Transitions Between Domains of Activity as “Domestications of the Eye” for the Learning of Mathematics with GGBot

We present a theoretical study that allows us to attempt framing in an embodied perspective the effectiveness of the drawing robot GGBot in the learning of geometry. The aim of the article is to set the intertwining of activity, semiotics, perception, and knowledge at the crossover of Radford’s theory of objectification (TO) and Borba and Villareal’s notion of humans-with-media. Such a crossover is articulated in four building blocks: (1) processes of objectification and the role of semiotic means of objectification, where we state that digital artifacts such as the GGBot change the topology of the semiotic means of objectification; (2) cognition is sensuous and learning is a process of domestication of the eye, where perception is theoretically shaped by the interaction with GGBot; (3) GGBot and humans-with-media, where we outline new thinking collectives and their modes of activity; (4) domestication of the eye triggered by transitions between domains of activity. Each building block of our theoretical discussion is empirically anchored to four episodes involving primary school students’ learning geometrical figures using the GGBot. To conclude, we focus on two basic concepts of geometrical thinking that unfold in the shift between domains.