Lecture by Anna Shvarts (Lomonosov Moscow State University)

Development of mathematical perception in embodied student-tutor collaboration

Visual representations are an essential part of mathematical concepts; at the same time, extensive evidence exposes that novices and experts perceive the visual material differently. The culture-historical approach suggests that the process of acquiring a mathematical perception is a transformation from the naïve form of perception to the cultural one through collaboration between a learner and a teacher. Joint attention between them appears to be a valuable theoretical construct that allows to follow and to understand the dynamics and effectiveness of this collaboration. Our multimodal data sources from the student-tutor pairs include the video of gestures, the audio of verbal utterances and the dual eye-tracking data. The micro-ethnographical analysis of two episodes, namely the learning of Cartesian coordinates and derivation of the parabola formula, revealed strong coordination between student’s and tutor’s perception-action processes. Following the culture-historical approach, the theory of complex dynamical systems and an enactivist perspective we consider student-tutor collaboration as an intersubjective distributed perception-action system. During the teaching and learning processes, the system is moved from intersubjective embodied coupling towards independency of the student’s perception and action processes from the tutor.