GeoGebra Augmented Reality with Mathematics Undergraduate Students: A Computational Fuzzy Semiotics Analysis

This research focuses on designing and implementing teaching strategies using GeoGebra Augmented Reality (AR) to improve the conceptualization of specific mathematical objects. Referring to Duval’s theory of semiotic representations, our research hypothesis is that AR facilitates students in manipulating different semiotic representations, boosting their motivation and engagement, and improving their mathematical conceptualization process. We describe a teaching sequence on paraboloids, framed by the Method of Varied Inquiry and Marton’s Variation Theory, which involved thirty undergraduate students in Mathematics. The research methodology is not limited to a qualitative analysis of video-recorded activity. It is also based on a further quantitative analysis of the learner’s status, described through the parameters of conceptualization, inquiry, and emotions, using a Fuzzy Cognitive Map. The results show how the AR activity successfully engaged and guided students to characterize paraboloids by easing the transition between different semiotic representations, from the graphical to the analytical and vice versa.