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Learning Calculus with Augmented Reality and Virtual Environments

In this paper, we present how spatial visualization skills can be developed in engineering students, using augmented reality and remote virtual environments in calculus courses. Two tools have been specifically developed for this purpose: AVRAM (Remote Virtual Environments for the Learning of Mathematics), which allows the visualization and manipulation of surfaces in a virtual three-dimensional space and ARC (Augmented Reality in Calculus), which uses activity cards for each multivariable calculus topic. This paper describes the type of skills that can be developed with the use of these two apps in the dynamic visualization framework and presents some activities that have the purpose of developing logical thinking and problem solving and spatial abstraction skills. More than 1200 students have used these apps. The results of their use in calculus classes indicate an increase in students' engagement, visualization skills and a significant improvement in final grades.