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

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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).