Abstract
The paper describes the behavior of a grade 10 student, Karim, while giving meaning to a mathematics concept (the derivative) under the guidance of an instructor (Omar) within an augmented reality (AR) environment. In the analysis, the following theoretical lenses are used: the semiotic bundle, which is based on a semiotic and embodied approach to teaching/learning processes, and the conceptual blending, an adaptation of the Fauconnier and Turner construct to analyze cognitive models of subjects immersed in an AR environment. The two lenses are adopted to investigate how the representations produced in the AR environment and Karim’s gestures, utterances, postures, and gazes intertwine and contribute to the formation of AR-blends, conveying new knowledge about the function–derivative mathematical relationship. The analysis reveals two main dialectic attitudes in the student: an “outside” attitude, embodied in the way he “observes” the AR setting, and an “inside” attitude, shown by the way he “acts” within it and grasps the relationship between the graphs of some elementary functions and those of their derivatives. Such dialectic is the real motor of Karim’s progressive meaning-making of the mathematical situation, and it is deeply intertwined with the specific features of the considered AR environment.