USING VIRTUAL AND AUGMENTED REALITY IN THE CALCULUS CLASSROOM
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Education, nowadays, is going through a transition process. ``New Students'' require tools that allow them to improve their technical knowledge and, besides that, strengthen soft skills such as communication and teamwork. Developments that use Virtual Reality and Augmented Reality as a means for teaching have shown to have positive impacts on factors such as understanding, motivation and agility in the learning process of university students. In this article we describe the development of two tools, one based on Virtual Reality and one on Augmented Reality, to teach Multivariate Calculus to university students. The applications through experimentation and collaborative observation, allow them to understand concepts such as functions, quadratic surfaces, directional derivative, traces and contour lines. Both applications provide students and educators the change to experiment though digital environments used in a class in multivariate calculus. Each application includes two different roles: student and educator. The student is an observer. The professor and the students are represented through avatars that interact with each other. The educator role is more complex, allowing the user to create and modify functions and quadratic surfaces and create planes that intersect the surfaces that represent the functions. Students within the Virtual Reality environment experience ran the application on their phones. They used Virtual Reality glasses to immerse themselves in the experience and a remote Bluetooth controller to walk through the virtual environment. They were able to walk on and under the displayed mathematical functions. The instructor, on the other hand, created and modified those functions and directed the learning experience showing different interactions among planes and surfaces. The instructor ran the VR application on a computer. Meanwhile, students using the Augmented Reality application, were able to visualize functions and surfaces through the camera of their phones when pointing to the marker. Each student had the possibility of pointing to any place within the surface with a green dotted marker. They could also observe overlapping with the surfaces. The instructor had the same functionalities as in the virtual reality application. This study showed that almost all students encountered the experience satisfying and helpful. They thought it was revealing in many ways, allowing them to visualize abstract surfaces and traces easily. Also, some students pointed out their wish of including these experiences since the beginning of the course. In the full article, we plan to describe the creation of both VR and AR applications and provide data on the student perceptions.