ИСТИНА

Visual representations in mathematics have on the one hand serious explanatory potential, and on the other hand they need themselves to be perceived in a special theoretical way in order to become mathematically meaningful. Radford (2010), following Marx, suggests that students’ eyes need to become ‘theoreticians’ in order to perceive what the teacher sees in visual diagrams. The main method that is used in plenty of researches, is the detailed qualitative analysis of video frames with gestures, verbal protocols and prosody features. This method allowed showing the importance of the students’ involvement into social practice, where the teacher’s gestures and prosodic rhythms form the students’ objectification of the diagram meaning (e.g. Radford, 2010), a well as the importance of special joint orientation that the participants of the dialogue need to acquire (e.g. Roth, 2008). However, the students’ perceptive processes and images are studied through the mediation of the student’s writings, drawings and verbal expressions. The eye-tracking technology allows dwelling immediately into the student’s perception during learning. By means of the eye-tracker, accompanied with an external video camera, we were able to analyze video records of shared activity between an adult and a student, as we synchronized them with tracks of the students’ eyemovements. We could grasp the potential and the limits of the adult’s guidance, since we considered the change of the gaze direction as a result of both the adult’s guidance and the student’s personal learning activity. The additional advantage of the current research method is the involvement of a second eye-tracker, in order to follow the adult’s perception as well. It gives the unique chance to analyze the moments of joint attention, which are the situations when two people are looking at the same object and at the same time they are both aware of each other’s focus of attention. Joint attention is considered as a crucial mechanism for children development (Tomasello & Farah, 1986) and it might be essential for the acquiring of the meaning of semiotic representations in mathematics, within joint orientation (Seeger, 2008; Roth, 2008). It is exactly joint attention that takes place when a teacher manages to guide a student’s attention in a cultural way. Five pairs of a parent and a first grade child took part in our dual eye-tracking study, concerning the Cartesian coordinates. The results show that when the adult manages to achieve joint attention with the student, it is a mixture of the adult’s guidance and the student’s anticipation: the gesture can be inaccurate, the verbal expression can involve an unknown term, but the student manages to decode the meaning from its traces in different semiotic registers, in accordance with the aim that was given in the original task. Thus the dual eye-tracking technology makes vivid what is usually covered from a researcher’s analysis of videos.