Аннотация:In this paper we explore the perceptual actions that allow one to perceive pictures as
representing mathematical concepts. The research is based on the cultural–historical approach.
Following V.V. Davydov’s ideas on theoretical and, particularly, mathematical thinking, we
consider a mathematical concept as being based on a historically determined method of action.
Using the eye-tracking system we analyzed the difference between school students, university
students, and expert mathematicians in their perception of special pictures (so called ‘external
visual representations of the theoretical concept’) when performing a set of tasks, namely
choosing a point with given coordinates from a set of points. A normal expert-novice research
analysis of dwell time in relevant and irrelevant areas of interest was used. We also compared the
gaze paths, the number of visual fixations, and the time each group required to perform the tasks.
The directions of the saccades were also analyzed, and our data showed that the vertical and
horizontal saccades along the axes prevailed over saccades along other directions, a fact that may
be considered as a trace of the ‘Cartesian plane’ concept. The data showed that experts performed
the tasks faster and with fewer fixations and they also were able to use additional knowledge
flexibly in organizing their perceptive actions. Our results show the fundamental interlacing of
conceptual structures and visual processes, in which the latter are organized in accordance with
prior knowledge. The specificity of the experts’ Cartesian plane perception corresponds to the late
stages of the historical development of this concept. We consider this fact as an empirical
confirmation of the relevance of the term “theoretical perception”.