展CalcPlot 3D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。它还将通过解决可视化对学生理解三维概念的影响来填补现有教育研究的空白。 三位来自不同机构的教授（社区学院，私立4年制，公立4年制）将与美国和墨西哥的教师合作：（1）设计和测试CalcPlot 3D中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CalcPlot 3D的功能，以适应新概念的探索，并解决微分方程，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CalcPlot 3D，可以在更多的平台上工作，包括平板电脑和手机;（4）进行并发表研究，调查学生如何通过使用可视化和动态概念探索来理解多变量微积分概念的变化;以及（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，以及促进用户反馈和研究的交流，扩大用户基础并使其多样化。谁参加这个项目的学生将有助于填充在科学，技术，工程和数学（STEM）更好地准备和更多样化的劳动力。

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